Find the median of the data 11, 16, 33, 15, 51, 18, 71, 75, 22, 17.

Correct option is C

Given:

The data set is: 11, 16, 33, 15, 51, 18, 71, 75, 22, 17.

Formula Used:

If n is odd:

Median = $$\text{Value at position}\frac{n+1}{2}$$​​

If n is even:

Median = $$\frac{\text{Value at position}\frac{n}{2}+ \text{Value at position}(\frac{n}{2}+1)}{2}$$​​

Solution:

Arranging the data in ascending order:

11,15,16,17,18,22,33,51,71,75

So, n = 10 (even)

Since n is even,​​

Median = $$\frac{\text{Value at position}\frac{10}{2}+ \text{Value at position}(\frac{10}{2}+1)}{2}$$​​

Median = $$\frac{\text{Value at position 5th place} + \text{Value at position 6th place}}{2}$$​​

Median = $$\frac{18+22}{2} = \frac{40}{2} = 20$$​​

Thus, The median of the data set is 20.