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stat794 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/794.png | Jiahong designed a magnetic dartboard game as shown in the figure, where AB=BC=CD. If a dart is randomly thrown once and hits the dartboard, which of the following statements is correct? | C. The probability of hitting Zone ③ is the highest. | ['The probability of hitting area ④ is the greatest.', 'The probability of hitting area ② is the greatest.', 'The probability of hitting area ③ is the greatest.', 'The probabilities of hitting the three areas are the same.'] | multi_choice |
stat795 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/795.png | As shown in the figure, points A, B, C, D, and E are vertices of small squares. First, two points are randomly selected from A, B, C, then one point is randomly selected from D, E to form a triangle. What is the probability that the triangle formed is an isosceles triangle? ( ) | A | ['1/3', '1/6', '2/9', '1/4'] | multi_choice |
stat796 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/796.png | The soil in Shanxi is fertile and well-sunlit, which makes it suitable for the cultivation of corn. Corn is one of the major economic crops in the Shanxi region. The laboratory staff of the quality inspection center recorded the germination test results of a certain type of corn seed under the same conditions as shown in the table below:
| Batch Size | 300 | 500 | 800 | 700 | 2000 | 2000 | 3000 |
|------------|-----|-----|-----|-----|------|------|------|
| Number of Germinations | 284 | 475 | 762 | 1948 | 1895 | 2847 |
| Germination Frequency | 0.947 | 0.95 | 0.953 | 0.948 | 0.927 | 0.949 |
The approximate germination probability of these corn seeds is ( )
A. 0.93
B. 0.94
C. 0.95
D. 0.96 | C | ['0.93', '0.94', '0.95', '0.96'] | multi_choice |
stat798 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/798.png | As shown in the figure, there is a circuit AB controlled by the switches shown in the diagram. What is the probability that closing any two of the five switches a, b, c, d, e cannot form a circuit? ( ). | B | ['1/5', '2/5', '3/5', '4/5'] | multi_choice |
stat8 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/8.png | A handful of beans is randomly scattered within the circle shown in the diagram (regions A, B, and C). The beans are most likely to fall in the _________ region (fill in A, B, or C). | A. | NULL | free_form |
stat80 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/80.png | In an opaque bag, there is 1 red ball, 2 white balls, and a certain number of black balls. Xiao Yu shakes the bag to mix the balls evenly and randomly picks one ball, records its color, and then puts it back into the bag. After repeating this operation multiple times, Xiao Yu calculated the frequency of drawing the red ball and created a line plot as shown. What is the probability of randomly drawing two balls from the bag such that one is red and the other is white? | 1/5 | NULL | free_form |
stat802 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/802.png | A middle school is conducting after-school services, including four sports activities: table tennis, basketball, volleyball, and football. To determine students' favorite sport, a survey is conducted among 200 randomly selected students (each student chooses only one activity). The survey results are represented as a pie chart. Which of the following statements is incorrect?
A. The number of students who prefer basketball is 30.
B. The number of students who prefer football is the highest.
C. The central angle of the sector for 'table tennis' is 72°.
D. The number of students who prefer volleyball accounts for 10% of the surveyed students. | A | ['The number of students who like basketball the most is 30.', 'The number of students who like soccer the most is the largest.', "The central angle corresponding to 'table tennis' is 72 degrees.", 'The number of students who like volleyball the most accounts for 10% of the surveyed students.'] | multi_choice |
stat803 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/803.png | The purchase price and selling price of a certain product for each of the months from January to April are shown in the chart. The month with the maximum unit profit for the sold product is ( ). | B. February | ['January', 'February', 'March', 'April'] | multi_choice |
stat804 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/804.png | As shown in the figure, A, B, C, D, E, and F are six equidistant points on circle ⊙O. Student A randomly selects three points to form a triangle, and student B uses the remaining points to form another triangle. What is the probability that the triangles drawn by students A and B are congruent? ( ) | B | ['1', '1/2', '2/9', '1/3'] | multi_choice |
stat805 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/805.png | As summer approaches, a school organizes students to participate in a summer camp. The camp is divided into four projects: swimming, basketball, football, and tennis. The statistical charts shown in the figure reflect the number of students registered for these four projects (each student can only choose one). However, some data in the two charts are obscured and cannot be seen clearly. Based on the other data, the number of students choosing the basketball project is ( ). | D | ['70 people', '50 people', '30 people', '24 people'] | multi_choice |
stat806 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/806.png | When a school reading club recruits new members, it evaluates three assessment items: adaptability, knowledge reserve, and reading level. The overall score is determined according to the proportions shown in the diagram. If Xiaohua scores 90, 86, and 92 on these three items respectively, what is Xiaohua's overall score? | B | ['90.1 points', '89.4 points', '91 points', '88 points'] | multi_choice |
stat807 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/807.png | Jialu counted the number of boys and girls in the eighth grade of a certain school across four classes. Which of the following is correct? | B. The number of boys in Class 8 (3) is twice the number of girls. | ['Class 8(2) has the fewest students', 'The number of boys in Class 8(3) is twice the number of girls', 'Class 8(4) has more girls than boys', 'Class 8(2) and Class 8(4) have the same number of students'] | multi_choice |
stat808 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/808.png | The 'five educations' hold an important position and role in basic education. Among them, physical education is aimed at enhancing students' physical fitness, developing physical and athletic abilities, and helping students cultivate habits of physical exercise and hygiene. To strengthen physical activity, Xiao Ming created a daily exercise plan and recorded his progress. The chart below shows the time Xiao Ming spent on physical activities during a certain week. Which of the following statements is incorrect? ( )
