what is statistics 
statistics is a branch of applied mathematics that involves the collection description analysis and inference of conclusions from quantitative data the mathematical theories behind statistics rely heavily on differential and integral calculus linear algebra and probability theory people who do statistics are referred to as statisticians they re particularly concerned with determining how to draw reliable conclusions about large groups and general events from the behavior and other observable characteristics of small samples these small samples represent a portion of the large group or a limited number of instances of a general phenomenon dennis madamba investopediaunderstanding statisticsstatistics are used in virtually all scientific disciplines such as the physical and social sciences as well as in business the humanities government and manufacturing statistics is fundamentally a branch of applied mathematics that developed from the application of mathematical tools including calculus and linear algebra to probability theory in practice statistics is the idea that we can learn about the properties of large sets of objects or events a population by studying the characteristics of a smaller number of similar objects or events a sample gathering comprehensive data about an entire population is too costly difficult or impossible in many cases so statistics start with a sample that can be conveniently or affordably observed statisticians measure and gather data about the individuals or elements of a sample then they analyze this data to generate descriptive statistics they can then use these observed characteristics of the sample data which are properly called statistics to make inferences or educated guesses about the unmeasured characteristics of the broader population known as the parameters statistics informally dates back centuries an early record of correspondence between french mathematicians pierre de fermat and blaise pascal in 1654 is often cited as an early example of statistical probability analysis 1descriptive and inferential statisticsthe two major areas of statistics are known as descriptive statistics which describes the properties of sample and population data and inferential statistics which uses those properties to test hypotheses and draw conclusions descriptive statistics include mean average variance skewness and kurtosis inferential statistics include linear regression analysis analysis of variance anova logit probit models and null hypothesis testing descriptive statistics mostly focus on the central tendency variability and distribution of sample data central tendency means the estimate of the characteristics a typical element of a sample or population it includes descriptive statistics such as mean median and mode variability refers to a set of statistics that show how much difference there is among the elements of a sample or population along the characteristics measured it includes metrics such as range variance and standard deviation the distribution refers to the overall shape of the data which can be depicted on a chart such as a histogram or a dot plot and includes properties such as the probability distribution function skewness and kurtosis descriptive statistics can also describe differences between observed characteristics of the elements of a data set they can help us understand the collective properties of the elements of a data sample and form the basis for testing hypotheses and making predictions using inferential statistics inferential statistics is a tool that statisticians use to draw conclusions about the characteristics of a population drawn from the characteristics of a sample and to determine how certain they can be of the reliability of those conclusions based on the sample size and distribution statisticians can calculate the probability that statistics which measure the central tendency variability distribution and relationships between characteristics within a data sample provide an accurate picture of the corresponding parameters of the whole population from which the sample is drawn inferential statistics are used to make generalizations about large groups such as estimating average demand for a product by surveying a sample of consumers buying habits or attempting to predict future events this might mean projecting the future return of a security or asset class based on returns in a sample period regression analysis is a widely used technique of statistical inference used to determine the strength and nature of the relationship the correlation between a dependent variable and one or more explanatory independent variables the output of a regression model is often analyzed for statistical significance which refers to the claim that a result from findings generated by testing or experimentation is not likely to have occurred randomly or by chance it s likely to be attributable to a specific cause elucidated by the data having statistical significance is important for academic disciplines or practitioners that rely heavily on analyzing data and research mean median and modethe terms mean median and mode fall under the umbrella of central tendency they describe an element that s typical in a given sample group you can find the mean descriptor by adding the numbers in the group and dividing the result by the number of data set observations the middle number in the set is the median half of all included numbers are higher than the median and half are lesser the median home value in a neighborhood would be 350 000 if five homes were located there and valued at 500 000 400 000 350 000 325 000 and 300 000 two values are higher and two are lower mode identifies the number that falls between the highest and lowest values it appears most frequently in the data set understanding statistical datathe root of statistics is driven by variables a variable is a data set that can be counted that marks a characteristic or attribute of an item for example a car can have variables such