Question

For the data set below, which value is in the 75th percentile?
$1,3,3,4,6,7,7,7,8,9,9,10,12,15,16,17$

• A. 16
• B. 9
• C. 12
• D. 15

Answer 1

Answer: (C)

12

$1,3,3,4,6,7,7,7,8,9,9,10,12,15,16,17$

Logic:- first quartile lies halfway between the lowest valve of the Median & the third Quartile lies halfway between the Median & the largest value.

$N=16$

Third quartile or $75$ percentile

$=\frac{3(n+1)}{4}$th term

$=\frac{3\times 17}{4}={12.75}^{th}$ term

$={12}^{th}$ term $+0.75\times ({13}^{th}$ term$-{12}^{th}$ term$)$

$=10+0.75\times (12-10)$

$=10+0.75\times 2$

$=11.5\approx 12$.