Line graph of Xiao Ming's weekly physical activity time
A. Xiao Ming spent the least time on physical activities on Saturday.
B. The difference in time spent on physical activities between Thursday and Saturday is 1 hour.
C. Xiao Ming spent 60 minutes on physical activities on Tuesday.
D. From Thursday to Sunday, Xiao Ming's time spent on physical activities continuously decreased. | D | ['Xiaoming participated in the least amount of physical exercise on Monday.', 'The difference in time spent on physical exercise between Thursday and Friday is 1 hour.', 'The duration of physical exercise on Tuesday is 60 minutes.', 'The time spent on physical exercise from Monday to Friday decreases day by day.'] | multi_choice |
stat809 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/809.png | A certain school organizes a one-time hot volleyball team competition for all classes across nine grades. Each class selects 7 students to form a participating team. The one-time hot volleyball scores (units: count) of the 7 students selected from Grade 9 (Class 1) are shown in the figure. Which of the following conclusions is correct ( )? | B. The mode is 26 | ['The median is 17', 'The mode is 26', 'The average score is 20', 'The variance is 0'] | multi_choice |
stat810 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/810.png | As shown in the figure, two people, A and B, each hold a set of playing cards. They each randomly draw one card, denoting the numbers on A's and B's cards as m and n, respectively. What is the probability that −2 ≤ m − n ≤ 2? | B. 5/12 | ['1/3', '5/12', '1/2', '2/3'] | multi_choice |
stat811 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/811.png | As shown in the figure, there is a spinning wheel. The central angles of sectors 1, 2, and 4 are 60°, 70°, and 80°, respectively. If the wheel is spun randomly, what is the probability that the pointer will land on sector 3? ( ) | B | ['1/2', '5/12', '1/3', '4/9'] | multi_choice |
stat812 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/812.png | A class conducted two jump rope competitions, and the results (units: jumps per minute) of 20 randomly selected students from the class for both events were recorded, described, and analyzed. If the average score of the two jump rope attempts for these students falls in the range 130 ≤ x ≤ 140, how many students' results meet this criterion? | B. 5 students | ['6', '5', '4', '3'] | multi_choice |
stat813 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/813.png | The maximum temperatures of Cities A and B during the first 5 days of March are shown in the diagram. Which of the following options is incorrect? | B | ['The median of the maximum temperatures of both cities Jia and Yi is 6 degrees Celsius.', 'The mode of the maximum temperature in Jia city is 4 degrees Celsius.', 'The maximum temperature of Jia city is relatively stable compared to Yi city.', 'The average of the maximum temperatures in Yi city is 6 degrees Celsius'] | multi_choice |
stat814 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/814.png | As shown in the graph, it depicts the temperature curve and precipitation bar chart of a given location. Based on the information in the graph, which of the following statements is correct? ( ) | D | ['In January, the average temperature is below 0°C, and the precipitation is high.', 'From April to October, the temperature gradually rises.', 'After July, the precipitation gradually decreases.', 'The winter is cold and the summer is hot, with more precipitation in July and August.'] | multi_choice |
stat815 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/815.png | As shown in the figure, there are 4 cards with the same shape, size, and texture, and the front sides of the cards are printed with the shown symbols, while the backsides are identical. The 4 cards are shuffled and placed face down on the table. If one card is randomly selected, what is the probability that the selected card's front pattern is both axisymmetric and centrosymmetric ( )? | C | ['1/4', '3/4', '1/2', '1'] | multi_choice |
stat816 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/816.png | A survey was conducted on students from Class 901 and Class 902 in a school about their "most favorite ball sports" using a pie chart (as shown in the diagram). Which of the following statements is correct? | D | ['The number of students in Class 901 who like football the most is less than the number of students in Class 902 who like football the most.', 'The number of students in Class 901 who like basketball the most is the same as the number of students in Class 902 who like basketball the most.', 'The number of students in Class 901 who like football the most is the same as the number of students in Class 902 who like basketball the most.', 'The number of students in Class 902 who like basketball the most is the same as the number of students who like football the most.'] | multi_choice |
stat817 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/817.png | The daily average temperature statistics for a city's June are shown in the figure. What are the mode and median of the data set of daily average temperatures? | C. 21, 22 | ['21, 21', '21, 22.5', '21, 22', '22, 22'] | multi_choice |
stat819 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/819.png | To supervise schools in implementing the requirement of 'sunlight exercise for one hour every day' for students, the inspection team investigated the weekly exercise time outside of physical education classes for 50 students in a class at a certain school and created a bar chart as shown. What are the mode and median of the exercise times of the surveyed students ( )? | D | ['7h, 7.5h', '7.5h, 7h', '7.5h, 7.5h', '7h, 7h'] | multi_choice |
stat82 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/82.png | A school's statistical chart for the number of trees planted by 5 groups during a tree-planting activity is shown in the diagram. What is the average number of trees planted per group? | 5 | NULL | free_form |
