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The median of 100 observations grouped in classes of equal width is 25 . If the median class interval is 20-30 and the number of observations less than 20 is 45 , then the frequency of median class is
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Verified Answer
The correct answer is:
10
10
Median is given as
$$
M=l+\frac{\frac{N}{2}-F}{f} \times C
$$
where
$l=$ lower limit of the median - class
$f=$ frequency of the median class
$N=$ total frequency
$F=$ cumulative frequency of the class just before the median class
$C=$ length of median class
Now, given, $M=25, N=100, F=45$, $C=20-30=10, l=20$.
$\therefore$ By using formula, we have
$$
\begin{aligned}
& 25=20+\frac{50-45}{f} \times 10 \\
& 25-20=\frac{50}{f} \Rightarrow 5=\frac{50}{f} \Rightarrow f=10
\end{aligned}
$$
$$
M=l+\frac{\frac{N}{2}-F}{f} \times C
$$
where
$l=$ lower limit of the median - class
$f=$ frequency of the median class
$N=$ total frequency
$F=$ cumulative frequency of the class just before the median class
$C=$ length of median class
Now, given, $M=25, N=100, F=45$, $C=20-30=10, l=20$.
$\therefore$ By using formula, we have
$$
\begin{aligned}
& 25=20+\frac{50-45}{f} \times 10 \\
& 25-20=\frac{50}{f} \Rightarrow 5=\frac{50}{f} \Rightarrow f=10
\end{aligned}
$$
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