The mean of the following distribution is 54, find the missing frequency x

CI 0-20 20-40 40-60 60-80 80-100

F 16 14 24 26 x

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Solution

Midpoint 10 30 50 70 90

F 16 14 24 26 x

Find out the midpoint of Cl by adding the range and dividing by 2
Mean=total Cl /total frequency

mean=(1016 + 3014 + 5024 +7026 +90*x ) / (16+14+24+26+x)

=> mean= (3600+ 90x)/ (80+x)
Given mean=54
=> 54(80 +x) =(3600+ 90x)
=> 4320 +54x=3600+90x
720=36x
x=720/36 = 20

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