Find the standard deviation of the following data

Asked by admin @ 31/08/2021 in Math viewed by 358 People

Compute standard deviation for the following data.
21 12 23 12 14 15 16 19 20 25

Answered by admin @ 31/08/2021

We have explained Step-by-step for the following data:

21 12 23 12 14 15 16 19 20 25

For the Standard Deviation.

The mean is:

21 +12+ 23+ 12 +14 +15 +16 +19 +20 + 25

= 177/10= 17.7.

So,

μ = 17.7

subtracting the Mean and squaring the result

By the formula:

(xi - mu)^2

xi is are the individual x values

21 12 23 12 14 15 16 19 20 25, etc...

In other words x1 = 21, x2 = 12, x3 = 23, etc.

for each value, subtract the mean and square the result

(21- 17.7)2 = 10.89

(12 - 17.7)2 = 32.49

(23 - 17.7)2 = 28.09

(12 -17.7)2 = 32.49

(14- 17.7)2 = 13.69

(15- 17.7)2 = 7.29

(16 - 17.7)2 = 2.89

(19-17.7)2 =1.69

(20-17.7)2=5.29

(25-17.7)2=53.29

The results are:

10.89 32.49 28.09 32.49 13.69 7.29 2.89 1.69 5.29 53.29

Then the mean of these squared differences.

First add up all the values from the previous step.

10.89+ 32.49 + 28.09 + 32.49 + 13.69 + 7.29 + 2.89 + 1.69 + 5.29 + 53.29=188.1

Mean of squared differences = (1/10) × 188.1 = 18.81

Take the square root of that:

square root of [ (1/N) times Sigma i=1 to N of (xi - mu)^2 ]

σ = √(18.81) = 4.3370.

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