Question

Find the value of following data is 21.6, Find the value of p

Xi=6,12,18,24,30,36 and Fi=5,4,p,6.4,6

Answer 1

$\tt{\begin{array}{|c|c|c|}\cline{1-3} x_{i} & f_{i} & f_{i}\times x_{i} \\ \cline{1-3} 6 & 5 & 30 \\ \cline{1-3} 12 & 4 & 48 \\ \cline{1-3} 18 & p & 18p \\ \cline{1-3} 24 & 6 & 144 \\ \cline{1-3} 30 & 4 & 120 \\ \cline{1-3} 36 & 6 & 216 \\ \cline{1-3} & \sum f_{i}=(25+p) & \sum(f_{i}\times x_{i})=(558+18p)\\\cline{1-3} \end{array}}$

Mean

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

$\tt{\rightarrow \dfrac{558+18p}{25+p}}$

But,

Given

Mean = 21.6

Therefore,

$\tt{\rightarrow \dfrac{558+18p}{25+p}=21.6}$

⇒ (558 + 18p) = 540 + 21.6p

⇒ 3.6p = 18

$\tt{\rightarrow p=\dfrac{18}{3.6}}$

$\tt{\rightarrow p=\dfrac{\cancel{180}}{\cancel{36}}}$

= 5

Hence,

p = 5

Answer 2

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