Question

the mean of the yellowing data. 2:6 yfind the warne, gee
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Answer 1

Question :-

The mean of following data is 21.6 find the value of p.

Solution :-

Given Data :

$</p><p>\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c} \bf f_i& \bf x_i\\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 5 & \sf 6 \\ \\ \sf 4 & \sf 12 \\ \\ \sf p & \sf 18 \\ \\ \sf6& \sf 24 \\ \\ \sf4& \sf 30 \\ \\ \sf6& \sf 36\end{array}} \\ \end{gathered}\end{gathered}\end{gathered}$

Frequency Table :-

$\small\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c|c} \bf f_i& \bf x_i& \bf f_i x_i\\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 5 & \sf 6 & \sf 5 \times 6 = 30 \\ \\ \sf 4 & \sf 12 & \sf 4 \times 12 = 48\\ \\ \sf p & \sf 18&\sf p \times 18 = 18p \\ \\ \sf 6& \sf 24&\sf 6 \times 24 = 144\\ \\ \sf 4 & \sf 30&\sf 4 \times 30 = 120\\ \\ \sf 6 & \sf 36&\sf 6 \times 36 = 216 \\ \frac{\qquad \qquad}{} &&\frac{\qquad \qquad}{} \\ \sf \sum f_i = 25 + p&& \sum \sf f_i x_i = 558 + 18p\end{array}} \\ \end{gathered}\end{gathered}\end{gathered}$

Now,

$\sf:\longmapsto{ mean = \frac{\sum f_i x_i}{\sum f_i x_i} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf : \longmapsto{21.6 = \frac{558 + 18p}{25 + p} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf : \longmapsto{21.6(25 + p) = 558 + 18p} \\ \\ \sf : \longmapsto{540 + 21.6p = 558 + 18}p \\ \\ \sf : \longmapsto{21.6p - 18p = 558 - 540} \\ \\ \sf : \longmapsto{3.6p = 18} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf : \longmapsto{p = \frac{18}{3.6} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf : \longmapsto \red{p = 5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Verification :-

$\sf:\longmapsto{mean = \frac{558 + 18p}{25 + p} } \: \: \: \: \: \: \: \: \\ \\ \sf:\longmapsto{21.6 = \frac{558 +18( 5)}{25 + 5} } \: \: \: \: \: \: \: \\ \\ \sf:\longmapsto{21.6 = \frac{558 + 90}{30} } \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf:\longmapsto{21.6 = \frac{648}{30} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf:\longmapsto{21.6 \times 30 = 648} \: \: \: \: \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{648 = 648} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

${\boxed{\bf{\green{Hence \: Verified \: ✔}}}}$

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