Question

If the mean of the following data is 18.75, find the value of p

Xi = 10,15,p,25,30 and Fi = 5,10,7,8,2

Answer 1

Answer:

mean=summation XiFi

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summation of Fi

summation of XiFi=460+7p

summation of Fi=32

18.75=460+7p

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32

600=460+7p

600-460=7p

140=7p

p=140

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7

.•.p=20

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Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Questions}}}}$

$\begin{array}{|c|c|c|}\cline{1-3} x_{i} & f_{i} & f_{i}\times x_{i} \\ \cline{1-3} 10 & 5 & 50 \\ \cline{1-3} 15 & 10 & 150 \\ \cline{1-3} p & 7 & 7p \\ \cline{1-3} 25 & 8 & 200 \\ \cline{1-3} 30 & 2 & 60 \\ \cline{1-3} & \sum f_{i}=32 & \sum(f_{i}\times x_{i})=(460+7p)\\\cline{1-3} \end{array}$

Mean

$\tt{\rightarrow \dfrac{\sum(f_{i}\times x_{i})}{\sum f_{i}}}$

$\tt{\rightarrow \dfrac{460+7p}{32}}$

But,

Given

Mean = 18.75

Therefore,

$\tt{\rightarrow \dfrac{460+7p}{32}=18.75}$

460 + 7p = (18.75 × 32)

460 + 7p = 600

7p = 600 - 460

7p = 140

$\tt{\rightarrow p=\dfrac{\cancel{140}}{\cancel{7}}}$

p = 20

Hence we get,

p = 20