[ASSIGNMENT #1 DISPLAYS FOR QUANTITATIVE VARIABLES 1) In a college health course, 65 students. Participated in a physical tness 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. (10 marks} 12 1.7" 19' 22 19 26 15 14 22 11 22 25 2? 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 1? 22 26 1.7" 31 25 23 25 26 12 14 17 15 16 19 14 2) The data below represent the midterm grades for 24 students enrolled in an electrical engineering course. Create a stemandleaf display of the data. Use split stems. Let the upper leaf represent digits 0-4 and the lower leaf represent 5-9. (10 marks] 85 T"? 93 91 74 65 68 97 88 59 74 83 85 '72 63 .79 71 51 86 7G 90 175 '78 69 3) Show belmv are the histogram and smnmary statistics for the weekly salaries (in dollars) of 24 randomly selected employees of a company: B) Neither, because these are not quantitative data. C) Median, because the IQR is smaller than the standard deviation. D) Mean, because the distribution is quite symmetric. E) Median, because of the outliers. 17) Here is the stem-and-leaf display of the midterm test scores for the Human Resources Management class. (5 marks) 5 9 6 358 7 24479 8 3558 9 137 Would you use the median or the mean to describe the centre of this distribution? A) Median, because the data are skewed to the left. B) Mean, because the data are skewed to the left. C) Mean, because the data are quite symmetric. D) Mean, because the data are skewed to the right. E) Median, because the data are skewed to the right.10 count N 600 1200 1800 2400 3000 3600 4200 Weekly Salaries ($) Count | Mean | Median | StdDev | Min | Max | Q1 | Q3 24 978.8 705 765.7 310 3700 510 1225 Choose the boxplot that represents the given data and explain your reasons for your answer. (10 marks) I II III IV V 4000 4000 4000 4000 4000 3000 30OO 3000 Weekly Salaries ($) Weekly Salaries ($) Weekly Salaries ($) Weekly Salaries ($) Weekly Salaries ($) 2000 2000 2000 2000 2000 1000 1000 1000 1000 1000 A) I B) II C) III D) IV E) V4) The display shows le 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. (5 marks] #0? Students Height (in) nu an be :2 re Height (in) A) The distribution of the heights of Grade 12 students is bimodal, with a mode at around 65 inches and the other mode around 21 inches. The students' heights are between 60 mches and 2'4 imzhes. The two modes would likely represent the average heights of the male and female students. B) The distribution of the heights of IGrade 12 students is mmodal centred at 68, with a heights ranging from 60 inches to 76 inches. The two peaks would likely represent the average heights of the male and female students. C) The distribution of the heights of Grade 12 students is bimodal, with a mode at around 62 inches and the other mode around 74 inches. No student has a height below 60 inches or above .76 inches. The two modes would likely represent the average heights of the male and female students. D) The distribution of the heights of Grade 12 students is bimodal, with a mode at around 65 inches and the other mode around 21 inches. No student has a height below 60 inches or above 2'6 inches. The two modes would likely represent the average heights of the male and female students. E) The distribution of the heights of Grade 12 students is uniform centred at 68, with a heights ranging from 60 inches to 5'6 inches. The two peaks would likely represent the average heights of the male and female students. CllllE 6) Here are the number of basketball games that Parminder Singh attended over the last several seasons. Find the median of the data. (5 marks) 1 15 17 21 3E} 3D 49 A) 17 games B) 24 games C) 21 games D) 30 games E) 25.5 games SPREAD 7) The test scores of 19 students are listed below. Find the upper quartile (Q3) by hand. (5 marks) 36 45 49 53 56 59 61 62 65 67 71 75 79 82 88 90 92 97 A) 55.5 B) 82.0 C) 65.0 D) 79.0 E) 80.5 8) The weights, in kilograms, of 18 randomly selected adults are given below. Find the range. (5 marks) 54.4 74.8 84.8 64.9 54.0 59.9 57.6 70.8 81.2 72.1 81.6 91.6 51.7 66.2 68.5 76.2 78.5 65.3 A) (51.7 kg, 91.6 kg) B) (54.4 kg. 91.6 kg) C) 91.6 kg D) 37.2 kg E) 39.9 kg 9) Here are some summary statistics for all of