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Question

Write the median clas of the following distribution:

Class010102020303040405050606070Frequency448101284


Solution

Class Mid-point(x) Frequency(f) (fx) Cumulative frquency
0-10 5 4 20 4
10-20 15 4 60 4+4=8
20-30 25 8 200 8+8=16
30-40 35 10 350 16+10=26
40-50 45 12 540 26+12=38
50-60 55 8 440 38+8=46
60-70 65 4 260 46+4=50
   
  ∑f = 50
  ∑(fx) = 1870
 


Mean = fxf=187050 = 37.4

A median group is in the range of  30 - 40, as we have mean 37.4

And
Formula for median L+N2Cfbfm×w
Here
L is the lower class boundary of the group containing the median =  30
n is the total number of data =  50
(fb) is the cumulative frequency of the groups before the median group =  16
(fm) is the frequency of the median group = 10
w is the group width =  10
So,
Median = 30+5021610×10 = 30+ 25 - 16 = 39  

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