Question:
Median of the following frequency distribution is
Median of the following frequency distribution is
Show Hint
For grouped data,
\[
\boxed{
\text{Median}
=
l+\frac{\left(\dfrac{N}{2}-cf\right)}{f}\times h
}
\]
where \(cf\) is the cumulative frequency preceding the median class.
Updated On: Jul 15, 2026
- \(32\)
- \(33\)
- \(34\)
- \(35\)
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The Correct Option is C
Solution and Explanation
Step 1: Find the total frequency.
\[
N=8+13+10+7+12=50.
\]
Hence,
\[
\frac{N}{2}=25.
\]
Step 2: Locate the median class. The cumulative frequencies are \[ \begin{array}{|c|c|} \hline \text{Class} & \text{Cumulative frequency} \hline 10-20 & 8 20-30 & 21 30-40 & 31 40-50 & 38 50-60 & 50 \hline \end{array} \] Since \(25\) lies in the class \(30-40\), \[ l=30,\quad h=10,\quad f=10,\quad cf=21. \]
Step 3: Apply the median formula. \[ \text{Median} = l+\frac{\left(\frac{N}{2}-cf\right)}{f}\times h \] \[ = 30+\frac{25-21}{10}\times10 \] \[ =30+4=34. \]
Step 4: Final conclusion. \[ \boxed{34} \] Hence, the correct option is \(\boxed{(C)}\).
Step 2: Locate the median class. The cumulative frequencies are \[ \begin{array}{|c|c|} \hline \text{Class} & \text{Cumulative frequency} \hline 10-20 & 8 20-30 & 21 30-40 & 31 40-50 & 38 50-60 & 50 \hline \end{array} \] Since \(25\) lies in the class \(30-40\), \[ l=30,\quad h=10,\quad f=10,\quad cf=21. \]
Step 3: Apply the median formula. \[ \text{Median} = l+\frac{\left(\frac{N}{2}-cf\right)}{f}\times h \] \[ = 30+\frac{25-21}{10}\times10 \] \[ =30+4=34. \]
Step 4: Final conclusion. \[ \boxed{34} \] Hence, the correct option is \(\boxed{(C)}\).
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