Exam 3: Displaying and Summarizing Quantitative Data

Here are the average mathematics achievement scores for ninth graders in 34 counties.Find the standard deviation. 595 588 587 586 582 580 561 555 551 548 542 540 538 537 534 532 524 523 515 512 501 498 493 489 485 483 465 462 458 444 435 431 407 380

Here are some summary statistics for annual snowfall in a certain town compiled over the last 15 years: lowest $\text { amount } = 18$ cm, $\text { mean } = 49$ cm, $\text { median } = 42$ cm, $\text { range } = 82$ cm, $\mathrm { IQR } = 50 ,$ $\mathrm { Q } 1 = 20 \text {, }$ standard $\text { deviation } = 10$ cm.Between what two values are the middle 50% of snowfall found?

The semester point totals of 16 students are listed below.Find the interquartile range (IQR)by hand. 787 640 820 677 475 611 527 667 574 687 875 512 592 460 542 490

Here is the stem-and-leaf display of the midterm test scores for the seventh-period typing class. 5 6 7 8 9 9 358 24479 3558 137 Would you use the median or the mean to describe the centre of this distribution?

The local Tupperware dealers earned the following commissions,in dollars,last month. $1863.64 $4955.86 $3482.51 $2342.19 $4773.76 $4720.40 $2050.10 $4263.18 $4897.60 $3314.73 Round your answer to the nearest cent.

Here are costs (in dollars)of 12 refrigerators.Find the range. 845 970 635 545 1445 1070 670 745 780 1270 535 1045

Here are the weekly winnings for several local poker players: $100,$50,$125,$75,$80,$60,$110,$150,$300,$700,$115,$75,$1000,$5000.Which is a better summary of the scores,the mean or the median? Explain.

Shown below are the boxplot and summary statistics for the heights,in centimetres,of a class of Grade 3 students in Halifax,NS. Count 32 Mean 114.2 Median 114.5 StdDev 7.7 Min 100 Max 134 Q1 107.5 Q3 118 Which measures of centre and spread would you use for this distribution?

The annual incomes,in dollars,of several doctors are listed below. 130,000 132,000 188,000 242,000 238,000 148,000 114,000 833,000 200,000 151,000

The number of days off that 30 police officers took in a given year are provided below.Create a histogram of the data using bins 2 days wide. 10 1 3 5 4 7 5 1 0 9 11 1 5 4 1 7 7 11 0 6 6 1 5 7 10 1 1 5 6 0

The weights,in kilograms,of the members of the varsity football team are listed below.Create a stem-and-leaf display of the data.Use split stems by separating each stem into 5 stems. 72 76 71 75 80 76 65 82 70 76 70 75 72 67 78 74 66 86 80 68 80 74 85 82

Shown below are the histogram and summary statistics for the reading scores of 29 fifth graders. Count Mean Median StdDev Min Max Q1 Q3 29 4.2 4.6 1.3 1.3 5.9 3.5 5.4 Which measures of centre and spread would you use for this distribution?

A consumer group surveyed the prices for a certain item in five different stores and reported the mean price to be $15.If you visited four of these stores and found their prices to $10,$15,$17,and $25,what is the price of this item at the fifth store?

Here are some summary statistics for last year's basketball team scoring output: lowest $\text { score } = 19$ points, $\text { mean } = 55$ points, $\text { median } = 49$ points, $\text { range } = 96$ points, $\mathrm { IQR } = 52$ $\mathrm { Q } 1 = 22$ standard $\text { deviation } = 6$ points.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

Students were asked to make a histogram of the number of corn snakes collected in Will County,Illinois from 1985 to 2006.They were given the data in the form of a stem-and-leaf display shown below: 0 1 2 3 4 5 6 24 17899 01378 699 224 7 035 $5~|$ $7$ = 57 corn snakes One student submitted the following display: a)Comment on this graph. b)Create your own histogram of the data.

Here are some statistics for the annual Wildcat golf tournament: lowest score = 56,mean $\text { score } = 90 \text {, }$ $\text { median } = 98 \text {, }$ $\text { range } = 94 \text {, }$ $\mathrm { IQR } = 106 \text {, }$ $\mathrm { Q } 1 = 36$ standard $\text { deviation } = 11 \text {. }$ Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

A small company employs a supervisor at $1300 a week,an inventory manager at $900 a week,5 stock boys at $400 a week,and 3 drivers at $500 a week.

The test scores of 40 students are listed below. 25 35 43 44 47 48 54 55 56 57 59 62 63 65 66 68 69 69 71 71 73 73 74 76 77 77 78 79 80 81 81 82 83 85 89 92 93 94 97 98 Choose the boxplot that represents the given data. I II III IV V

The following data consists of the heights,in centimetres,of 15 randomly selected female high school students and 15 randomly selected male high school students. $\text { Women: }$ 128 150 118 166 142 122 137 110 175 152 145 126 139 111 170 $\text { Men: }$ 140 153 199 186 169 136 176 162 196 155 173 190 141 166 153 Choose the back-to-back stemplot that represents the given data. I Men Women 11 018 12 268 6 13 79 10 14 25 533 15 02 962 16 06 63 17 5 60 18 96 19 II Men Women 11 01 12 268 6 13 79 10 14 25 533 15 024 962 16 6 63 17 05 96 18 96 19 III Men Women 11 018 12 268 6 13 79 10 14 25 533 15 02 962 16 6 63 17 05 6 18 960 19 IV Men Women 11 018 12 26 6 13 789 10 14 25 533 15 02 96 16 6 632 17 05 6 18 960 19 V Men Women 11 018 12 26 6 13 789 1 14 25 533 15 02 96 16 6 632 17 05 6 18 960 19

Here are the average mathematics achievement scores for ninth graders in 32 counties.Find the standard deviation. 599 585 574 572 569 565 564 551 539 534 531 528 525 524 519 501 488 480 478 475 471 465 458 443 427 410 409 389 380 382 355 314