stat822 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/822.png | A school conducted a random survey among some students to understand the time they spend on physical exercise each day on average in a week. The statistics are shown in the chart: The mode and median of the exercise times of these students are ( ). A. 9, 7 B. 9, 9 C. 1, 1 D. 1, 1.5 | C | ['9, 7', '9, 9', '1, 1', '1, 1.5'] | multi_choice |
stat823 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/823.png | As shown in the figure, the spinning wheel is divided into four sectors of equal area, with the words 'I', 'Love', and 'Home' written in each sector. Fixing the pointer, the spinning wheel is spun twice. What is the probability that the words pointed to by the pointer form the phrase 'Love Home'? ( ) | B | ['1/4', '1/8', '1/10', '1/16'] | multi_choice |
stat825 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/825.png | 8. A dart is randomly thrown onto the rhombus target board ABCD shown in the figure, where points E, F, G, and H are the midpoints of the sides of the rhombus. If the dart is equally likely to land at any point on the board, what is the probability that the dart lands in the shaded region? ( ) | B | ['1/3', '1/2', '2/3', '3/4'] | multi_choice |
stat827 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/827.png | A school purchased four types of stationery (A, B, C, and D) as prizes to reward students. The quantity of the stationery is shown in the chart. It is known that there are 60 pieces of type A stationery. What is the total number of all four types of stationery? | C. 200 pieces | ['400 pieces', '300 pieces', '200 pieces', '180 pieces'] | multi_choice |
stat828 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/828.png | The black hair doesn't know to study diligently early, and the white head regrets reading late. A mathematics interest group at a school randomly surveyed some students about their favorite types of extracurricular books and created two statistical charts based on the results: If the school has a total of 1,200 students, approximately how many students at the school prefer science books? A. 120 students B. 360 students C. 480 students D. 600 students | C | ['120 people', '360 people', '480 people', '600 people'] | multi_choice |
stat829 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/829.png | On a certain day, workers in a workshop processed only 5, 6, 7, and 8 parts per worker. The data for that day is shown in the figure, but one value is missing. It is only known that 7 is the median of the number of parts processed that day. If the number of workers who processed 7 parts is x, what is the minimum value of x? | C. 19 | ['17', '18', '19', '20'] | multi_choice |
stat83 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/83.png | A shooting team conducted five shooting tests, and the test scores of players A and B are shown in the figure. The variances of scores for players A and B are denoted as S²_A and S²_B, respectively. Determine whether S²_A ______ S²_B (fill in '<' or '='). | > | NULL | free_form |
stat831 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/831.png | In order to ensure the physical and mental health of students and improve their satisfaction with school meals, the school conducted a cafeteria satisfaction survey among all students. Satisfaction is represented in scores ranging from low to high as 1, 2, 3, 4, and 5, divided into five levels. Survey personnel randomly selected 40 questionnaires, and the data was organized into a statistical chart as shown. Which of the following statements is incorrect? ( ) | B. The mode is 16 points | ['The average score is 3.325.', 'The mode is 16.', 'The median score is 3.5.', 'The range is 4.'] | multi_choice |
stat832 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/832.png | Four people are seated around a circular table as shown in the diagram, with the 4 seats labeled as ①, ②, ③, and ④. Two individuals, A and B, are equally likely to occupy any 2 of the 4 seats. What is the probability that A and B sit opposite to each other? | C | ['1/2', '2/3', '1/3', '1/4'] | multi_choice |
stat833 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/833.png | A school conducted a biology project-based practical research activity, where the teacher guided the students to understand plants through a combination of hands-on experiments and consulting materials. The table below records the results of germination experiments on the seeds of a certain plant under the same conditions. The germination rate scores were recorded as 10, 9, 8, etc., and the results were rounded to three decimal places. An eighth-grade student organized the score data and drew the following statistical charts. Which of the following judgments is correct? A. a=8, b=7 B. The average scores of the seventh and eighth grades are the same. The variance of the seventh grade is smaller than that of the eighth grade, indicating that the scores of the seventh grade fluctuate more, so the eighth grade scores are better. C. Among the students who performed particularly well in this competition, approximately 336 students achieved excellent results. D. Based on the data in the table, it can be estimated that the probability of germination of the plant seeds is 0.901 (results rounded to three decimal places). | D | ['a = 8, b = 7', 'The average score of the seventh grade is similar to that of the eighth grade, indicating that the performance of the eighth grade fluctuates greatly, and the performance of the seventh grade is better.', 'According to the pie chart, it is estimated that the number of outstanding students in the seventh grade is 326.', 'According to the data in the table, it can be estimated that the average germination rate of the plant seeds is 0.901 (the result is reserved to three decimal places).'] | multi_choice |
stat834 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/834.png | As shown in the figure, a line chart is drawn based on the math test scores of two students, A and B, over five tests. Comparing the scores of A and B, which of the following statements is correct ( ).
