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13.Statistics
hard
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
Similar Questions
If the variance of the frequency distribution is $160$ , then the value of $\mathrm{c} \in \mathrm{N}$ is
| $X$ | $c$ | $2c$ | $3c$ | $4c$ | $5c$ | $6c$ |
| $f$ | $2$ | $1$ | $1$ | $1$ | $1$ | $1$ |
