Question

2. Consider the data set 8.5 8.2 7.0 7.0 4.9 9.6 8.5 8.8 8.5 8.7 6.5 8.2 7.6 1.5 9.3 8.0 7.7 2.9 9.2 6.9 a. Find the percentile rank of 6.5 b. Find the percentile rank of 7.7.

Answer 1

the data needs to be organized into ascending order

Position	X (Asc. Order)
1	1.5
2	2.9
3	4.9
4	6.5
5	6.9
6	7.0
7	7.0
8	7.6
9	7.7
10	8.0
11	8.2
12	8.2
13	8.5
14	8.5
15	8.5
16	8.7
17	8.8
18	9.2
19	9.3
20	9.6

(a)For percentile rank of X=6.5,

Let k be the number of values in the dataset that are less than X=6.5. Here k=3.

So Percentile Rank =k / n​

=3 / 20​ = 0.15 =15%

(b)

For percentile rank of X=7.7,

Let k be the number of values in the dataset that are less than X=7.7. Here k=8.

So Percentile Rank =k / n​

=8 / 20​ = 0.4 =40%