Question

The waiting times (in minutes) for 11 customers at a supermarket are:

12 9 15 6 4 7 9 11 14 2 6

The first quartile for these data is:

The second quartile for these data is:

The third quartile for these data is:

The approximate value of the 60th percentile for these data is:

The percentile rank for the customer who waited 11 minutes is:

72.72%

80.00%

68.33%

63.64%

Answer 1

The first quartile for these data is 25th percentile:

.The sample size is n = 11 . The provided sample data are shown in the table below:

X
12
9
15
6
4
7
9
11
14
2
6

We need to compute the 25% percentile based on the data provided.

Position	X (Asc. Order)
1	2
2	4
3	6
4	6
5	7
6	9
7	9
8	11
9	12
10	14
11	15

The next step is to compute the position (or rank) of the 25% percentile. The following is obtained:

Since the position found is integer, the 25% percentile corresponds to the value in the position 3^th in the data organized in ascending order, so then looking at the table we find directly that the 25% percentile is 6.

This completes the calculation and we conclude that P_25​=6.

The second quartile for these data is 50th percentile:

We need to compute the 50% percentile based on the data provided.

Position	X (Asc. Order)
1	2
2	4
3	6
4	6
5	7
6	9
7	9
8	11
9	12
10	14
11	15

The next step is to compute the position (or rank) of the 50% percentile. The following is obtained:

Since the position found is integer, the 50% percentile corresponds to the value in the position 6^th in the data organized in ascending order, so then looking at the table we find directly that the 50% percentile is 9.

This completes the calculation and we conclude that P_50​=9

The third quartile for these data is 75th percentile:

We need to compute the 75% percentile based on the data provided.

Position	X (Asc. Order)
1	2
2	4
3	6
4	6
5	7
6	9
7	9
8	11
9	12
10	14
11	15

The next step is to compute the position (or rank) of the 75% percentile. The following is obtained:

Since the position found is integer, the 75% percentile corresponds to the value in the position 9^th in the data organized in ascending order, so then looking at the table we find directly that the 75% percentile is 12.

This completes the calculation and we conclude that P_75​=12

The approximate value of the 60th percentile for these data is:

We need to compute the 60% percentile based on the data provided.

Position	X (Asc. Order)
1	2
2	4
3	6
4	6
5	7
6	9
7	9
8	11
9	12
10	14
11	15

The next step is to compute the position (or rank) of the 60% percentile. The following is obtained:

Since the position found is integer, the 60% percentile corresponds to the value in the position 7^th in the data organized in ascending order, so then looking at the table we find directly that the 60% percentile is 9.

This completes the calculation and we conclude that P_60​=9

The percentile rank for the customer who waited 11 minutes is:

Position	X (Asc. Order)
1	2
2	4
3	6
4	6
5	7
6	9
7	9
8	11
9	12
10	14
11	15

11 lies at 8th value:

Percentile = 8/11 = 0.7272 = 72.72%