If the mean of the following frequency distribution is $7$ , find the value of $p$ .
variables 2 3 5 10 13
Frequency 4 8 p 12 6

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Solution

Mean $= \frac{2 \times 4 + 3 \times 8 + 5 \times p + 10 \times 12 + 13 \times 6}{4 + 8 + p + 12 + 6} = 7$
$\Rightarrow 8 + 24 + 5 p + 120 + 78 = 7 (30 + p)$
$\Rightarrow 32 + 120 + 78 + 5 p = 210 + 7 p$
$\Rightarrow 120 + 110 - 210 = 7 p - 5 p$
$\Rightarrow 230 - 210 = 2 p \Rightarrow 20 = 2 p \Rightarrow p = 10$

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If the mean of the following frequency distribution is 7, find the value of p.variables2351013Frequency48p126

Mean=2×4+3×8+5×p+10×12+13×64+8+p+12+6=7⇒8+24+5p+120+78=7(30+p)⇒32+120+78+5p=210+7p⇒120+110−210=7p−5p⇒230−210=2p⇒20=2p⇒p=10

If the mean of the following frequency distribution is $7$ , find the value of $p$ .
variables 2 3 5 10 13
Frequency 4 8 p 12 6