**Instructions**: This calculator of descriptive statistics for grouped data calculates the sample mean, variance and standard deviation for grouped data. Grouped data is specified in class groups instead of individual values. It comes with ranges of values associated with a frequency. For example, one range could be 2 - 6 and the frequency could be, say, 8, another range could be 7 - 10, with a frequency of 4, etc.

## How to Use this Descriptive Statistics Calculator for Grouped Data?

Calculating descriptive statistics for grouped data is similar to computing descriptive statistics for a regular sample of data, only that in the case of grouped data, we have less information about the data. We don't know the precise values of the data, but we have ranges where the data lies in

In principle, in order to compute descriptive statistics for grouped data we need to estimate a proxy for the values that belong to a certain class/interval, by computing the midpoint of the interval. Such midpoint will serve as the best possible *representative* of all the points in the class.

Once the midpoints are computed, the sample mean, variance and standard deviation are obtained as follows:

\[ \bar X = \frac{ 1}{n}\left(\sum_{i=1}^n M_i \cdot f_i \right) \] \[ var(X) = \frac{ 1}{n-1}\left(\sum_{i=1}^n M_i^2 \cdot f_i - \frac{1}{n}\left(\sum_{i=1}^n M_i \cdot f_i \right)^2 \right) \] \[ SD(X) = \sqrt{\frac{ 1}{n-1}\left(\sum_{i=1}^n M_i^2 \cdot f_i - \frac{1}{n}\left(\sum_{i=1}^n M_i \cdot f_i \right)^2 \right)}\]