what are descriptive statistics 
descriptive statistics are brief informational coefficients that summarize a given data set which can be either a representation of the entire population or a sample of a population descriptive statistics are broken down into measures of central tendency and measures of variability spread measures of central tendency include the mean median and mode while measures of variability include standard deviation variance minimum and maximum variables kurtosis and skewness jessica olahunderstanding descriptive statisticsdescriptive statistics help describe and explain the features of a specific data set by giving short summaries about the sample and measures of the data the most recognized types of descriptive statistics are measures of center for example the mean median and mode which are used at almost all levels of math and statistics are used to define and describe a data set the mean or the average is calculated by adding all the figures within the data set and then dividing by the number of figures within the set for example the sum of the following data set is 20 2 3 4 5 6 the mean is 4 20 5 the mode of a data set is the value appearing most often and the median is the figure situated in the middle of the data set it is the figure separating the higher figures from the lower figures within a data set however there are less common types of descriptive statistics that are still very important 1people use descriptive statistics to repurpose hard to understand quantitative insights across a large data set into bite sized descriptions a student s grade point average gpa for example provides a good understanding of descriptive statistics the idea of a gpa is that it takes data points from a range of individual course grades and averages them together to provide a general understanding of a student s overall academic performance a student s personal gpa reflects their mean academic performance descriptive statistics especially in fields such as medicine often visually depict data using scatter plots histograms line graphs or stem and leaf displays 2 we ll talk more about visuals later in this article types of descriptive statisticsall descriptive statistics are either measures of central tendency or measures of variability also known as measures of dispersion measures of central tendency focus on the average or middle values of data sets whereas measures of variability focus on the dispersion of data these two measures use graphs tables and general discussions to help people understand the meaning of the analyzed data measures of central tendency describe the center position of a distribution for a data set a person analyzes the frequency of each data point in the distribution and describes it using the mean median or mode which measures the most common patterns of the analyzed data set measures of variability or measures of spread aid in analyzing how dispersed the distribution is for a set of data for example while the measures of central tendency may give a person the average of a data set it does not describe how the data is distributed within the set so while the average of the data might be 65 out of 100 there can still be data points at both 1 and 100 measures of variability help communicate this by describing the shape and spread of the data set range quartiles absolute deviation and variance are all examples of measures of variability 3consider the following data set 5 19 24 62 91 100 the range of that data set is 95 which is calculated by subtracting the lowest number 5 in the data set from the highest 100 distribution or frequency distribution refers to the number of times a data point occurs alternatively it can be how many times a data point fails to occur consider this data set male male female female female other the distribution of this data can be classified as univariate vs bivariatein descriptive statistics univariate data analyzes only one variable it is used to identify characteristics of a single trait and is not used to analyze any relationships or causations for example imagine a room full of high school students say you wanted to gather the average age of the individuals in the room this univariate data is only dependent on one factor each person s age by gathering this one piece of information from each person and dividing by the total number of people you can determine the average age bivariate data on the other hand attempts to link two variables by searching for correlation two types of data are collected and the relationship between the two pieces of information is analyzed together 4 because multiple variables are analyzed this approach may also be referred to as multivariate let s say each high school student in the example above takes a college assessment test and we want to see whether older students are testing better than younger students in addition to gathering the ages of the students we need to find out each student s test score then using data analytics we mathematically or graphically depict whether there is a relationship between student age and test scores the preparation and reporting of financial statements is an example of descriptive statistics analyzing that financial information to make decisions on the future is inferential statistics descriptive statistics and visualizationsone essential aspect of descriptive statistics is graphical representation visualizing data distributions effectively can be incredibly powerful and this is done in several ways histograms are tools for displaying the distribution of numerical data they divide the data into bins or intervals and represent the frequency or count of data points falling into each bin through bars of varying heights histograms help identify the shape of the distribution central tendency and variability of the data another visualization is boxplots boxplots also known as box and whisker plots provide a concise summary of a data distribution by highlighting key summary statistics including the median middle line inside the box quartiles edges of the box and potential outliers points outside or the whiskers boxplots visually depict the spread and skewness of the data and are particularly useful for comparing distributions across different groups or variables descriptive statistics and outlierswhenever descriptive statistics are being discussed it s important to note outliers outliers are data points that significantly differ from other observations in a dataset these could be errors anomalies or rare events within the data detecting and managing outliers is a step in descriptive statistics to ensure accurate and reliable data analysis to identify outliers you can use graphical techniques such as boxplots or scatter plots or statistical methods such as z score or iqr method these approaches help pinpoint observations that deviate substantially from the overall pattern of the data the presence of outliers can have a notable impact on descriptive statistics skewing results and affecting the interpretation of data outliers can disproportionately influence measures of central tendency such as the mean pulling it towards their extreme values for example the dataset of 1 1 1 997 is 250 even though that is hardly representative of the dataset this distortion can lead to misleading conclusions about the typical behavior of the dataset depending on the context outliers can often be treated by removing them if they are genuinely erroneous or irrelevant alternatively outliers may hold important information and should be kept for the value they may be able to demonstrate as you analyze your data consider the relevance of what outliers can contribute and whether it makes more sense to just strike those data points from your descriptive statistic calculations descriptive statistics vs inferential statisticsdescriptive statistics have a different function from inferential statistics which are data sets that are used to make decisions or apply characteristics from one data set to another imagine another example where a company sells hot sauce the company gathers data such as the count of sales average quantity purchased per transaction and average sale per day of the week all of this information is descriptive as it tells a story of what actually happened in the past in this case it is not being used beyond being informational now let s say that the company wants to roll out a new hot sauce it gathers the same sales data above but it uses the information to make predictions about what the sales of the new hot sauce will be the act of using descriptive statistics and applying characteristics to a different data set makes the data set inferential statistics we are no longer simply summarizing data we are using it to predict what will happen regarding an entirely different body of data in this case the new hot sauce product 