A. Student A has a higher average score and a larger variance
B. Student A has a higher average score and a smaller variance
C. Student B has a higher average score and a larger variance
D. Student B has a higher average score and a smaller variance | C | ["Student A's average score is higher, with a larger variance.", "Student A's average score is higher, with a smaller variance.", "Student B's average score is higher, with a larger variance.", "Student B's average score is higher, with a smaller variance."] | multi_choice |
stat835 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/835.png | A school's student conduct evaluation at the end of the term emphasizes five areas with a weight ratio of 3:2:2:1:2 to determine the final score. Based on the scores detailed in the chart for student Wang Lin this semester, what would Wang Lin's final conduct score be? | C | ['9.2', '9.1', '9.3', '9.4'] | multi_choice |
stat837 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/837.png | As shown in the figure, the spinning wheel consists of 8 sectors of equal area. The shaded sections are gray, and the rest are white. When the spinning wheel is spun once and stopped, what is the probability that the pointer lands in the gray region? | B | ['1/8', '1/4', '1/3', '1/2'] | multi_choice |
stat838 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/838.png | In order to investigate the sales of different brands of shirts, the math interest group of a school collected and analyzed the weekly sales of two brands, A and B. The following chart shows the sales trends of the two brands over a week. Which of the following statements is correct? ( ) | D | ['The sales of clothing A are more stable than those of clothing B.', 'The average sales of clothing B are higher than those of clothing A.', 'The trend of sales changes for clothing A is the same as that for clothing B.', 'The sales of clothing A are better than those of clothing B.'] | multi_choice |
stat839 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/839.png | As shown in the figure, it is a line chart of the monthly extracurricular reading volumes of all the students in a class from January to August last year. Which of the following statements is correct?
A. The average monthly reading volume is 60.
B. The median monthly reading volume is 50.
C. The mode of the monthly reading volume is 58.
D. The variance of the monthly reading volume is 47. | C | ['The average number of readings per month is 60', 'The median number of readings per month is 50', 'The mode of the number of readings per month is 58', 'The variance of the number of readings per month is 47'] | multi_choice |
stat84 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/84.png | Biological research shows that the higher the rate of photosynthesis in plants, the more organic matter is synthesized per unit of time. To understand the photosynthesis rates of two soybean varieties, A and B, researchers selected five plants from each variety and measured their photosynthesis rates (unit: μmol⋅m⁻²⋅s⁻¹) under the same experimental conditions. The statistical results are as follows:
Variety First Plant Second Plant Third Plant Fourth Plant Fifth Plant Average
A 32 30 25 28 22 25
B 25 25 25 25 25 25
Which soybean variety exhibits a more stable photosynthesis rate? (Fill in 'A' or 'B') | B | NULL | free_form |
stat840 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/840.png | If a small ball freely rolls on the floor as shown in the diagram and randomly stops on one of the square blocks, what is the probability that it ultimately stops in the shaded area? ( ) | B | ['5/16', '1/3', '5/8', '1/2'] | multi_choice |
stat841 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/841.png | In order to understand the progress of the "National Fitness" activity in a certain residential area, a volunteer conducted statistics on the exercise time of 50 adults living in this community and created the bar chart as shown. Based on the information provided in the chart, the mode, median, and average weekly exercise time of these 50 people are ( ). | A | ['6h, 6h, and 5.68h', '6h, 4h, and 5.6h', '4h, 4h, and 5.64h', '4h, 4h, and 5.7h'] | multi_choice |
stat842 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/842.png | April 23, 2024, marks the 29th World Book Day. A school has a total of 800 students. To understand the students' reading habits in April, a random survey of 80 students was conducted, and the data was presented in the form of a statistical chart. Estimate the number of students in the entire school who read 2 books. ( ) | B. 140 students | ['60 students', '140 students', '200 students', '240 students'] | multi_choice |
stat843 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/843.png | A school of 500 students participated in a test. The test scores are all greater than or equal to 60 and less than 100. The frequency distribution of the score ranges is shown in the table (each score range includes the minimum value but not the maximum value). How many students scored in the 70~80 score range? | 150 | NULL | free_form |
stat844 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/844.png | The age distribution of the women's volleyball team members in a certain school is shown in the table below:
| Age | 13 | 14 | 15 |
| Number of People | 4 | 7 | 4 |
What is the average age of the women's volleyball team members in this school? ______ years old. | 14. | NULL | free_form |
stat845 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/845.png | A city encourages residents to save water. To understand the water usage of residents, 20 households were randomly selected for inspection of their water consumption in a certain month, as shown in the table. What is the average water consumption for these 20 households in that month (in tons)? | 5.8 | NULL | free_form |
stat846 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/846.png | In order to understand the physical fitness status of ninth-grade girls in our city, 27 girls were selected from each of Class A and Class B in a certain school to perform a one-minute rope jumping test. The test results are shown in the table. If jumping more than 105 times per minute is considered excellent, what is the relationship between the excellence rates of Class A and Class B? | Class A < Class B | NULL | free_form |
stat847 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/847.png | According to the Municipal Housing Authority's statistics, the number of ordinary residential transactions in eight counties and districts of our city during a certain week this year is shown in the table below:
