Question

An amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes; mean = 114.15)

118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118

What is the 65th percentile?

What is the 90th percentile?

What do these mean?

Answer 1

The data is rearranged as

45,99,108,116,1 18,118,118,119,120,121,124,130,148

According to question the 65th percentile can be found by

Let total no are 13 and

65th percentile is 0.65×13=8.45 hence we choose the closest integer as 8th no hence choosing from the left from min to maxmum 8th is 119 hence 119 is the 65th percentile .

Again similarly

For 90th percentile

0.90×13= 11.7 hence selecting 12th no as 90th percentile hence we get 130 as the 90th percentile.

The percentile means that lets say in tgetgetabove question 90th percentile it explains that 90 % of data is below the 130 value in the data set . Hence if we say kth percentile we are saying that k % of data fall behind the number that lies on kth percentile