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Question: The distance (in miles) run by 8 athletes per day are given. Find the value that corresponds to the 40th percentile.
4.2, 5.8, 4.5, 5.1, 3.8, 4.6, 3.2, 5.4, 4.3, 4.4


A ) 4.2 miles
B ) 3.8 miles
C ) 4.55 miles
D ) 4.35 miles

Steps to derive

1 Write the distances run by athletes in increasing order.
3.2, 3.8, 4.2, 4.3, 4.4, 4.5, 4.6, 5.1, 5.4, 5.8

2 To determine the distance corresponding to the 40th percentile, compute c = n.p100, where n is the number of athletes, p the percentile.

3 c = 10×40100 = 4, which is a whole number.

4 So, the distance in miles corresponding to the 40th percentile is mean of 4th and 5th distances in the order; which is 4.3+4.42 = 4.35.

5 So, 4.35 miles corresponds to the 40th percentile.



Hence the right answer is Option D

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