Question

The data list shows the scores of ten students in Mr. Smith's math class. 61, 67, 81, 83, 87, 88, 89, 90, 98, 100 What is the standard deviation, to the nearest tenth, of the data if the scores represent a sample of Mr. Smith's students? a0 What is the standard deviation, to the nearest tenth, of the data if the scores represent the entire population of Mr. Smith's students? a1

Answer 1

Answer: The standard deviation of the sample will be 11.6.

The standard deviation of the population will be 12.31.

Explanation:

Mr Smith's math class scores : 61, 67, 81, 83, 87, 88, 89, 90, 98, 100

Number of terms,N = 10

`Mean=\mu =\frac{\text{sum of all the terms}}{\text{total number of terms}}`

`\mu =(61+67+81+83+87+88+89+90+98+100)/(10)=(844)/(10)=84.4`

Standard deviation of the sample:

`\sigma=\sqrt{(1)/(N)\sum_(i=1)^n(x_i-\mu )^2}=\sqrt{(1)/(10)(1364.4)}=11.68`

Standard deviation for the population:

`\sigma=\sqrt{(1)/(N-1)\sum_(i=1)^n(x_i-\mu )^2}=\sqrt{(1)/(9)(1364.4)}=12.31`

The standard deviation of the sample will be 11.6.

The standard deviation of the population will be 12.31.