Question

Find the mean of the following distribution by deviation method C.I=0-9,10-19,20-29,30-39,40-49 AND FI=8,15,20,45,12 What is the solution to the question

Answer 1

Mean of the given data = 28.2962

Step-by-step explanation:

We are given the following frequency distribution below;

    C.I.              Frequency (f)              X             d = $\frac{X-A}{h}$              $f \times d$

   0 - 9                     8                         4.5              -2.22               -17.76

  10 - 19                   15                        14.5             -1.11                  -16.65

  20 - 29                 20                A = 24.5              0                        0

  30 - 39                 45                       34.5              1.11                  49.95

  40 - 49                12                        44.5              2.22              26.64      

   Total                  100                                                                   42.18        

Now, the mean formula using step-deviation method is given by;

                  Mean,  $\bar X$ =  $A + \frac{\sum f \times d }{\sum f} \times h$

where, A = assumed mean = 24.5

            h = class size i.e. gap between class intervals = 9

           $\sum f$ = 100

          $\sum f \times d$ = 42.18

So, putting values into the formula, we get;

                 Mean =  $24.5 + \frac{42.18 }{100} \times 9$

                           =  24.5 + 3.7962

                           =  28.2962

Therefore, mean of the given distribution by deviation method is 28.2962.

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