June 5, 2009 Statistics mini-project: Heart rates page 1 Statistics mini-project: Heart rates In this mini-project, you will participate in the collection of a set of data, then carry out all of the statistical methods that we have learned in the past several classes. Special instructions regarding calculator use: For most of the assignment, you may use your calculator only for arithmetic, not for the statistical features (found under STAT and STATPLOT). Only in questions 5, 6, and 7 are you permitted to use the statistics features to help get your answers. However, for the rest of the assignment, you may use these features to check the answers that you ve found by hand. Gathering data 0. In class, we will have all students measure their heart rates (the number of times that the heart beats in a minute, also known as a pulse). Record the class s data here. Note: If you were absent from class on this day, you ll need to copy these numbers from a classmate or our Web site. Representing the data 1. Make a stemplot (stem-and-leaf display) of the class s heart rates.
June 5, 2009 Statistics mini-project: Heart rates page 2 2. Make a histogram (grouped bar graph) of the class s heart rates. Use a bar width of 5 (for example, one of the bars will represent the interval 55 h.r. < 60). Each bar of your histogram must be labeled to show what interval of heart rates it represents, and how many heart rates fell in that interval. Measures of center 3. Calculate each of the following for the heart rate data. You must show work and/or explain how you get your answer. Just giving an answer by itself will not get credit. If any of your answers are that the number does not exist or cannot be found, explain why. a. Find the mean. b. Find the median. c. Find the mode.
June 5, 2009 Statistics mini-project: Heart rates page 3 Quartiles and boxplot 4. Find the first quartile for the class s heart rates. You must do this by yourself, not on the calculator. Show all the work leading to the answer. Remember that the first quartile is the median of all the data below the median. Don t worry if your results are close to, but not equal to, other students results. Nitpicky decisions about whether to include the median itself in the median of the lower half computation change the result, but not by much in a realistic data set. 5. a. Enter the list of heart rates into your calculator. Use the 1-Var Stats command to get the rest of the five-number-summary. Record it here: minimum = third quartile = first quartile = maximum = median = b. Make a boxplot (box-and-whisker plot) on your calculator. Fill in these screens to show what you did on the calculator. c. Redraw the boxplot above the number line given below. 30 40 50 60 70 80 90 100
June 5, 2009 Statistics mini-project: Heart rates page 4 Comparison Suppose that last year s class did the same project, and had the heart rates shown in the stemplot given here. 6. Answer these questions comparing last year s class to your class. You may get the numbers needed to answer the questions either by yourself or from the calculator. Either way, you must state the numbers leading to your conclusion. a. Which class had the greater average for its heart rates? 4 8 5 3 4 6 6 9 6 0 2 3 3 4 7 8 7 0 1 4 4 5 6 9 8 1 9 b. Which class had the greater median for its heart rates? c. Which class had the greater third quartile for its heart rates? 7. Answer these further questions comparing last year s class to your class. a. The range of a set of data is the difference between the maximum and minimum values. The heart rates for last year s class had a range of 81 48 = 33. Find the range for your class, and identify which class had the greater range. b. Draw boxplots for both your class and last year s class above this number line. Using your calculator s statistical features is allowed here. 30 40 50 60 70 80 90 100
June 5, 2009 Statistics mini-project: Heart rates page 5 Probabilities 8. Give answers to these probability questions as fractions. You may make use of facts that you have found in previous problems. a. Suppose a student is randomly chosen from your class. What is the probability that this student s heart rate will be less than 60? b. Suppose a student is randomly chosen from your class. What is the probability that this student s heart rate will be less than 60 or greater than 70? c. Suppose a student is randomly chosen from last year s class. What is the probability that this student s heart rate will be greater than the average for that class? d. Suppose a student is randomly chosen from last year s class. What is the probability that this student s heart rate will be greater than the third quartile for that class? e. Suppose that a student is randomly chosen from your class and a student is randomly chosen from last year s class. What is the probability that both students will have a heart rate greater than 65?