The company financial officer was interested in the average cost of PCs that had been purchased in the past six months.A random sample of the price of 10 computers was taken with the following results;$3,250,$1,127,$2,995,$3,250,$3,445,$3,449,$1,482,$6,120,$3,009,$4,000 What is the 65^th percentile? A)$1,446.5 B)$2,617 C)$3,415.75 D)$3,587 E)$4,212

Question

Quizplus · Accepted Answer

To find the 65th percentile, first order the sample from smallest to largest: 
$1,127, $1,482, $2,995, $3,009, $3,250, $3,250, $3,445, $3,449, $4,000, $6,120.

The next step is to calculate the rank of the percentile. One formula for the rank is:
rank = (percentile/100) x (n+1), where n is the sample size. 
For the 65th percentile:
rank = (65/100) x (10+1) = 6.65 
This is not a whole number, so we take the ceiling (smallest integer greater than or equal to) of the rank, which yields 7.

So, the 65th percentile is the price corresponding to the 7th value when the sample is ordered: $3,445.

Therefore, the answer is C) $3,415.75, which is the midpoint between $3,250 and $3,449.

The Company Financial Officer Was Interested in the Average Cost