How to Find Sample Standard Deviation?

How to Find Standard Deviation (SD) of a Sample ?

SD of a Sample Calculation

A sample is a collection of data that is selected from the population using a defined method or procedure. This tutorial helps you to learn how to calculate the sample standard deviation (SD).

Formula :
SD of Sample =√Σ (X -M)²/ (n - 1)
Where,
X = Elements
M = Mean
n = Number of Elements

Step 1:
Consider the data of a sample as :3,7,1,18,20
From the data, we can calculate the mean as : (3+7+1+18+20 ) / 5
= 49 / 5
Mean = 9.8

Step 2:
Substituting the below values in the formula of sample SD,
SD of Sample = √{[(3-9.8)²+ (7-9.8)²+ (1-9.8)²+ (18-9.8)²+ (20-9.8)²] / (5 -1)}
= √{[(-6.8)²+ (-2.8)²+ (-8.8)²+ (8.2)²+ (10.2)²] / 4}
= √{46.24 + 7.84 + 77.44 + 67.24 + 104.04 / 4}
= √(302.8 / 4)
= √(75.7)
Hence, the standard deviation of a sample is8.7

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