Exam 3: Displaying and Summarizing Quantitative Data

Here are some summary statistics for the size of forest fires last year: smallest fire = 74 acres, $\text { mean } = 451$ acres, $\text { median } = 451$ acres, $\text { range } = 7926$ acres, $\mathrm { IQR } = 387$ $Q 1 = 180 ,$ standard deviation = 61 acres.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

Here are the prices for 8 different CD players.Find the standard deviation. $254 $323 $268 $446 $222 $313 $308 $144

The weights (in kilograms)of 27 dogs are listed below.Find the standard deviation. 1.7 2.0 2.2 2.2 2.4 2.5 2.5 2.5 2.6 2.6 2.6 2.6 2.6 2.7 2.8 2.8 2.8 2.9 2.9 2.9 3.0 3.0 3.1 3.1 3.3 3.6 4.2

Which set has the largest standard deviation? Set 1 Set 2 3 7 7 7 10 3 6 7 8 10

A medical study of the effects of on Drug X asked adult volunteers to take a heart-rate test one hour after taking Drug X.Some took a placebo (a pill containing no active ingredients),some were given a regular dose of Drug X,and others were given half a regular dose of Drug X.Here are the 5-number summaries for each group's scores on the test (# of beats that the heart rate increased when timed for 60 seconds): Q1 Median Q3 Max Placebo 13 0 1 2 3 5 Half Dose 13 1 2 3 5 8 Reg. Dose 13 1 2 3 7 9 a)Describe the W's for these data. b)Name the variables and classify each as categorical or quantitative. c)Write a few sentences comparing the results of the three groups (create parallel boxplots to help you,if necessary.)

The stem-and-leaf display shows the results of a math test written by 30 students. 10 0 9 11 8 01111123556689 7 556889 6 3778 5 48 4 3 4 2 7 1 0

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 spread,the standard deviation or the IQR? Explain.

Here are some summary statistics for the recent English exam: lowest $\text { score } = 31 \text {, }$ mean $\text { score } = 67 \text {, }$ $\text { median } = 81.2 \text {, }$ $\text { range } = 79 \text {, }$ $\mathrm { IQR } = 60 \text {, }$ $\mathrm { Q } 1 = 27 \text {, }$ standard $\text { deviation } = 8.6 \text {. }$ Between what two values are the middle 50% of the scores found?

The weekly salaries (in dollars)of 24 randomly selected employees of a company are shown below,and displayed on the following boxplot. 310 320 450 460 470 500 520 540 580 600 650 700 710 840 870 900 1000 1200 1250 1300 1400 1720 2500 3700 Find the mean and the median.Which is the most appropriate measure of centre?

In a college health course,65 students participated in a physical fitness assessment.One measure used in the assessment was body fat.The body fat percentages for the 65 students is given below.Create a histogram of the data using bins that are 2% wide. 12 17 19 22 19 26 15 14 22 11 22 25 27 13 24 14 16 28 27 16 25 27 15 17 30 14 28 28 24 29 24 10 23 35 12 16 25 13 23 25 28 27 24 27 27 12 18 24 17 17 22 26 17 31 25 23 25 26 12 14 17 15 16 19 14

In May 2014,17 coffee shops in Toronto charged the following amounts,in dollars,for a large cup of coffee (including tax).The lower stem contains leaves with the digits 0-4 and the upper stem contains leaves with digits 5-9. Large Coffee Prices 2.1 2.1 2.0 2.0 1.9 1.9 78 68 0233 567778 344 Key: 1.9 $|~6$ = $1.96

A local ice cream shop hand scoops each of its ice cream cones.The cones vary in weight from 140 grams to 305 grams with a mean of 181 grams and a standard deviation of 34 grams.The quartiles and median weights are 148,246,and 202 grams.Find the range and IQR of the weights.

John liked to order the all-you-can-eat shrimp at his favorite restaurant.Here are the number of shrimp he ate during his last five visits to the restaurant. 15,16,13,15,10

Shown below are the boxplot and the histogram for the highest temperatures ever recorded (in °F)in 32 different states in the U.S.A. i)What features of the distribution can you see in both the histogram and the boxplot? ii)What features of the distribution can you see in the histogram that you could not see in the boxplot?

Here are some statistics for the annual Wildcat golf tournament: lowest $\text { score } = 57$ mean $\text { score } = 97$ $\text { median } = 105$ $\text { range } = 93$ $I Q R = 109$ $\mathrm { Q } 1 = 39$ standard $\text { deviation } = 14$ Between what two values are the middle 50% of the scores found?

The speed vehicles travelled on a local road was recorded for one month.The speeds ranged from 52 km/h to 67 km/h with a mean speed of 56 km/h and a standard deviation of 7 km/h.The quartiles and median speeds were 55 km/h,64 km/h,and 53 km/h.Suppose during the month,one driver was clocked at 25 km/h. Which of the summary statistics might not change if that data value was added to the distribution?

A student at a local university took a total of 20 exams during freshman year.The student recorded the exam scores as percentages and created the following stem-and-leaf display.The lower stem contains leaves with the digits 0-4 and the upper stem contains leaves with digits 5-9.In addition to describing the distribution,give a reason to account for the shape of this distribution. Exam Grades 9 9 8 8 7 7 6 6 5 555555678 2344 5678 9 14 Key: 9 $|~3$ = 93%

The data below represent the midterm grades for 24 students enrolled in an electrical engineering course.Create a stem-and-leaf display of the data.Use split stems.Let the upper leaf represent digits 0-4 and the lower leaf represent 5-9. 85 77 93 91 74 65 68 97 88 59 74 83 85 72 63 79 51 86 70 71 90 75 78 69

Here are some summary statistics for annual snowfall in a certain town compiled over the last 15 years: lowest $\text { amount } = 19$ cm, $\text { mean } = 40$ cm, $\text { median } = 33$ cm, $\text { range } = 81$ cm, $\mathrm { IQR } = 45 \mathrm {~cm} \text {, }$ $\text { Q1 } = 16 \mathrm {~cm} \text {, }$ standard $\text { deviation } = 11$ cm.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

The display shows the heights of Grade 12 students at a local high school,collected so that the students could be arranged with shorter ones in front and taller ones in back for a class photograph.In addition to describing the distribution,give a reason to account for the shape of this distribution.