calculations of missing frequencies

Question

 

In the frequency distribution of 100 families given below, the number of families corresponding to expenditure groups 20—40 and 60—80 are missing from the table. However, the median is known to be 50. Find the missing frequencies.

Expenditure 0—20 20—40 40—60 60—80 80—100
No. of families 14       ?        28         ?         15

 

please show a step by step answer for more understanding

 

Answer 1

Hi Umaymah,

 

Exp     Frequency      cumulative freq

 

0-20        14                  14             

 

20-40        x                  14+x

 

40-60        28                 42+x

 

60-80         y                  42+x+y

 

80-100      15                 57+x+y 

                ____

                 100

As total no of families = 100=N

so 57+x+y=100....eq 1

 

Median(formula) = Lower limit + {N/2-Cum freq}* Class length

                                                     freq

 

N/2 = 100/2= 50

Median = 40+ { 50 -(14+x)}*20     

                          28

 

50 = 40+ {36-x}*20/28

10 = (36-x)5/7

 

70=180 -5x

5x =110

x= 22

 

now substituting value of x in eq 1, 57+x+y = 100,

                                                   57 + 22+y=100

                                                                y=21

the number of families corresponding to expenditure groups 20—40 is = 22 and 60—80  is = 21 in  the table