Question

These data show the ring size for a sample of 8 men 12 10 11.5,11.5, 12, 9, 9 , 11 what is the best approximation of the standard deviation of the ring size data

Answer 1

Standard deviation of ring size is 1.253

Explanation:

We are given the following data-set:

12, 10, 11.5, 11.5, 12, 9, 9, 11

n = 8

Formula:

`\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}`

where
`x_i` are data points,
`\bar{x}` is the mean and n is the number of observations.

`Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}`

`Mean =\displaystyle(86)/(8) = 10.75`

Sum of squares of differences = 1.5625 + 0.5625 + 0.5625 + 0.5625 + 1.5625 + 3.0625 + 3.0625 + 0.0625 = 11

`S.D = \sqrt{\displaystyle(11)/(7)} = 1.253`

Answer 2

Given the data above N=8
mean is (12+10+11.5+11.5+12+9+9+11)/8
thus, mean = 10.75
Sample standard, s= √(∑(x-m)²)/(n-1)
= 1.172
I therefore, believe that the best approximation of standard deviation is 1.17