Consider the given data with frequency distribution x i 3 8 11 10 5 4 f i 5 2 3 2 4 4 Match each entry in List-I to the correct entries in List-II. List-I List-II P The mean of the above data is 1 2 . 5 Q The median of the above data is 2 5 R The mean deviation about the mean of the above data is 3 6 S The mean deviation about the median of the above data is 4 2 . 7 5 2 . 4 The correct option is
A. P → 3   Q → 2   R → 4   S → 5
Arranging the given data in ascending order we get, x i 3 4 5 8 10 11 f i 5 4 4 2 2 3 Now finding the mean of the above data we get, Mean = 3 × 5 + 8 × 2 + 11 × 3 + 10 × 2 + 5 × 4 + 4 × 4 5 + 2 + 3 + 2 + 4 + 4 = 15 + 16 + 33 + 20 + 20 + 16 20 = 120 20 = 6 Now, median = 1 2 10 th + 11 th   observation = 1 2 5 + 5 = 5 Hence, Mean deviation about mean will be, = 3 × 5 + 2 × 4 + 1 × 4 + 2 × 2 + 4 × 2 + 5 × 3 20 = 54 20 = 2 . 7 And Mean deviation about median = 2 × 5 + 1 × 4 + 0 + 3 × 2 + 5 × 2 + 6 × 3 20 = 4 . 8 20 = 2 . 4 P → 3 ;   Q → 2 ;   R → 4 ;   S → 5 ∴ Option A is correct.
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