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 ( ):
Population Variance ( ):

5. Calculate the Standard Deviation ( )

The standard deviation is the square root of the variance.

Final Answer:
If calculating the Population Standard Deviation:
If calculating the Sample Standard Deviation ( ):