The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2, 3, 5, 10, 11, 13, 15, 21, then the mean deviation about the median of all the 10 observations is

Options:

1. 7

2. 5

3. 4

4. 6

Correct Answer: 5

Explanation

Step 1:

Mean of 10 observations = 9 ⇒ Sum of all observations = 10 × 9 = 90

Step 2:

Sum of given 8 observations = 2 + 3 + 5 + 10 + 11 + 13 + 15 + 21 = 80

Step 3:

Sum of remaining 2 observations = 90 − 80 = 10 Let them be x and y ⇒ x + y = 10

Step 4:

Arrange observations in ascending order. Median = average of 5th and 6th terms = (10 + 11)/2 = 10.5

Step 5:

Find mean deviation about median:

|2−10.5| + |3−10.5| + |5−10.5| + |10−10.5| + |11−10.5| + |13−10.5| + |15−10.5| + |21−10.5| = 45

Mean deviation = 45 ÷ 9 = 5

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