Question

The median of the following frequency distribution is 24 find the value of X

Answer 1

Answer:

Value of X = 25

Step-by-step explanation:

We are given following frequency distribution below;

  Age in years        No. of persons (f)          Cumulative frequency (cf)

       0 - 10                          5                                               5

      10 - 20                        25                                             30

      20 - 30                         x                                             30 + x

      30 - 40                        18                                            48 + x

      40 - 50                        7                                           55 + x    

                                    ∑f = 55 + x  

We are given the median of the  distribution is 24. Since 24 lies in the interval of 20 - 30, so the median class is 20 - 30.

Median formula = $x_L + \frac{\frac{N}{2} - cf}{f_m} *c$

where, $x_L$ = lower limit of median class = 20

            N =  ∑f = 55 + x    

            $f_m$ = frequency of median class = x

            cf = cumulative frequency of just above the median class = 30

             c = width of class interval = 10

So,  24 = $20 + \frac{\frac{55+x}{2} - 30}{x} *10$

      24 - 20 = $\frac{\frac{55+x}{2} - 30}{x} *10$

            4 = $\frac{\frac{55+x}{2} - 30}{x} *10$

          0.4*x = $\frac{55+x-60}{2}$

           0.4*x = (x-5)/2

           0.4*x*2 = x - 5

             x - 0.8*x = 5

                x = 5/0.2 = 25

Therefore, value of missing frequency, x = 25 .