Question:
The scores of a batsman in 10 different test matches were 42, 38, 48, 70, 46, 63, 55, 34, 54, and 44. What is the mean deviation about the median of these scores?
The scores of a batsman in 10 different test matches were 42, 38, 48, 70, 46, 63, 55, 34, 54, and 44. What is the mean deviation about the median of these scores?
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To calculate the mean deviation, first find the median and then calculate the absolute difference between each number and the median. Finally, find the average of these differences.
Updated On: Apr 17, 2025
- 6.5
- 6.8
- 8.6
- 9.4
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The Correct Option is B
Solution and Explanation
First, arrange the scores in ascending order:
34, 38, 42, 44, 46, 48, 54, 55, 63, 70.
The median of these 10 numbers is the average of the 5th and 6th numbers:
\[
\text{Median} = \frac{46 + 48}{2} = 47
\]
Now, calculate the mean deviation:
\[
\text{Mean deviation} = \frac{|34 - 47| + |38 - 47| + |42 - 47| + |44 - 47| + |46 - 47| + |48 - 47| + |54 - 47| + |55 - 47| + |63 - 47| + |70 - 47|}{10}
\]
The total is \( 68 \), so the mean deviation is \( \frac{68}{10} = 6.8 \).
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