QJEEM23Ma9a0e: JEE Main 2023 Mathematics - Class 11 JEEM23Ma9a0e Solution: If the mean of the frequency distribution .tg…

Question

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If the mean of the frequency distribution

Class :	0-10	10-20	20-30	30-40	40-50
Frequency :	2	3	$x$	5	4

is 28, then its variance is __________.

Accepted Answer

Given mean is 28

\begin{array}{ll}\text { So, } \frac{2 \times 5+3 \times 15+x \times 25+5 \times 35+4 \times 45}{14+x}=28 \\\\\Rightarrow \frac{10+45+25 x+175+180}{14+x}=28 \\\\\Rightarrow 310+25 x=392+28 x \\\\\Rightarrow 3 x=18 \Rightarrow x=6\end{array}

\begin{aligned}&amp; \therefore \text { Variance }=\left(\frac{\sum x_i^2 f_i}{\sum f_i}\right)-(\text { mean })^2 \\\\&amp; =\left(\frac{2 \times 5^2+3 \times 15^2+6 \times 25^2+5 \times 35^2+4 \times 45^2}{20}\right)-(28)^2 \\\\&amp; =\left(\frac{50+675+3750+6125+8100}{20}\right)-(28)^2 \\\\&amp; =\left(\frac{18700}{20}\right)-(28)^2 \\\\&amp; =935-784=151\end{aligned}

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