Multiple choice

The runs scored by Virat in 7 different matches are given as: $89,91,54,66,13,97,06$ Calculate the mean deviation about the median for this data.

  1. $31.26$
  2. $30.06$
  3. $29.142$
  4. $27.85$
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C Correct answer
Explanation

Data: 06, 13, 54, 66, 89, 91, 97. Median is 66. Deviations from 66: |6-66|=60, |13-66|=53, |54-66|=12, |66-66|=0, |89-66|=23, |91-66|=25, |97-66|=31. Sum = 204. Mean deviation = 204/7 = 29.142.

AI explanation

Arranging the runs in ascending order gives 6, 13, 54, 66, 89, 91, 97, making the median 66. The mean deviation about the median is found by taking the sum of the absolute differences between each observation and the median, then dividing by the number of observations. The absolute deviations are 60, 23, 12, 0, 23, 25, and 31, which sum to 204. Dividing this sum by 7 gives a mean deviation of 29.142.

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