Question:
The mean deviation about the mean for the following data is
\[
\begin{array}{c|cccc}
x_i & 1 & 2 & 4 & 7\\
\hline
f_i & 3 & 2 & 4 & 1
\end{array}
\]
The mean deviation about the mean for the following data is
\[
\begin{array}{c|cccc}
x_i & 1 & 2 & 4 & 7\\
\hline
f_i & 3 & 2 & 4 & 1
\end{array}
\]
Show Hint
First find the mean, then multiply each absolute deviation by its frequency.
Updated On: Jun 3, 2026
- $3$
- $2$
- $1.5$
- $1.6$
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Concept
Mean deviation about mean is \[ \frac{\sum f_i|x_i-\bar x|}{\sum f_i}. \]
Step 2: Meaning
Compute the mean: \[ \bar x=\frac{1(3)+2(2)+4(4)+7(1)}{3+2+4+1} =\frac{30}{10}=3. \]
Step 3: Analysis
Then \[ \sum f_i|x_i-\bar x| = 3|1-3|+2|2-3|+4|4-3|+1|7-3|. \] \[ =3(2)+2(1)+4(1)+1(4) =16. \] Therefore \[ \text{M.D.} = \frac{16}{10} = 1.6. \]
Step 4: Conclusion
Hence the mean deviation about the mean is $1.6$.
Final Answer: (D)
Mean deviation about mean is \[ \frac{\sum f_i|x_i-\bar x|}{\sum f_i}. \]
Step 2: Meaning
Compute the mean: \[ \bar x=\frac{1(3)+2(2)+4(4)+7(1)}{3+2+4+1} =\frac{30}{10}=3. \]
Step 3: Analysis
Then \[ \sum f_i|x_i-\bar x| = 3|1-3|+2|2-3|+4|4-3|+1|7-3|. \] \[ =3(2)+2(1)+4(1)+1(4) =16. \] Therefore \[ \text{M.D.} = \frac{16}{10} = 1.6. \]
Step 4: Conclusion
Hence the mean deviation about the mean is $1.6$.
Final Answer: (D)
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