**Instructions:** Use this Descriptive Statistics Calculator to enter the sample data below and the solver will provide step-by-step calculation of the basic descriptive statistics, such as the mean, median, mode, variance, standard deviation, range, quartiles, 5-number summary, etc.

## Descriptive Statistics Calculator

Descriptive Statistics corresponds to measures and charts that are derived from *sample* and are intended to provide information about the population being studied. Two basic types of descriptive statistics are the * measures of central tendency* and the *measures of dispersion*.

The measures of central tendency intend to give an idea of the location of the distribution. Examples of central tendency measures are the sample mean \(\bar X\), the median and the mode. Examples of measures of dispersion are the sample variance \(s^2\), the standard deviation \(s\), and the range among others.

The charts that usually presented in a descriptive statistics report are the histogram and box plot, which give a very clear picture of the distribution of the variable that is being sampled.

Different measures are more appropriate than others for certain cases. For example, certain measures like the mean are very sensitive to outliers, and therefore, when a sample has strong outliers or it is very skewed, the preferred measure of central tendency would be the median instead of the sample mean

### Descriptive Statistics Typically Reported

Usually, different formats are used, depending on the context of the sample data. Often times, the 5-number summary is reported, which consists of the Minimum, the first quartile, the median, the third quartile and the Maximum.

### What if I have Grouped Data

Grouped data needs to be handled differently. When having grouped data, especially the type of data where we know the frequency associated to a given range of data, we need to proceed differently using an approximation of a midpoint to represent a range of data. In that case you would instead use this descriptive statistics calculator for grouped data.

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