County/District Gulou Donghai Guanyun Guannan Xinpu Haizhou Lianyun District Development Zone
Transactions (units) 105 101 53 72 110 50 56 88
What is the median number of ordinary residential transactions during this week? ________ units. | 80 | NULL | free_form |
stat848 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/848.png | The highest temperature statistics for each day of a week in a certain city are as follows:
Highest temperature (℃): 25 26 27 28
Number of days: 1 2 1 3
What is the median and mode of this data? | 27; 28 | NULL | free_form |
stat849 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/849.png | A store sold 11 shirts on a certain day, and the collar sizes are tallied in the following table:
Collar size (unit: cm): 38, 39, 40, 41, 42
Number of shirts: 1, 3, 4, 2, 1
List the mode of the collar sizes of these 11 shirts as ___________ cm and the median as ___________ cm. | 39 40 | NULL | free_form |
stat85 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/85.png | Focusing on the implementation of the 'Double Reduction' policy, highlighting the features of winter vacation homework. A school has selected high-quality special winter vacation homework, divided into four categories: A (Festival Culture), B (Safety and Epidemic Prevention), C (Labor Practice), and D (Winter Olympics Sports). Based on the statistical results shown in the chart, how many pieces of B-class homework are there? | 20 | NULL | free_form |
stat850 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/850.png | In a class of 45 students, the donation amounts during the school's 'Love Overflows Campus' fundraising event are shown in the table below. What is the average donation amount for this class? ________ yuan. | 24 | NULL | free_form |
stat851 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/851.png | A school organized students to participate in a tree-planting activity. After the activity, the tree-planting details of 50 students from Class A, Grade 9, were recorded and summarized in the following statistical table:
Number of trees planted | 3 | 4 | 5 | 6
Number of students | 20 | 15 | 10 | 5
What was the average number of trees planted per student among these 50 students? | 4 | NULL | free_form |
stat852 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/852.png | A construction team has 14 employees, and the types of jobs and corresponding monthly salaries per person are as follows: The on-site construction team underwent an adjustment: 2 carpenters were reduced, 1 electrician and 2 masons were added. Compared with before the adjustment, the variance of the monthly salaries of the team _______ (fill in 'decreases', 'remains unchanged', or 'increases'). | increases | NULL | free_form |
stat853 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/853.png | During a data compilation process of a certain experiment, the frequency of occurrence of an event is shown in the table below:
| Number of Trials | 10 | 50 | 100 | 500 | 2000 |
|------------------|---------|---------|---------|---------|---------|
| Frequency of Event | 0.245 | 0.248 | 0.251 | 0.253 | 0.252 |
Estimate the probability of the event occurring _______ (accurate to 0.01). | 0.25 | NULL | free_form |
stat854 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/854.png | To understand the residents' water usage, Xiao Ming randomly surveyed 20 households in a certain community, and the results are as follows:
Monthly water usage (m³) 4 5 6 7
Number of households 4 5 6 5
What is the mode of the monthly water usage among these 20 households? ____m³. What is the median? ____m³. | 5 5.5 | NULL | free_form |
stat855 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/855.png | The results of 5 shooting training sessions (unit: rings) for two students, A and B, are shown in the table below.
A: 7, 8, 9, 8, 8
B: 6, 7, 8, 8, 8
Compare the variances of the 5 shooting results for A and B, labeled as S_A² and S_B². The result is: S_A² __ S_B². (Options are '>', '=' or '<') | < | NULL | free_form |
stat856 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/856.png | To understand the mathematics learning status of 3600 ninth-grade students in the entire district, test scores of 600 randomly selected students were used as a sample and grouped as follows (each group includes the minimum value but excludes the maximum value). Based on the information in the table, estimate the total number of students across the district scoring between 70 and 80: ________. | 1620. | NULL | free_form |
stat857 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/857.png | In order to understand the vision condition of middle school students in a certain district, 500 middle school students from that district were randomly selected for a survey. The sample data was organized into the table below:
Vision Below 4.7 4.7 4.8 4.9 Above 4.9
Number of students 102 98 80 93 127
Based on the sampling survey results, estimate the number of middle school students in the district (totaling 12,000) with vision not less than 4.8. | 7200 | NULL | free_form |
stat858 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/858.png | A machine tool produces a certain part, and during the four days from June 6 to June 9, the number of defective parts produced is shown in the following table:
Date: June 6, June 7, June 8, June 9
Number of defective parts: 1, 0, 2, a
If the only mode of the defective parts is 1, then the variance of 1, 0, 2, a equals ____. | 1/2 | NULL | free_form |
stat859 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/859.png | Based on the data in the table above, which student has better and more stable performance? | Student B. | NULL | free_form |
stat86 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/86.png | As shown in the figure, two identical freely rotating spinners A and B are given. Spinner A is divided into three equal parts, labeled with the numbers 2, 0, and -1, respectively. Spinner B is divided into four equal parts, labeled with the numbers 3, 2, -2, and -3, respectively. If both spinners A and B are spun simultaneously and stop at positions where the pointers indicate the corresponding numbers x and y on spinners A and B (in cases where the pointer lands on the boundary of two sections, the spinners are spun again), what is the probability that the point (x, y) falls in the second quadrant of a Cartesian coordinate system? ________ | 1/6 | NULL | free_form |
