Question

The medians for the first 7 odd natural numbers (1, 3, 5, 7, 9, 11, 13) and the first 6 odd natural numbers (1, 3, 5, 7, 9, 11) respectively are _____ .

• A.
  7, 6
• B.
  6, 7
• C.
  7, 7
• D.
  7, 5

Answer 1

The correct option is A

7, 6

For both the sets of numbers, the numbers are in ascending order. If number of observations (n) is odd, the median is is ${\frac{(n+1)}{2}}^{th}$ term. If number of numbers n is even, the median will be average of ($\frac{n}{2}$)${}^{th}$ and ($\frac{n}{2}+1$)${}^{th}$ term.

In the first set of numbers, the number of terms is 7. Using above formula, the median term is $4^{th}$ term, which is 7.
In the $2^{nd}$ set of numbers, the median is the average of $3^{rd}$ and $4^{th}$ terms. These are 5 and 7. The average of 5 and 7 is 6.

For $1^{st}$ set, median = 7.

For $2^{nd}$ set, median = 6.