Question

cylinder от под
20. The following table gives the number of goals scored by 71 leading players in international
football matches. Find the standard deviation of the data.
Class interval 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70
Frequency
8
12
17
14
9
7
4​

Answer 1

Standard deviation = 16.79

Step-by-step explanation:

We are given with the following frequency distribution data which gives the number of goals scored by 71 leading players in international  football matches.;

Class Interval    Frequency (f)      X       $X \times f$     $(X-\bar X)^{2}$         $f \times (X-\bar X)^{2}$

    0 - 10                     8                    5         40         664.09            5312.72

   10 - 20                   12                   15        180        248.69           2984.28

   20 - 30                   17                  25       425        33.29              565.93

   30 - 40                   14                  35        490        17.89              250.46

   40 - 50                    9                  45        405        202.49           1822.41

   50 - 60                    7                  55        385        587.09           4109.63

   60 - 70                    4                 65        260        1171.69          4686.76  

     Total                     71                            2185                             19732.19    

Now, firstly, we have to find the mean of the following data.

So, the mean of the frequency distribution is given by the following formula;

              Mean, $\bar X$  = $\frac{\sum X \times f}{\sum f}$

                               = $\frac{2185}{71}$ = 30.77

Also, Standard deviation formula for the given data is given by the following formula;

           Standard deviation = $\sqrt{\frac{\sum f \times (X-\bar X)^{2} }{\sum f - 1} }$

In this formula, in the denominator we have subtracted 1 as we considered the given data as sample data.

  So, Standard deviation = $\sqrt{\frac{19732.19 }{71 - 1} }$

                                         = $\sqrt{\frac{19732.19 }{70} }$ = 16.79

Therefore, the standard deviation of the data is 16.79.