stat860 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/860.png | 10. Class A and Class B held a competition to test the speed of Chinese character input on a computer. The number of characters input per minute by participating students was recorded and summarized in the following table. Based on the table, the following conclusions were drawn: (1) The average scores of students in Class A and Class B are the same; (2) The number of excellent students (those who input more than 150 characters per minute are considered excellent) in Class B is greater than in Class A; (3) The variation in scores of Class A is smaller than that of Class B. Which of the above conclusions are correct? (Fill in the numbers) | (1), (2) | NULL | free_form |
stat861 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/861.png | According to the following statistical chart, answer the question: The fruit sales revenue of the supermarket in October is ______ the fruit sales revenue in November (please choose '>' or '<'). | > | NULL | free_form |
stat862 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/862.png | The age statistics of 47 students in a certain class are shown in the following table:
Age (years): 13 14 15 16
Number of students: 2 22 22 1
What is the mode of the students' ages in this class? | 14 and 15 | NULL | free_form |
stat863 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/863.png | To understand the electricity usage at home in April (30 days), Xiao Ming recorded the meter readings at the same time for 8 consecutive days at the beginning of the month:
Date (day): 1, 2, 3, 4, 5, 6, 7, 8
Meter readings (kWh): 104, 110, 116, 121, 126, 132, 138, 144
(1) The average daily electricity consumption of Xiao Ming's family is ______ kWh;
(2) If the electricity rate is 0.56 yuan/kWh, estimate the electricity bill for April at Xiao Ming's home as ______ yuan. | 6; 100.8 | NULL | free_form |
stat864 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/864.png | In the 'Reading Festival' activity on campus, the average number of books read by each student in a certain class over a week was investigated, and the collected data was compiled into a 'Weekly Reading Statistics Table,' as shown in the figure. What is the average number of books read per student in this class over the week? | 2.5 | NULL | free_form |
stat865 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/865.png | Teacher Wang has collected statistics about the uniform sizes of 40 students in his class as follows:
Sizes:
S M L XL XXL
Frequency:
0.05 0.1 0.2 0.3 0.025
How many students in the class wear uniforms of size 'L'? | 8 | NULL | free_form |
stat866 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/866.png | A certain shooting athlete's shooting performance is recorded under the same conditions as follows:
Number of shots: 20, 40, 60, 80, 100
Number of times hitting "above 9 rings": 16, 32, 48, 64, 80
Frequency of hitting "above 9 rings" (results rounded to two decimal places)
Based on the stability of the frequencies, estimate the probability of the athlete hitting "above 9 rings" in a single shot. (Result rounded to one decimal place). | 0.8 | NULL | free_form |
stat867 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/867.png | To promote the 'Capital Citizens' Health and Hygiene Covenant,' a class held a 'Seven-Step Handwashing Method' competition. Xiao Ming's individual scores are as shown in the table below (all scores are based on a percentage scale):
Category Written Test Practical Operation Promotion Display
Score (points) 96 98 96
If written tests account for 30%, practical operations for 50%, and promotion displays for 20%, calculate the comprehensive score of the participant on a percentage scale. Xiao Ming's final score is ________. | 97 | NULL | free_form |
stat868 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/868.png | In a speech competition held at a certain middle school, the judges gave the following scores to Xiaoming's speech. Then Xiaoming's average score is ______. | 93 | NULL | free_form |
stat869 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/869.png | A shopping mall has a freely spinning roulette wheel. It is stipulated that customers who spend more than 30 yuan can spin the wheel once. When the roulette stops, the pointer falls on a specific area, and the customer wins the corresponding prize. The following table is a set of statistical data collected during the promotion:
Number of roulette spins: 1000, 200, 300, 500, 1000
Number of times the pointer lands in the 'pen' area: 65, 122, 190, 306, 601
If you spin the roulette once in this mall, the probability of winning a pen is approximately ________ (rounded to 0.1). | 0.6 | NULL | free_form |
stat87 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/87.png | In order to understand students' reading habits, a survey was conducted on some sixth-grade students in a school, and the corresponding frequency distribution histogram was listed (as shown in the figure) (each group contains the minimum value but not the maximum value) (0-1 hour: 4 students, 1-2 hours: 10 students, 2-3 hours: 14 students, 3-4 hours: 16 students, 4-5 hours: 6 students). If there are a total of 200 students, the number of sixth-grade students at this school whose reading time is not less than 3 hours is _____. | 88 | NULL | free_form |
stat870 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/870.png | Divide the heights of the girls in a certain class into three groups, as shown in the table below. Then the value of α is ________. | 6 | NULL | free_form |
stat871 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/871.png | In an opaque bag, there are a finite number of balls with n different colors. Among these are balls of two specific colors. A study group performs an experiment by thoroughly stirring the balls in the bag, randomly drawing one ball, recording its color, and then returning it to the bag before repeating the process. The following table contains statistical data collected during the experiment: Based on the table conditions and probability fundamentals, the following analysis is provided: ① It can be directly inferred from the frequency that the probability of drawing a white ball is approximately 0.6. ② It can be determined that the probability of drawing a white ball in one attempt is about 0.6. Which of these two statements is correct? | ② | NULL | free_form |
stat872 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/872.png | The quality inspection results of a batch of basketballs are as follows:
Number of basketballs sampled: 100, 200, 400, 600, 800, 1000
Frequency of premium basketballs: 93, 192, 376, 564, 752, 941
Frequency of premium basketballs: 0.93, 0.96, 0.94, 0.94, 0.94, 0.94
The estimated probability that a randomly selected basketball from this batch is premium is ________. (accurate to 0.01) | 0.94 | NULL | free_form |
