# Descriptive Statistics

## What are 'Descriptive Statistics'

Descriptive statistics are brief descriptive coefficients that summarize a given data set, which can be either a representation of the entire population or a sample of it. Descriptive statistics are broken down into measures of central tendency and measures of variability, or spread. Measures of central tendency include the mean, median and mode, while measures of variability include the standard deviation or variance, the minimum and maximum variables, and the kurtosis and skewness.

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## BREAKING DOWN 'Descriptive Statistics'

Descriptive statistics, in short, help describe and understand 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 the mean, median and mode, which are used at almost all levels of math and statistics. However, there are less-common types of descriptive statistics that are still very important.

People 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 wide range of exams, classes and grades, and averages them together to provide a general understanding of a student's overall academic abilities. A student's personal GPA reflects his mean academic performance.

## Measures of Descriptive Statistics

All descriptive statistics, whether they be the mean, median, mode, standard deviation, kurtosis or skewness, are either measures of central tendency or measures of variability. These two measures use graphs, tables and general discussions to help people understand the meaning of the data being analyzed.

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 measure the most common patterns of the data set being analyzed.

Measures of variability, or the measures of spread, aid in analyzing how spread-out 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 doesn't describe how the data is distributed within the set. So, while the average of the data may 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.

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