Interpreting Percentiles In Exercises 29–32, use the ogive, which represents the cumulative frequency distribution for quantitative reasoning scores on the Graduate Record Examination in a recent range of years. (Adapted from Educational Testing Service)

What percentile is a score of 170? How should you interpret this?

In Exercises 17–19, use the data set, which represents the points recorded by each player on the Winnipeg Jets in the 2019–2020 NHL season. (Source: National Hockey League)

8 8 8 6 0 73 26 1

0 5 58 1 7 5 10 63

0 5 10 0 31 5 15 45

16 29 10 73 5 3 0 65

Construct a frequency distribution for the data set using eight classes. Include class limits, midpoints, boundaries, frequencies, relative frequencies, and cumulative frequencies.

Construct a frequency distribution for the data set using the indicated number of classes. In the table, include the midpoints, relative frequencies, and cumulative frequencies. Which class has the greatest class frequency and which has the least class frequency.

Textbook Spending

Number of classes: 6

Data set: Amounts (in dollars) spent on textbooks for a semester 91 472 279 249 530 376 188 341 266 199 142 273 189 130 489 266 248 101 375 486 190 398 188 269 43 30 127 354 84 319

Construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe any patterns.

Reaction Times

Number of classes: 8

Data set: Reaction times (in milliseconds) of 30 adult females to an auditory stimulus 507 389 305 291 336 310 514 442 373 428 387 454 323 441 388 426 411 382 320 450 309 416 359 388 307 337 469 351 422 413

Matching In Exercises 13–16, match the distribution with one of the graphs in Exercises 9–12. Justify your decision.

The frequency distribution of mileages of service vehicles at a business where a few vehicles have much higher mileages than the majority of vehicles

The data set represents the number of minutes a sample of 27 people exercise each week.

108 139 120 123 120 132 123 131 131

157 150 124 111 101 135 119 116 117

127 128 139 119 118 114 127 142 130

a. Construct a frequency distribution for the data set using five classes. Include class limits, midpoints, boundaries, frequencies, relative frequencies, and cumulative frequencies.

What Would You Do? You work at a bank and are asked to recommend the amount of cash to put in an ATM each day. You do not want to put in too much (which would cause security concerns) or too little (which may create customer irritation). The daily withdrawals (in hundreds of dollars) for 30 days are listed. 72 84 61 76 104 76 86 92 80 88 98 76 97 82 84 67 70 81 82 89 74 73 86 81 85 78 82 80 91 83

Construct a relative frequency histogram for the data. Use 8 classes.

Construct a cumulative frequency distribution and an ogive for the data set using six classes. Then describe the location of the greatest increase in frequency.

Retirement Ages

Data set: Retirement ages of 35 English professors 72 62 55 61 53 62 65 66 69 55 66 63 67 69 55 65 67 57 67 68 73 75 65 54 71 57 52 58 58 71 72 67 63 65 61

Constructing a Frequency Distribution and a Relative Frequency Histogram In Exercises 37–40, construct a frequency distribution and a relative frequency histogram for the data set using five classes. Which class has the greatest relative frequency and which has the least relative frequency?

Taste Test

Data set: Ratings from 1 (lowest) to 10 (highest) provided by 36 people after taste-testing a new flavor of protein bar 2 6 9 2 9 9 6 10 5 8 7 6 5 10 1 4 9 3 4 5 3 6 5 2 4 9 2 9 3 3 6 5 1 9 4 2