Steps for Calculations of Standard Deviation

We can calculate the standard deviation using following steps:

Step 1: Calculate the mean (average) of the data set.

Step 2: For each data point, subtract the mean and square the difference.

Step 3: Sum the squared differences.

Step 4: Divide the sum of squared differences by N – 1 (for sample standard deviation) or N (for population standard deviation).

Step 5: Take the square root of the result.

Example on Standard Deviation Calculation

Let’s calculate the standard deviation of the following data set: {2, 4, 5, 7, 9}

Step 1: Calculate the mean for the data

Mean = (2 + 4 + 5 + 7 + 9) / 5 = 5.4

Step 2: Calculate the squared deviations from the mean.

• (2 – 5.4)² = 11.56
• (4 – 5.4)² = 1.96
• (5 – 5.4)² = 0.16
• (7 – 5.4)² = 2.56
• (9 – 5.4)² = 13.69

Step 3: Sum the squared deviations from the mean.

Σ(xi – μ)² = 11.56 + 1.96 + 0.16 + 2.56 + 13.69 = 29.93

Step 4: Divide the sum of squared differences by N – 1.

29.93 / (5 – 1) = 5.99

Take the square root of the result.

s = √5.99 ≈ 2.45

Therefore, the sample standard deviation of the data set is approximately 2.45.

Read More,

• Mean in Statitics
• Variance
• Mean, Variance and Standard Deviation
• Mean Absolute Deviation
• Normal Distribution

Standard Deviation is a measure of how data is spread out around the mean. It is a statistical tool used to determine the amount of variation or dispersion of a set of values from the mean. A low standard deviation indicates that the data points are clustered closely around the mean, while a high standard deviation means that the data points are spread across a wide range of values.

In this article, we will discuss how to calculate Standard Deviation using a formula.