If the mean of the following data is $20.2$ then the value of $p$ is
x 10 15 20 25 30
f 6 8 p 10 6

40

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20

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60

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None

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Solution

The correct option is B $20$
$f = 6, 8, p, 10, 6$ $x = 10, 15, 20, 25, 30 m e a n = 20.2 \frac{\sum f_{i} x_{i}}{\sum f_{i}} = 20.2 \sum f_{i} x_{i} = (10 \times 6) + (15 \times 8) + (20 p) + (25 \times 10) + (30 \times 6) = 610 + 20 p \sum f_{i} = 6 + 8 + p + 10 + 6 = 30 + p \frac{\sum f_{i} x_{i}}{\sum f_{i}} = 20.2 610 + 20 p = 20.2 (30 + p) => 20.2 p - 20 p = 610 - 606 => 0.2 p = 4 => p = 20$

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If the mean of the following data is 20.2 then the value of p isx1015202530f68p106

The correct option is B 20f=6,8,p,10,6x=10,15,20,25,30mean=20.2∑fixi∑fi=20.2∑fixi=(10×6)+(15×8)+(20p)+(25×10)+(30×6)=610+20p∑fi=6+8+p+10+6=30+p∑fixi∑fi=20.2610+20p=20.2(30+p)=>20.2p−20p=610−606=>0.2p=4=>p=20

If the mean of the following data is $20.2$ then the value of $p$ is
x 10 15 20 25 30
f 6 8 p 10 6