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Question

The mean of following frequency table is 50.
If the total of frequency is 120. Then the missing frequencies f1,f2 are respectively
Class02020404060608080100Frequency17f132f219

A
24,28
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B
28,24
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C
25,27
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D
27,25
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Solution

The correct option is B 28,24
Given : Class02020404060608080100Frequency17f132f219

Total frequency =120, then
17+f1+32+f2+19=120f1+f2=52 (1)
We know the mean
¯¯¯x=fixiNx1=xi+xf2=0+202=10x2=xi+xf2=20+402=30x3=xi+xf2=40+602=50x4=xi+xf2=60+802=70x5=xi+xf2=80+1002=90
Therefore,
¯¯¯x=f1x1+f2x2+f3x3+f4x4+f5x5N50=17×10+f1×30+32×50+f2×70+19×901206000=170+30f1+1600+70f2+17106000=30f1+70f2+34802520=30f1+70f23f1+7f2=252 (2)

Solving equation s(1) and (2), we get
f1=28, f2=24

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