Question

(d) Determine the mean and standard deviation for the following series.
Class Interva Frequency
70- 80 7
60- 70 11
50- 60 22
40- 50 0
30- 40 15
20 - 30 5​

Answer 1

Mean = 51.67

Standard deviation = 15.26

Step-by-step explanation:

We are given with the following frequency distribution data below;

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

    20 - 30                    5                25        125         711.29             3556.45

    30 - 40                    15               35        525        277.89           4168.35

    40 - 50                    0                45          0          44.49                  0

    50 - 60                   22               55        1210       11.09               243.98

    60 - 70                    11                65        715         177.69            1954.59

    70 - 80                     7               75        525        544.29         3810.03  

    Total                       60                         3100                             13733.4    

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

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

                               = $\frac{3100}{60}$ = 51.67

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 = $\sqrt{\frac{13733.4 }{60 - 1} }$

                                         = $\sqrt{\frac{13733.4 }{59} }$ = 15.26

Therefore, the mean and standard deviation for the following series is 51.67 and 15.26 respectively.