Standard deviation is a key statistical measure that helps you understand the variability or dispersion of a set of data points. In simple terms, it tells you how spread out the numbers are from the mean (average) value. In this article, we will take you through an example to demonstrate how to calculate standard deviation step by step.

Let’s consider an example dataset: 5, 8, 12, 15, and 20.

Step 1: Calculate the Mean (Average)

First, add the values together:

5 + 8 + 12 + 15 + 20 = 60

Next, divide the sum by the total number of values in the dataset (in this case, 5):

60 / 5 = 12

The mean (average) of the dataset is therefore 12.

Step 2: Calculate Each Deviation From The Mean

Now we need to find out how far each value in our dataset is from the mean:

5 – 12 = -7

8 – 12 = -4

12 – 12 = 0

15 – 12 = 3

20 – 12 = 8

Step 3: Square Each Deviation From The Mean

Find the square of each deviation we calculated in step 2:

(-7)² = 49

(-4)² = 16

(0)² = 0

(3)² = 9

(8)² =64

Step 4: Calculate the Mean of Squared Deviations

Add up the squared deviations and divide by the total number of values in our dataset:

(49 +16 +0 +9 +64) /5 =

(138) /5 =27.6

This value is known as variance.

Step 5: Calculate Standard Deviation

To find standard deviation, take the square root of the variance:

√27.6 ≈ 5.25

So, the standard deviation of the example dataset is approximately 5.25.

This means that, on average, each value in the dataset is about 5.25 units away from the mean. With this information, researchers and data analysts can understand how spread out or clustered the data points are, allowing for better decision-making and more accurate predictions.

In summary, calculating the standard deviation of a dataset involves finding the mean, calculating each deviation from the mean, squaring those deviations, finding the mean of squared deviations (variance), and finally taking the square root of variance. With a firm grasp on calculating standard deviation, you’re better prepared to understand and analyze various types of data in real-world scenarios.