Question

If the mean of the following frequency distribution is 24, find the value of p.
Class. Frequency
0-10. 3
10-20. 4
20-30. p
30-40. 3
40-50. 2
​

Answer 1

$\sf \bold{\underline{\underline{\pink{Question:-}}}}$

If the mean of the following frequency distribution is 24, find the value of p.

$\begin{lgathered}\begin{tabular}{| c | c | c | c | c | c | }\cline{1-6} \bf{Class} & \sf{0-10} & \sf{10-20} & \sf{20-30} & \sf{30-40} & \sf{40-50} \\ \cline{1-6}\bf{Frequency} & \sf{3} & \sf{4} & \sf{p} & \sf{3} & \sf{2} \\ \cline{1-6} \end{tabular}\end{lgathered}$

$\sf \bold{\underline{\underline{\pink{AnswEr:-}}}}$

$\begin{lgathered}\begin{tabular}{| c | c | c | c | }\cline{1-4} \bf{class interval} & \bf{Frequency (fi)} & \bf{class mark (xi)} & \bf{fixi}\\ \cline{1-4}\sf{0 - 10} & \sf{3} & \sf{5} & \sf{15}\\ \cline{1-4}\sf{10-20} & \sf{4} & \sf{15} & \sf{60}\\ \cline{1-4}\sf{20-30} & \sf{p} & \sf{25} & \sf{25p}\\ \cline{1-4}\sf{30-40} & \sf{3} & \sf{35} & \sf{105}\\ \cline{1-3}\sf{40-50} & \sf{2} & \sf{45} & \sf{90}\\ \cline{1-4}\sf{Total } & \sf{} & \sum\limits\sf\ fi \sf\ = p + 12 & \sum\limits\sf\ fixi \sf\ = 25p + 270 \\ \cline{1-4} \end{tabular}\end{lgathered}$

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☯ $\sf {\underline{\purple{Mean\;of\;the\;data\;is\;givEn\;by,}}}$

$\maltese\;{\underline{\boxed{\sf{\pink{ \overline{x} = \dfrac{\sum fixi}{\sum fi}}}}}}$

$:\implies\sf 24 = \dfrac{25p + 270}{p + 12}$

☯ $\sf {\underline{\purple{Cross\;-\; Multiplication\;-}}}$

$:\implies\sf 24(p + 12) = 25p + 270$

$:\implies\sf 24p + 288 = 25p + 270$

$:\implies\sf 24p - 25p = 270 - 288$

$:\implies\sf - p = - 18$

$:\implies\sf \blue{p = 18}$ ★

$\dag\;\sf \underline{Hence,\;value\;of\;p\;is\;18.}$

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Answer 2

${\huge{\bf{\green{\mathfrak{\boxed{\boxed{Heya}}}}}}}$

The value of p is 20.

Explanation:

Given : The mean of the data is 24.

To find : The value of p?

Solution :

The data can be arranged as,

Class Intervals⠀ Frequency (f) ⠀Class Marks (x)

0-10 ⠀ ⠀⠀⠀ 15 ⠀ ⠀⠀ ⠀5 ⠀⠀⠀⠀⠀⠀75

10-20 ⠀ ⠀ ⠀⠀ 20 ⠀⠀⠀ 15 ⠀⠀⠀⠀⠀⠀300

20-30 ⠀⠀⠀ ⠀ 35 ⠀ ⠀⠀ 25 ⠀⠀⠀⠀⠀⠀875

30-40 ⠀⠀⠀⠀⠀ p ⠀ ⠀⠀ ⠀35 ⠀⠀⠀⠀⠀35p

40-50 ⠀ ⠀⠀ ⠀ 10 ⠀ ⠀ ⠀ 45 ⠀⠀⠀⠀⠀⠀450

Total

The mean of the data is given by,

Therefore, the value of p is 20.

Thanks❤️