Use the Sample Variance Definition to find the variance and

Idilwsiw2

Idilwsiw2

Answered question

2021-11-29

Use the Sample Variance Definition to find the variance and standard deviation of the data. Round the answers to one decimal place.
8, 7, 3, 2, 10, 4

Answer & Explanation

Ida Perry

Ida Perry

Beginner2021-11-30Added 20 answers

Step 1
As per the definition of sample variance, the variance is mathematically defined as the average of squared differences of the sample data from their mean.
Now, the mean of the given data is obtained as:
x=xin
=8+7+3+2+10+46
=5.66
Step 2
Therefore, the required variance of the data is obtained as:
σ2=(xix)2n1
=(85.66)2+(75.66)2+(35.66)2+(25.66)2+(105.66)2+(45.66)261
=9.866729.9
And the required standard deviation is obtained as:
σ=9.86672
=3.141133.1
Therefore, the required variance and standard deviation of the data is obtained as 9.9 and 3.1.

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