If mean of frequency distribution Class: 0-10 10-20 20-30 30-40 40-50 Frequency 2 3 x 5 4 is 28 , th

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13.Statistics

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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 $........$.

A

$150$

B

$152$

C

$153$

D

$151$

(JEE MAIN-2023)

Solution

Given mean is $=28$

$\frac{2 \times 5+3 \times 15+x \times 25+5 \times 35+4 \times 45}{14+x}=28$

$x =6$

$\text { Variance }=\left(\frac{\sum x_i^2 f_i}{\sum f_i}\right)-(\text { mean })^2$

$\text { Variance }==\frac{2 \times 5^2+3 \times 15^2+6 \times 25^2+5 \times 35^2+4 \times 45^2}{20}-(28)^2$

$=151$

Standard 11

Mathematics

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