Find the variance and the standard deviation for the frequencydistribution of th

Question

Find the variance and the standard deviation for the frequencydistribution of the data representing the number of milesthat 15 runners ran during one week. Round your final answer to onedecimal place.


         Class                                Frequency                    Midpoint
     5.5-10.5                                   2                                    8
    10.5-15.5                                  3                                   13
    15.5-20.5                                  1                                   18
    20.5-25.5                                  5                                   23
    25.5-30.5                                  1                                   28
    30.5-35.5                                  1                                   33
    35.5-40.5                                  2                                   38



Variance:_____ Standard deviation:____

Explanation / Answer

Find the varianceand the standard deviation for the frequency distribution ofthe data representing the number of miles that 15 runners randuring one week. Round your final answer to one decimalplace. {Variance} = 94.5 {Standard Deviation} = 9.7 EXPLANATION: {Sample Size} = N = 15 {Sample Mean} = E{X} = (1/N)*(X) = 21.67 {Mean Of Squared X} = E{X^2} = 564.11 {Sample Variance} = Var{X} = E{X^2}- (E{X})^2 = 94.52 {Sample Standard Deviation} = s = Sqrt[Var{X} ] = 9.722 .

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