as make model year mileage color or condition by combining the variables across a set of data such as the colors of all cars in a given parking lot statistics allows us to better understand trends and outcomes there are two main types of variables first qualitative variables are specific attributes that are often non numeric many of the examples given in the car example are qualitative other examples of qualitative variables in statistics are gender eye color or city of birth qualitative data is most often used to determine what percentage of an outcome occurs for any given qualitative variable qualitative analysis often does not rely on numbers for example trying to determine what percentage of women own a business analyzes qualitative data the second type of variable in statistics is quantitative variables quantitative variables are studied numerically and only have weight when they re about a non numerical descriptor similar to quantitative analysis this information is rooted in numbers in the car example above the mileage driven is a quantitative variable but the number 60 000 holds no value unless it is understood that is the total number of miles driven quantitative variables can be further broken into two categories first discrete variables have limitations in statistics and infer that there are gaps between potential discrete variable values the number of points scored in a football game is a discrete variable because statistics also makes use of continuous quantitative variables these values run along a scale discrete values have limitations but continuous variables are often measured into decimals any value within possible limits can be obtained when measuring the height of the football players and the heights can be measured down to 1 16th of an inch if not further statisticians can hold various titles and positions within a company the average total compensation for a statistician with one to three years of experience was 81 885 as of december 2023 this increased to 109 288 with 15 years of experience 2statistical levels of measurementthere are several resulting levels of measurement after analyzing variables and outcomes statistics can quantify outcomes in four ways there s no numerical or quantitative value and qualities are not ranked nominal level measurements are instead simply labels or categories assigned to other variables it s easiest to think of nominal level measurements as non numerical facts about a variable example the name of the president elected in 2020 was joseph robinette biden jr outcomes can be arranged in an order but all data values have the same value or weight although they re numerical ordinal level measurements can t be subtracted against each other in statistics because only the position of the data point matters ordinal levels are often incorporated into nonparametric statistics and compared against the total variable group example american fred kerley was the second fastest man at the 2020 tokyo olympics based on 100 meter sprint times 3outcomes can be arranged in order but differences between data values may now have meaning two data points are often used to compare the passing of time or changing conditions within a data set there is often no starting point for the range of data values and calendar dates or temperatures may not have a meaningful intrinsic zero value example inflation hit 8 6 in may 2022 the last time inflation was this high was in december 1981 4outcomes can be arranged in order and differences between data values now have meaning but there s a starting point or zero value that can be used to further provide value to a statistical value the ratio between data values has meaning including its distance away from zero example the lowest meteorological temperature recorded was 128 6 degrees fahrenheit in antarctica 5statistics sampling techniquesit would often not be possible to gather data from every data point within a population to gather statistical information statistics relies instead on different sampling techniques to create a representative subset of the population that s easier to analyze in statistics there are several primary types of sampling simple random sampling calls for every member within the population to have an equal chance of being selected for analysis the entire population is used as the basis for sampling and any random generator based on chance can select the sample items for example 100 individuals are lined up and 10 are chosen at random systematic sampling calls for a random sample as well but its technique is slightly modified to make it easier to conduct a single random number is generated and individuals are then selected at a specified regular interval until the sample size is complete for example 100 individuals are lined up and numbered the seventh individual is selected for the sample followed by every subsequent ninth individual until 10 sample items have been selected stratified sampling calls for more control over your sample the population is divided into subgroups based on similar characteristics then you calculate how many people from each subgroup would represent the entire population for example 100 individuals are grouped by gender and race then a sample from each subgroup is taken in proportion to how representative that subgroup is of the population cluster sampling calls for subgroups as well but each subgroup should be representative of the population the entire subgroup is randomly selected instead of randomly selecting individuals within a subgroup not sure which major league baseball player should have won most valuable player last year statistics often used to determine value is often cited when the award for best player is awarded 6 statistics can include batting average number of home runs hit and stolen bases uses of statisticsstatistics is prominent in finance investing business and in the world much of the information you see and the data you re given is derived from statistics which are used in all facets of a business 