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\begin{array}{|c|c|c|c|c|}
\hline Class Interval & 1-5 & 6-10 & 11-15 & 16-20 \\
\hline Frequency & 3 & 7 & 6 & 5 \\
\hline
\end{array} Consider the following statements in respect of the above frequency distribution.
I. The median is contained in the modal class.
II. The distribution is bell-shaped. Which of the above statements is/are correct?
Options:
\hline Class Interval & 1-5 & 6-10 & 11-15 & 16-20 \\
\hline Frequency & 3 & 7 & 6 & 5 \\
\hline
\end{array} Consider the following statements in respect of the above frequency distribution.
I. The median is contained in the modal class.
II. The distribution is bell-shaped. Which of the above statements is/are correct?
Solution:
2932 Upvotes
Verified Answer
The correct answer is:
Neither I nor II
\begin{array}{|c|c|c|}
\hline Class Interval & \mathrm{f} & cf \\
\hline 0.5-5.5 & 3 & 3 \\
\hline 5.5-10.5 & 7 & 10 \\
\hline 10.5-15.5 & 6 & 16 \\
\hline 15.5-20.5 & 5 & 21 \\
\hline Total & 21 & 50 \\
\hline
\end{array} $N=21$
$\frac{N}{2}=\frac{21}{2}=10.5$
Median class is $10.5-15.5$
Hence, Median $=10.5+\frac{10.5-10}{6} \times 5$
$=10.5+0.417=10.917$
Thus, median is not contained in the modal class and the distribution is not bell-shaped.
\hline Class Interval & \mathrm{f} & cf \\
\hline 0.5-5.5 & 3 & 3 \\
\hline 5.5-10.5 & 7 & 10 \\
\hline 10.5-15.5 & 6 & 16 \\
\hline 15.5-20.5 & 5 & 21 \\
\hline Total & 21 & 50 \\
\hline
\end{array} $N=21$
$\frac{N}{2}=\frac{21}{2}=10.5$
Median class is $10.5-15.5$
Hence, Median $=10.5+\frac{10.5-10}{6} \times 5$
$=10.5+0.417=10.917$
Thus, median is not contained in the modal class and the distribution is not bell-shaped.
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