Question

. Listed below are the top 10 annual salaries in mions of dollars of TV personalities Find the range, variance, and standard deviation for the sample data Genthese are the top 10 res do we know anything about the variation of salaries of TV personalities in general 42 40 39 31 23 20 1918 171 172 The range of the sample data is siin Typem integer or a decimal) The variance of the same data Round to two decimal places as needed The standard deviation of the sample data is on (Round to two decimal places as noded) is the standard deviation of the sample a good time of the variation of sales of TV persons in general A No, because the sample is not representative of the whole potion OB. No, because there is not in the same data OC Yesbecause the standard deviation is based estimator OD. Yesbecause the sample is random

Answer 1

The sample observation (x) is given as -

42 40 39 31 23 20 19 18 17.7 17.2

Number of observations = n = 10

Range = Maximum value - Minimum value = 42 - 17.2 =24.8           (Answer)

Before finding variance let us find mean first.

$\small Mean = \overline x = \frac{1}{n}\sum x=\frac{1}{10}[42+40+..+17.2]=26.69$

Now,

$\small Sample \ Variance=\frac{1}{n-1}\sum (x-\overline x)^2$

                                  $\small =\frac{1}{10-1}[(42-26.69)^2+(40-26.69)^2+...(17.2-26.69)^2]=105.06$         (Answer)

$\small Sample \ Standard \ deviation = \sqrt{Sample \ Variance}=\sqrt{105.06}=10.25$       (Answer)

A. No, because the sample is not representative of the whole population.