Question

34. Calculate the missing frequency from the following distribution, it being given that the median of the
distribution is 24.

age in years. no. of.persons.
0-10. 5
10-20. 25
20-30. ?
30-40. 18
40-50. 7​

Answer 1

Answer:

Missing frequency = 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 .

Answer 2

Answer:

Missing frequency = 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} *cx

L

+

f

m

2

N

−cf

∗c

where, x_Lx

L

= lower limit of median class = 20

N = ∑f = 55 + x

f_mf

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} *1020+

x

2

55+x

−30

∗10

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

x

2

55+x

−30

∗10

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

x

2

55+x

−30

∗10

0.4*x = \frac{55+x-60}{2}

2

55+x−60

0.4*x = (x-5)/2

0.4*x*2 = x - 5

x - 0.8*x = 5

x = 5/0.2 = 25