Answer to Question #350881 in Statistics and Probability for jordan

Question

Use the following cell phone airport data speeds​ (Mbps) from a particular network. Find P80.

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.5

0.6

0.7

0.8

0.8

0.9

0.9

0.9

1.1

1.1

1.3

1.3

1.4

2.1

2.3

2.5

2.7

2.7

2.9

3.2

3.8

4.5

5.4

5.8

7.5

8.3

8.5

8.8

9.5

9.6

9.6

9.7

10.2

10.4

12.9

13.5

14.3

15.6

15.6

15.6

15.7

25.8

Answer 1

The data are in ascending order.

Compute the position of the p^th percentile (index $i$ ):

$$i=\dfrac{p}{100}\times n=\dfrac{80}{100}\times50=40$$

The index $i$  is an integer ⇒ the 80^th percentile is the average of the values in the 40^th and 41^th positions (9.7 and 10.2 respectively)

Answer: the 80^th percentile is (9.7+10.2) / 2 = 9.95