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Question

Median of an even-numbered non-negative data set is 3. Determine the number of sets of values for the two central values of the data set when the data set is arranged in ascending order.

A
Zero
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B
Three
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C
Four
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D
Seven
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Solution

The correct option is C FourConsider a even number data set {a,b,c,d} such that a≤b≤c≤d. Median = Average of second and third data points ⇒ Median =b+c2 ⇒3=b+c2 ⇒b+c=6 We know, 6=0+6 6=1+5 6=2+4 6=3+3 6=4+2 and so on. However, c cannot be less than b, i.e., 3. ∴b+c=6=0+6⇒b=0,c=6 or, b+c=6=1+5⇒b=1,c=5 or, b+c=6=2+4⇒b=2,c=4 or, b+c=6=3+3⇒b=3,c=3 Hence, the possible pairs of two central values are {0,6},{1,5},{2,4} and {3,3}. ∴ There are four possible pairs.

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