Question

The local 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).

118, 124, 108, 116, 99, 125, 138, 118, 119, 121, 65, 130, 120

(1) What is the 90th percentile?

(2) What is the third quartile?

(3) What is the first quartile?

(4) What is the 10th percentile?

(5) What is the 65th percentile?

(6) What is the IQR?

(7) What are the lower and upper limits?

Answer 1

Kindly check explanation

Explanation:

Given the data:

118, 124, 108, 116, 99, 125, 138, 118, 119, 121, 65, 130, 120

Ordered data:

65, 99, 108, 116, 118, 118, 119, 120, 121, 124, 125, 130, 138

1.)

90th percentile :

0.9(n + 1)th term

n = sample size = 13

0.9(14) th term

= 12.6th term

= (12 + 13)th / 2

= (130 + 138) / 2

= 134

Third quartile (Q3) = 75th percentile

0.75(n + 1)th term

n = sample size = 13

0.75(14) th term

= 10.5th term

= (10 + 11)th / 2

= (124 + 125) / 2

= 124.5

What is the first quartile?

First quartile (Q1) :

0.25(n + 1)th term

n = sample size = 13

0.25(14) th term

= 3.5th term

= (3 + 4)th / 2

= (108 + 116) / 2

= 112

(4) What is the 10th percentile?

0.1(n + 1)th term

n = sample size = 13

0.1(14) th term

= 1.4th term

= (1 + 2)th / 2

= (65 + 99) / 2

= 82

(5) 65tb percentile :

0.65(n + 1)th term

n = sample size = 13

0.65(14) th term

= 9.1th term

= (9 + 10)th / 2

= (121 + 124) / 2)

= 122.5

(6) What is the IQR?

Q3 - Q1

124.5 - 112

= 12.5

(7) What are the lower and upper limits?

Maximum = 138

Minimum = 65