Calculate Standard Deviation for a Data Set

Published on July 5, 2026

Statistics

Learn how to calculate the population standard deviation for a given set of numbers by finding the mean, variance, and square root.

Question

Calculate SD : 1.24,5.19,1.62,9.54,2.63,4.25,5 .34

Answer

To calculate the Standard Deviation (SD) of the given data set, we follow these steps:

1. List the data points

The data set is:

Number of values (

) =

2. Calculate the Mean ()

The mean is the sum of all values divided by the number of values.

For precision in intermediate steps, let’s use

3. Calculate the squared deviations from the mean

We subtract the mean from each value and square the result:


1.24
5.19
1.62
9.54
2.63
4.25
5.34

4. Calculate the Variance ()

The variance is the average of these squared deviations.
(Note: If this is a sample, we divide by . If it is a population, we divide by . Usually, in statistics problems unless specified as a sample, we calculate the population SD or specify. We will provide the Population SD here).

Sum of squared deviations ():