the runners in a local 12 kilometre race: slowest time = 121 minutes mean = 76 minutes median = 76 minutes range = 91 minutes IQR =57 Q1 = 30D) 37.2 kg E) 39.9 kg 9) Here are some summary statistics for all of the runners in a local 12 kilometre race: slowest time = 121 minutes mean = 76 minutes median = 76 minutes range = 91 minutes IQR = 57 Q1 =30 standard deviation = 13 minutes Between what two values are the middle 50% of times? (5 marks) A) 30 and 87 B) 38 and 76 C) 15.2 and 60.8 D) 19 and 57 E) 121 and 30BOXPLOTS AND 5-NUMBER SUMMARY Find the five-number summary for the given data by hand. 10) The weekly salaries (in dollars) of sixteen government workers are listed below. (10 marks) 690 594 813 636 728 585 486 634 534 679 685 451 558 787 503 826 A) 451, 540, 635, 718.5, 826 dollars B) 451, 540, 634, 718.5, 826 dollars C) 451, 546, 635, 709, 826 dollars D) 451, 534, 634, 690, 826 dollars THE CENTRE OF SYMMETRIC DISTRIBUTIONS: THE MEAN 11) The students in a math class took the Scholastic Aptitude Test. Their math scores are shown below. Find the mean of the data. (5 marks) 567 630 350 353 503 356 354 552 470 482 A) 461.7 B) 476.0 C) 552.1 D) 452.6 E) 471.1 THE SPREAD OF SYMMETRIC DEVIATIONS: THE STANDARD DEVIATION 12) Here are the commutes (in kilometres) for a group of six employees. Find the standard deviation. (5 marks) 36.9 17.9 43.1 72.6 22.7 21.4 A) 421.6 B) 214.6 C) 72.6 D) 20.5 E) 98.9BOXPLOTS AND 5-NUMBER SUMMARY Find the five-number summary for the given data by hand. 10) The weekly salaries (in dollars) of sixteen government workers are listed below. (10 marks) 690 594 813 636 728 585 486 634 534 679 685 451 558 787 503 826 A) 451, 540, 635, 718.5, 826 dollars B) 451, 540, 634, 718.5, 826 dollars C) 451, 546, 635, 709, 826 dollars D) 451, 534, 634, 690, 826 dollars THE CENTRE OF SYMMETRIC DISTRIBUTIONS: THE MEAN 11) The students in a math class took the Scholastic Aptitude Test. Their math scores are shown below. Find the mean of the data. (5 marks) 567 630 350 353 503 356 354 552 470 482 A) 461.7 B) 476.0 C) 552.1 D) 452.6 E) 471.1 THE SPREAD OF SYMMETRIC DEVIATIONS: THE STANDARD DEVIATION 12) Here are the commutes (in kilometres) for a group of six employees. Find the standard deviation. (5 marks) 36.9 17.9 43.1 72.6 22.7 21.4 A) 421.6 B) 214.6 C) 72.6 D) 20.5 E) 98.913) Here are the average mathematics achievement scores for ninth graders in 32 counties. Find the standard deviation. (5 marks) 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 A) 75.3 B) 75 C) 73.3 D) 74.3 E) 75.5 14) Which set has the largest standard deviation? (5 marks) Set 1 Set 2 7 13 15 14 19 52 60 62 61 68 A) Set 2, because set 2 has a wider range and will have a smaller SD. B) Set 1, because set 1 has a narrower range and will have a larger SD. C) Set 1, because the minimum and maximum in set 1 are farther from the centre. D) Neither, because the values in set 2 are just the values in set 1 plus 45. E) Set 2, because the minimum and maximum in set 2 are farther from the centre.SUMMARY 15) A small company employs a supervisor at $1300 a week, an inventory manager at $800 a week, 7 stock boys at $400 a week, and 5 drivers at $700 a week. Which measure of centre best describes a typical wage at this company, the mean at $600 or the median at $550? (5 marks) A) Mean, because the distribution is symmetric. B) Median, because of the outlier $1300. C) Mean, because there are no outliers. D) Median, because the distribution is skewed to the left. E) Median, because of the outliers $800 and $1300. 16) Here are summary statistics of the four last digits of social security number of 500 customers, corresponding to the following histogram. (5 marks) Count 80 500 Mean 4919 StdDev 1556 60- Median 5009 # of Customers IOR 2009 40- 01 4018 03 6027 20- 1500 4000 6500 9000 Four Last Digits of Social Security Number Is the mean or median a "better" summary of the centre of the distribution? A) Neither, because these are not categorical data. B) Neither, because these are not quantitative data. C) Median, because the IQR is smaller than the standard deviation. D) Mean, because the distribution is quite symmetric. E) Median, because of the outliers