Question

Find the variance and the standard deviation for the following data: 57, 64, 43, 67, 49, 59, 44, 47, 61, 59.

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Answer 1

Answer:

Solution:

Given data: 57, 64, 43, 67, 49, 59, 44, 47, 61, 59

To find mean (μ):

Mean (μ)= ( 57+ 64+ 43+ 67+ 49+ 59+ 44+ 47+ 61+ 59)/10

= 550/10

Mean = 55

To find Variance (σ2):

Variance(σ2) = (xi – μ)2/n

=(22+92+122+122+62+42+62+42+112+82)/10

= 662/10

=66.2

Therefore, variance(σ2) = 66.2

To find standard deviation (σ):

To find the standard deviation, take the square root of variance, we get

Standard Deviation(σ) = √(σ2)

= √66.2 = 8.13

Therefore, the standard deviation is 8.13

Answer 2

Explanation:

Solution:

Given data: 57, 64, 43, 67, 49, 59, 44, 47, 61, 59

To find mean (μ):

Mean (μ)= ( 57+ 64+ 43+ 67+ 49+ 59+ 44+ 47+ 61+ 59)/10

= 550/10

Mean = 55

To find Variance (σ2):

Variance(σ2) = (xi – μ)2/n

=(22+92+122+122+62+42+62+42+112+82)/10

= 662/10

=66.2

Therefore, variance(σ2) = 66.2

To find standard deviation (σ):

To find the standard deviation, take the square root of variance, we get

Standard Deviation(σ) = √(σ2)

= √66.2 = 8.13

Therefore, the standard deviation is 8.13