Grouped Data Standard Deviation Calculator

What Is Grouped Data Standard Deviation?

When data is organized into class intervals with frequencies, you cannot compute the standard deviation from individual values alone. This calculator uses class midpoints and frequencies to estimate the mean, variance, and standard deviation of grouped data. Pair it with the Frequency Distribution Calculator or Descriptive Statistics Calculator for related analysis.

Formulas for Grouped Data

For each class interval, the midpoint is $M = \frac{a + b}{2}$, where $a$ and $b$ are the lower and upper limits. The sample mean is $\mu = \frac{\sum (M_i F_i)}{n}$, and the sample variance is:

$$\sigma^2 = \frac{\sum (F_i M_i^2) - n\mu^2}{n - 1}$$

The standard deviation is the square root of the variance: $\sigma = \sqrt{\sigma^2}$.