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

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

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    0
    2021-09-19T04:21:49+00:00

    Answer:

    Standard deviation of ring size is 1.253

    Step-by-step 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\frac{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\frac{11}{7}} = 1.253

    0
    2021-09-19T04:22:22+00:00

    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

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