Your Question:

The following data give the weights (in pounds) lost by 15 members of a health club at the end of two months after joining the club.

5 10 8

21 9 8

7 25 12 5 15 11 10

11 13

(a) Calculate the approximate value of the 82nd percentile, denoted P82.

P82=

(b) Find the percentile rank of 8.

Give the answer rounded to the nearest percent.

The percentile rank of 8 = i

%.

Step By Step Answers with Explanation

(a) Calculate the approximate value of the 82nd percentile, denoted P82:

To calculate the 82nd percentile (P82), you'll first need to arrange the data in ascending order. Once the data is sorted, you can find the position of the 82nd percentile and interpolate to find its approximate value.

Where N is the total number of data points, which is 15 in this case.

P82 position = (82 / 100) (15 + 1)

P82 ≈ Value at the 13th data point + (Fractional part of the position Difference between the values at the 14th and 13th data points)

P82 ≈ 15 + (0.12 (21 - 15))

(b) Find the percentile rank of 8:

To find the percentile rank of 8, you need to determine the percentage of data points that are less than or equal to 8.

Percentile Rank = (6 / 15) 100

Percentile Rank = (2/5) 100