2.5 Measure of Position

Use the data to identify any outliers. 16 27 1 32 15 5 18 9 20 14 17 19 16 10 21 28 14 36 18

1, 32, 36

The cholesterol levels (in milligrams per deciliter) of 30 adults are listed below. Find Q1. 154 156 165 165 170 171 172 180 184 185 189 189 190 192 195 198 198 200 200 200 205 205 211 215 220 220 225 238 255 265

180

In a data set with a minimum value of 54.5 and a maximum value of 98.6 with 300 observations, there are 186 points less than 81.2. Find the percentile for 81.2.

62

The test scores of 30 students are listed below. Which test scores are above the 75th percentile? 31 41 45 48 52 55 56 58 63 65 67 67 69 70 70 74 75 78 79 79 80 81 83 85 5 87 90 92 95 99

85, 85, 87, 90, 92, 95, 99

The cholesterol levels (in milligrams per deciliter) of 30 adults are listed below. Find the percentile that corresponds to a cholesterol level of 238 milligrams per deciliter. 154 156 165 165 170 171 172 180 184 185 189 189 190 192 195 198 198 200 200 200 205 205 211 215 220 220 225 238 255 265

90th percentile

The weights (in pounds) of 30 preschool children are listed below. Find the five-number summary. 25 25 26 26.5 27 27 27.5 28 28 28.5 29 29 30 30 30.5 31 31 32 32.5 32.5 33 33 34 34.5 35 35 37 37 38 38

Min = 25, Q1 = 28, Q2 = 30.75, Q3 = 34, Max = 38

Find the z-score for the value 79, when the mean is 55 and the standard deviation is 5

z = 4.80

The weights (in pounds) of 30 preschool children are listed below. Which weights are below the 25th percentile? 25 25 26 26.5 27 27 27.5 28 28 28.5 29 29 30 30 30.5 31 31 32 32.5 32.5 33 33 34 34.5 35 35 37 37 38 38

25, 25, 26, 26.5, 27, 27, 27.5

The cholesterol levels (in milligrams per deciliter) of 30 adults are listed below. Find the interquartile range for the cholesterol level of the 30 adults. 154 156 165 165 170 171 172 180 184 185 189 189 190 192 195 198 198 200 200 200 205 205 211 215 220 220 225 238 255 265

31

The ages of 10 grooms at their first marriage are listed below. Find the midquartile. 35.1 24.3 46.6 41.6 32.9 26.8 39.8 21.5 45.7 33.9

34.2

The birth weights for twins are normally distributed with a mean of 2353 grams and a standard deviation of 647 grams. Use z-scores to determine which birth weight could be considered unusual.

3647 g

Use the data to identify any outliers. 38 43 55 65 66 68 70 73 74 76 80 82 87 90 99

38, 43

A teacher gives a 20-point quiz to 10 students. The scores are listed below. What percentile corresponds to the score of 12? 20 8 10 7 15 16 12 19 14 9

40

Use the data to identify any outliers. 15 18 18 19 22 23 24 24 24 24 25 26 26 27 28 28 30 32 33 40 42

40, 42

The cholesterol levels (in milligrams per deciliter) of 30 adults are listed below. Find the percentile that corresponds to cholesterol level of 195. 154 156 165 165 170 171 172 180 184 185 189 189 190 192 195 198 198 200 200 200 205 205 211 215 220 220 225 238 255 265

50

The test scores of 30 students are listed below. Find the percentile that corresponds to a score of 74. 31 41 45 48 52 55 56 58 63 65 67 67 69 70 70 74 75 78 79 79 80 81 83 85 5 87 90 92 95 99

50th percentile

The test scores of 30 students are listed below. Find the five-number summary. 31 41 45 48 52 55 56 58 63 65 67 67 69 70 70 74 75 78 79 79 80 81 83 85 5 87 90 92 95 99

Min = 31, Q1 = 58, Q2 = 72, Q3 = 83, Max = 99

Use the box-and-whisker plot below to determine which statement is accurate.

One half of the cholesterol levels are between 180 and 211.

For the mathematics part of the SAT the mean is 514 with a standard deviation of 113, and for the mathematics part of the ACT the mean is 20.6 with a standard deviation of 5.1. Bob scores a 660 on the SAT and a 27 on the ACT. Use z-scores to determine on which test he performed better.

SAT

Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 75 and 2, respectively, and the distribution of scores is bell-shaped and symmetric. Suppose the trainee in question received a score of 68. Compute the trainee's z-score.

z = -3.50

A radio station claims that the amount of advertising per hour of broadcast time has an average of 12 minutes and a standard deviation equal to 1.2 minutes. You listen to the radio station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 15 minutes. Calculate the z-score for this amount of advertising time.

z = 2.50