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The following distribution shows the weekly pocket allowance (in $\text{Rs}$) of some children of a locality. The mean pocket allowance is ₹180. Find the value of $f$. Hence find the mode of given data.
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Correct Table: [$1\frac{1}{2}$ marks]
$\text{Mean} = \frac{\sum x_i f_i}{\sum f_i}$
$180 = \frac{7520 + 200f}{44 + f}$ [$1$ mark]
$f = 20$ [$\frac{1}{2}$ mark]
$\text{Mode} = 190 + \frac{20 - 13}{2(20) - 13 - 5} \times 20$ [$1\frac{1}{2}$ marks]
$= 196.36$ [$\frac{1}{2}$ mark]
$\text{Mean} = \frac{\sum x_i f_i}{\sum f_i}$
$180 = \frac{7520 + 200f}{44 + f}$ [$1$ mark]
$f = 20$ [$\frac{1}{2}$ mark]
$\text{Mode} = 190 + \frac{20 - 13}{2(20) - 13 - 5} \times 20$ [$1\frac{1}{2}$ marks]
$= 196.36$ [$\frac{1}{2}$ mark]