You are given the data set {14, 35, 44, 47, 49, 49, 50, 51, 56, N}, where N is an integer not necessarily greater than 56. What is the value of N?

(1) The mean of the data set is 44.3

(2) The median of the data set is 48.5
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Solution

Given:

• A data set {14, 35, 44, 47, 49, 49, 50, 51, 56, N}, where N is an integer

To find:

• The value of N

Analysing Statement 1
“The mean of the data set is 44.3”

• Mean of the set = \(\frac{(14 + 35 + 44 + 47 + 49 + 49 + 50 + 51 + 56 + N)}{10} = 44.3\)

o Implies, N = 443 – (14 + 35 + 44 + 47 + 49 + 49 + 50 + 51 + 56)

• Thus, we can find a unique value of N.

Therefore, statement 1 is sufficient

Analysing Statement 2
“The median of the set is 48.5”

• The median of the given set = \(\frac{(5^{th} term + 6^{th} term)}{2}\)
• One of the middle terms = 49, for any value of N
• Thus, \(48.5 = \frac{(49 + x)}{2}\)

o Implies, x = 48
o Since, there is no 48 in the set, the value of N must be 48

Therefore, statement 2 is sufficient

Hence, the correct answer is Option D.

Answer: D


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