Question:
Find the median of the following frequency distribution.
Find the median of the following frequency distribution.
Show Hint
Always locate the median class using cumulative frequencies before applying the median formula.
Updated On: Jun 15, 2026
- \(14\frac{1}{4}\)
- \(15\frac{3}{4}\)
- \(16\frac{2}{3}\)
- \(17\frac{1}{3}\)
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The Correct Option is C
Solution and Explanation
Step 1: Find total frequency. \[ N=5+8+10+12+9+6=50 \] \[ \frac{N}{2}=25 \]
Step 2: Prepare cumulative frequencies. \[ 5,\;13,\;23,\;35,\;44,\;50 \] The first cumulative frequency exceeding 25 is 35. Hence median class is \[ 16-20 \] Thus, \[ l=16,\quad h=4,\quad f=12,\quad c_f=23 \]
Step 3: Apply median formula. \[ \text{Median} = l+\frac{\frac N2-c_f}{f}\times h \] \[ =16+\frac{25-23}{12}\times4 \] \[ =16+\frac{8}{12} \] \[ =16+\frac23 \] \[ =16\frac23 \] \(16\frac23\)
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