stat873 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/873.png | There are two types of candies, A and B, with their unit prices and weights listed in the table below. If 2 kg of type A candy and 3 kg of type B candy are mixed together to form 5 kg of mixed candies, and the shopkeeper uses the weighted average to determine the unit price of the mixed candies, what will the unit price of these 5 kg mixed candies be (in yuan/kg)? | 24 | NULL | free_form |
stat874 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/874.png | There are two groups of data, A and B, as follows:
Group A: 11 12 13 14 15
Group B: 12 12 13 14 14
The variances of groups A and B are represented by s_A^2 and s_B^2, respectively. Then s_A^2 __ s_B^2 (fill in '>', '<', or '='). | > | NULL | free_form |
stat875 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/875.png | A class of students conducted an experiment of tossing thumbtacks, and the results are as follows:
Number of tosses/n 300 400 500 600 700
Times the tack landed on the point 122 158 193 236 274
Frequency of landing on the point 0.4067 0.3950 0.3860 0.3850 0.3914
Number of tosses/n 800 900 1000
Times the tack landed on the point 319 354 389
Frequency of landing on the point 0.3988 0.3931 0.3890
Based on the above information, estimate the probability of the tack landing on its point. Write the probability of the tack landing on its point ______ (accurate to 0.01). | 0.39 | NULL | free_form |
stat876 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/876.png | A watch factory sampled 10 watches to inspect their daily timing errors. The data is shown in the table below (unit: seconds):
Daily timing error: 0 1 2 3
Number of watches: 3 4 2 1
What is the average daily timing error for these 10 watches (in seconds)? | 1.1 | NULL | free_form |
stat877 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/877.png | In order to understand the vision condition of middle school students in our city, 200 middle school students were randomly selected from the district for investigation, and the sample data was organized into a table. Based on the survey results, estimate the number of middle school students with a vision of no less than 4.8 among the 16,000 students in the city: ______. | 9600 | NULL | free_form |
stat878 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/878.png | A ballet company recently recruited a group of female dancers. Their heights and corresponding numbers are shown in the table below:
Height (cm): 163 164 165 166 168
Number of people: 3 1 3 1 1
What is the variance of the heights of these dancers? ________. | 2 cm² | NULL | free_form |
stat879 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/879.png | What specific method should a forestry department adopt to investigate the survival rate of a certain type of sapling under specific conditions? The survival rate of saplings is a type of probability in practical problems. In this problem, it is unknown whether the two possible outcomes, 'survival' and 'non-survival,' have equal probabilities, so the survival rate must be estimated from the frequency. Under the same conditions, conduct a large number of transplantations of this type of sapling. In cases of 'survival,' calculate the survival frequency. As the number of transplantations increases, the frequency will become more stable, and the frequency can then be used as an estimate of the survival rate. The following is a simulation table. Please complete the missing values in the table and fill in the blanks below the table. | 0.9 | NULL | free_form |
stat88 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/88.png | A certain school’s seventh-grade cohort plans to offer four courses: paper cutting arts, poetry appreciation, Chinese martial arts, and technological innovation. Each student will choose one of these courses. To understand the preferences of the seventh-grade students for these courses, the school randomly selected 100 students for a survey. The survey results are displayed in a pie chart. Based on the pie chart, estimate the number of students out of 1,200 seventh-grade students who chose paper cutting arts. | 360 | NULL | free_form |
stat880 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/880.png | In a certain rope skipping competition, the results of the number of skips per minute by students in Class A and Class B are recorded as follows (unit: times):
| Class | Participants | Average Times | Median | Variance |
|-------|--------------|---------------|--------|----------|
| A | 45 | 135 | 140 | 180 |
| B | 45 | 135 | 135 | 130 |
Among the following three statements:
(1) The average score of Class A is lower than that of Class B;
(2) The variability in scores of Class A is greater than that of Class B;
(3) The number of excellent students in Class A (students with skipping times ≥150) is less than that in Class B.
Which of the above statements are correct? (Only write the numbers). | (2) (3) | NULL | free_form |
stat881 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/881.png | Xiaoling's family has a fish pond with 2500 carp. According to experience, the survival rate of the carp is about 80%. Now, preparations are being made to catch and sell the fish. To estimate the total weight of the carp in the pond, three rounds of sampling were conducted, and the following data was obtained:
Fish count average and the weight per fish:
First sampling: 20 fish, each weighing 1.6kg
Second sampling: 10 fish, each weighing 2.8kg
Third sampling: 10 fish, each weighing 2.0kg
What is the approximate total weight of all the carp in the pond (in kg)? | 3600 | NULL | free_form |
stat882 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/882.png | A long jump team is preparing to select one of the two athletes, A and B, who has more stable performance to participate in a competition. The table shows the results of 10 test performances (unit: meters) from these two athletes. Which athlete do you think should be selected to participate? Why? | A | NULL | free_form |
stat883 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/883.png | During the 'Save Every Drop of Water' campaign at a school, 10 students were selected from 200 students in a certain grade to report on their household water-saving efforts over a month. The compiled data is shown in the table below:
Water saved (t) | 0.5 | 1 | 1.5 | 2
Number of students | 2 | 3 | 4 | 1
Based on this data, estimate the total amount of water saved by the families of these 200 students over a month (in tons). | 240t | NULL | free_form |
