Sample Standard Deviation Calculator

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The sample standard deviation calculator is used to calculate the deviation or variation between set of

numbers. This calculator is used to estimate a sample based on the data and measures the variation.A

sample of data form a population, then the standard deviation of the data can be calculated by using the

population standard measures.



Example 1: Find the standard deviation for set of numbers listed below

5,7, 11, 13, 14


Step 1: Find the mean value.

Mean = (5+7+11+13+14) /5 = 50/5 = 10

Step 2: Find the variance. To calculate the variance, take the each number and subtract it form mean value,

then find the mean to get the result.

= (5-10) ^2 + (7-10) ^2+ (11-10) ^2+ (13-10) ^2+ (14-10) ^2

= (-5) ^2+ (-3) ^2+ (1) ^2+ (3) ^2+ (4) ^2

= 25 + 9 +1 +9 +16

=60

The Variance = 60/5 =12

Step 3: Square root of the Variance gives the Standard deviation

√12 =3.46101615

=3.46 (Rounded to two decimal places)



Example 2: Four friends scored the following marks in math test. Find the standard deviation.

30 33 37 40


Step 1: Find the mean value.

Mean = (30+33+37+40)/4 =140/4=35

Step 2:Find the variance. To calculate the variance, take the each number and subtract it form mean value,

then find the mean to get the result.

= (30-35) ^2+ (33-35) ^2+ (37-35) ^2+ (40-35) ^2

= (-5) ^2+ (-2) ^2+ (2) ^2+ (5) ^2

=25+4+4+25

= 58

The Variance = 58/4 =14.5

Step 3: Square root of the Variance gives the Standard deviation

√14.5 = 3.807886553

=3.81 (Rounded to nearest tenth).


 

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