Question:
The mean deviation from the median for the following data is:
The mean deviation from the median for the following data is:
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Mean deviation about median is calculated using \(\frac{\sum f|x-M|}{N}\), where \(M\) is the median.
Updated On: Jun 18, 2026
- \(0.75\)
- \(7.5\)
- \(0.65\)
- \(0.40\)
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The Correct Option is A
Solution and Explanation
Step 1: Find the total frequency.
\[ N=6+12+18+12=48 \]
Step 2: Find the median.
The cumulative frequencies are \[ 6,\quad 18,\quad 36,\quad 48. \] Since \[ \frac{N}{2}=\frac{48}{2}=24, \] the \(24^{th}\) observation lies at \(x=12\).
Therefore, \[ \text{Median}=12. \]
Step 3: Find mean deviation about median.
\[ \text{M.D.}=\frac{\sum f|x-M|}{N} \] \[ =\frac{6|10-12|+12|11-12|+18|12-12|+12|13-12|}{48} \] \[ =\frac{6(2)+12(1)+18(0)+12(1)}{48} \] \[ =\frac{12+12+0+12}{48} \] \[ =\frac{36}{48}=0.75. \]
Step 4: Final conclusion.
Therefore, \[ \boxed{0.75} \]
\[ N=6+12+18+12=48 \]
Step 2: Find the median.
The cumulative frequencies are \[ 6,\quad 18,\quad 36,\quad 48. \] Since \[ \frac{N}{2}=\frac{48}{2}=24, \] the \(24^{th}\) observation lies at \(x=12\).
Therefore, \[ \text{Median}=12. \]
Step 3: Find mean deviation about median.
\[ \text{M.D.}=\frac{\sum f|x-M|}{N} \] \[ =\frac{6|10-12|+12|11-12|+18|12-12|+12|13-12|}{48} \] \[ =\frac{6(2)+12(1)+18(0)+12(1)}{48} \] \[ =\frac{12+12+0+12}{48} \] \[ =\frac{36}{48}=0.75. \]
Step 4: Final conclusion.
Therefore, \[ \boxed{0.75} \]
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