Compute standard deviation for the following data.
21 12 23 12 14 15 16 19 20 25
Answers
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.
Answer :-
→ mean of data = (21 + 12 + 23 + 12 + 14 + 15 + 16 + 19 + 20 + 25)/10 = 504/10 = 17.7 .
so,
→ sum of (difference of weight)² = (21 - 17.7)² + (12 - 17.7)² + (23 - 17.7)² + (12 - 17.7)² + (14 - 17.7)² + (15 - 17.7)² + (16 - 17.7)² + (19 - 17.7)² + (20 - 17.7)² + (25 - 17.7)²= 10.89 + 32.49 + 28.09 + 32.49 + 13.69 + 7.29 + 2.89 + 1.69 + 5.29 + 53.29 = 188.1
then,
→ Variance = sum of (difference of weight)² / N - 1
→ Variance = 188.1 / 10 - 1
→ Variance = 188.1 / 9
→ Variance = 20.9
therefore,
→ Standard deviation = √(variance) = √(20.9) = 4.57 (Ans.)
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