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Question

# A, B, C are three sets of values as given below: A : 2, 3, 7, 1, 3, 2, 3 B : 7, 5, 9, 12, 5, 3, 8 C : 4, 4, 11, 7, 2, 3, 4 Which one of the following statements is correct?

A
Median of C = Mode of C
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B
Mean of C = Median of B
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C
Mean of A = Mode of C
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D
Median of B = Mode of A
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Solution

## The correct option is A Median of C = Mode of CWe know that, Mean=Sum of observationsNumber of observations Mean ofA=2+3+7+1+3+2+37=217=3 Mean ofB=7+5+9+12+5+3+87=497=7 Mean ofC=4+4+11+7+2+3+47=357=5 For Median, sorting A in ascending order, A : 1, 2, 2, 3, 3, 3, 7 Number of terms, n = 7 (Odd number of observations) ∴ Median = 4th observation which is 3. Now, sorting B in ascending order, B : 3, 5, 5, 7, 8, 9, 12 Number of terms, n = 7 (Odd number of observations) ∴ Median = 4th observation which is 7. Similarly, sorting C in ascending order, Number of terms, n = 7 (Odd number of observations) C : 2, 3, 4, 4, 4, 7,11 ∴ Median = 4th observation which is 4. The mode of a data set is the number that occurs most frequently. So, mode of A = 3 mode of B = 5 and mode of C = 4.

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