stat884 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/884.png | In an opaque bag, there are a number of identical balls differing only in color. A study group performs a ball-drawing experiment: the balls are shuffled, and then one ball is drawn at random, its color is recorded, and it is then returned to the bag. This process is repeated continuously. Below is a statistical dataset recorded during the activity:
Number of draws (n) 100 150 200 800 1000
Number of white balls (m) 59 96 116 295 480
Frequency of white balls (m/n) 0.59 0.64 0.58 0.59 0.06
The estimated probability of drawing a white ball is ______ (to one decimal place). | 0.6 | NULL | free_form |
stat885 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/885.png | A batch of knit sweaters is randomly inspected for quality, resulting in the following frequency table:
Number of items sampled (items) 100 150 200 500 700 1000
Frequency of qualified items 90 140 190 475 665 900
Probability of qualification 0.90 0.94 0.95 0.95 0.95 0.90
Estimate the number of defective items from a total of 2000 items in this batch. | 100 | NULL | free_form |
stat886 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/886.png | A certain type of rapeseed was tested for germination under the same conditions, and the results are shown in the table:
| Number of seeds per batch n | 100 | 300 | 400 | 600 | 1000 | 3000 |
|-----------------------------|-----|-----|-----|-----|------|------|
| Number of germinated seeds | 96 | 284 | 387 | 588 | 960 | 2848 |
| Germination frequency η | 0.960 | 0.947 | 0.968 | 0.980 | 0.960 | 0.949 |
Then it can be estimated that the probability of this type of rapeseed germination is _______ (to the nearest 0.01). | 0.95 | NULL | free_form |
stat887 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/887.png | The Xinjiang region is arid and is one of the three major cotton-producing areas in China, known for producing high-quality extra-long staple cotton. In a germination rate experiment of a certain variety of extra-long staple cotton seeds, researchers selected experimental fields with similar conditions and simultaneously sowed seeds, obtaining the following data:
Tested cotton 100 500 1000 2000 10000
Number of seeds
Number of germinated seeds 98 492 984 1920 9507
What is the approximate germination rate of this variety of extra-long staple cotton seeds? (Result accurate to 0.01). | 0.95 | NULL | free_form |
stat888 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/888.png | In order to implement the 'Double Reduction' policy, the school randomly surveyed the average daily sleep time of 30 students over a week. The statistical results are shown in the table below. What is the median sleep time of these surveyed students? ______ hours. | 8 | NULL | free_form |
stat889 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/889.png | The school plans to select one student from Wang Jing and Li Yu as a volunteer for the sports event. The selection criteria include Mandarin proficiency, sports knowledge, and tourism knowledge, with scores weighted by a ratio of 4:3:3. The selection scores for both students are shown in the table below. Who will ultimately be selected? | Li Yu | NULL | free_form |
stat89 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/89.png | As shown in the figure, a pie chart is made to represent the breakdown of Xiao Li's monthly phone expenses. What is the degree of the central angle of the segment representing text message fees? | 72° | NULL | free_form |
stat890 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/890.png | A middle school has 40 students participating in a speech competition. The scores of the participants are grouped and summarized as follows (scores are integers, full score is 100):
Score range (points): 61~70 71~80 81~90 91~100
Number of students: 5 10 16 9
In the pie chart, if the data is represented as a pie chart, the central angle of the sector corresponding to the 81~90 score range is ________°. | 9, 144 | NULL | free_form |
stat891 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/891.png | On March 12, 2022, the 44th Arbor Day of our country, a forestry department conducted a study on the survival rate of a certain type of sapling under certain conditions. Under the same conditions, a large number of these saplings were transplanted, and their survival status was recorded. The table below shows a set of statistical data during the transplantation process of this type of sapling:
Number of saplings transplanted (trees): 100 5000 8000 10000 15000 20000
Number of saplings surviving (trees): 87 4485 7224 8983 13443 18044
Survival rate of saplings: 0.870 0.897 0.903 0.898 0.896 0.902
Estimate the probability of survival for this type of sapling under these conditions. (Keep the result to two decimal places). | 0.9 | NULL | free_form |
stat892 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/892.png | The quality inspection results of a batch of table tennis balls are shown in the table below:
Number of table tennis balls sampled (x) | 100 | 500 | 1000 | 2000
Frequency of excellent products (m) | 48 | 475 | 949 | 1898
Frequency ratio of excellent products (m/x) | 0.48 | 0.95 | 0.949| 0.949
The estimated probability of randomly selecting an excellent table tennis ball from this batch is ________ (accurate to 0.01). | 0.95 | NULL | free_form |
stat893 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/893.png | 2. In order to select a representative from contestants A and B to participate in the district-level Chinese character dictation competition, the school tested both contestants in four aspects: expression ability, reading comprehension, comprehensive quality, and Chinese character dictation. Their respective scores (on a 100-point scale) are as follows:
| Contestant | Expression Ability | Reading Comprehension | Comprehensive Quality | Chinese Character Dictation |
| ---------- | ------------------ | --------------------- | --------------------- | --------------------------- |
| A | 85 | 78 | 79 | 75 |
| B | 80 | 83 | 82 | 73 |
If expression ability, reading comprehension, comprehensive quality, and Chinese character dictation account for 20%, 10%, 30%, and 40% respectively when calculating their weighted average scores, based on these scores, the contestant with the higher score is ________. | B | NULL | free_form |
stat894 | /home/yz979/scratch/chengye/math/data/original_set/statset/images/images/894.png | The table below shows the statistics of physical education test scores for 10 students in a certain class during the middle school entrance exam.
Scores (points): 30 25 20 15
Number of students: 2 2 4 2
If the average score is 23, the median is a, and the mode is b, then the value of a−b is ______. | 2.5 | NULL | free_form |
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