CHAPTER 1 Exploring Data 1.2 Displaying Quantitative Data with Graphs The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers
Displaying Quantitative Data with Graphs Learning Objectives After this section, you should be able to: DESCRIBE the overall pattern of a distribution and IDENTIFY any outliers IDENTIFY the shape of a distribution MAKE and INTERPRET histograms of quantitative data COMPARE distributions of quantitative data The Practice of Statistics, 5 th Edition 2
Histograms Quantitative variables often take many values. A graph of the distribution may be clearer if nearby values are grouped together. The most common graph of the distribution of one quantitative variable is a histogram. How to make a histogram: 1)Divide the range of data into classes of equal width. 2)Find the count (frequency) or percent (relative frequency) of individuals in each class. 3)Label and scale your axes and draw the histogram. The height of the bar equals its frequency. Adjacent bars should touch, unless a class contains no individuals. The Practice of Statistics, 5 th Edition 3
Number of States Histograms This table presents data on the percent of residents from each state who were born outside of the U.S. Frequency Table Class Count 0 to <5 20 5 to <10 13 10 to <15 9 15 to <20 5 20 to <25 2 25 to <30 1 Total 50 Percent of foreign-born residents The Practice of Statistics, 5 th Edition 4
NBA Scoring Averages The table presents the average points scored per game (PPG) for the 30 NBA teams in the 2012 2013 regular season. Team PPG Team PPG Team PPG Atlanta Hawks 98.0 Houston Rockets 106.0 Oklahoma City Thunder 105.7 Boston Celtics 96.5 Indiana Pacers 94.7 Orlando Magic 94.1 Brooklyn Nets 96.9 Los Angeles Clippers 101.1 Philadelphia 76ers 93.2 Charlotte Bobcats 93.4 Los Angeles Lakers 102.2 Phoenix Suns 95.2 Chicago Bulls 93.2 Memphis Grizzlies 93.4 Portland Trail Blazers 97.5 Cleveland Cavaliers 96.5 Miami Heat 102.9 Sacramento Kings 100.2 Dallas Mavericks 101.1 Milwaukee Bucks 98.9 San Antonio Spurs 103.0 Denver Nuggets 106.1 Minnesota Timberwolves 95.7 Toronto Raptors 97.2 Detroit Pistons 94.9 New Orleans Hornets 94.1 Utah Jazz 98.0 Golden State Warriors 101.2 New York Knicks 100.0 Washington Wizards 93.2 Because the smallest value is 93.2 and the largest value is 106.1, we choose classes of width 2 starting at 93 (93 to <95, 95 to <97, 97 to <99, 99 to <101, 101 to <103, 103 to <105, and 105 to <107). Here are a frequency histogram and a relative frequency histogram for these data. The relative frequency histogram looks exactly the same as the frequency histogram except for the vertical scale. The Practice of Statistics, 5 th Edition 5
Percent Frequency NBA Scoring Averages 9 8 7 6 5 4 3 2 1 0 93 95 97 99 PPG 101 103 105 30 107 25 20 15 10 5 0 93 95 97 99 PPG 101 103 105 107 The Practice of Statistics, 5 th Edition 6
Percent Frequency NBA Scoring Averages Now here are histograms using class widths of 1 starting at 93. The choice of class width can influence the appearance of a histogram. In the histograms below, we can see gaps from 99 to 100 and from 104 to 105. 5 4 3 2 1 18 16 0 93 95 97 99 PPG 101 103 105 107 14 12 10 8 6 4 2 0 93 95 97 99 101 103 105 107 PPG The Practice of Statistics, 5 th Edition 7
Histograms on the Calculator To graph this histogram on the calculator: 1. STAT, then edit. Enter values into list L1 using the enter button after each entry. 2. STAT PLOT (2 nd Y=), then 1 to enter plot1 3. Entries: on, Type: 3 rd window, Xlist: L1, Freq: 1, then GRAPH 4. Use ZOOM, Stat (9) to allow the calculator to generate a histogram 5. Use TRACE to examine it. 6. Use WINDOW to adjust the bins to something more uniform. Team PPG Team PPG Team PPG Atlanta Hawks 98.0 Houston Rockets 106.0 Oklahoma City Thunder 105.7 Boston Celtics 96.5 Indiana Pacers 94.7 Orlando Magic 94.1 Brooklyn Nets 96.9 Los Angeles Clippers 101.1 Philadelphia 76ers 93.2 Charlotte Bobcats 93.4 Los Angeles Lakers 102.2 Phoenix Suns 95.2 Chicago Bulls 93.2 Memphis Grizzlies 93.4 Portland Trail Blazers 97.5 Cleveland Cavaliers 96.5 Miami Heat 102.9 Sacramento Kings 100.2 Dallas Mavericks 101.1 Milwaukee Bucks 98.9 San Antonio Spurs 103.0 Denver Nuggets 106.1 Minnesota Timberwolves 95.7 Toronto Raptors 97.2 Detroit Pistons 94.9 New Orleans Hornets 94.1 Utah Jazz 98.0 Golden State Warriors 101.2 New York Knicks 100.0 Washington Wizards 93.2 The Practice of Statistics, 5 th Edition 8
Using Histograms Wisely Here are several cautions based on common mistakes students make when using histograms. Cautions! 1)Don t confuse histograms and bar graphs. 2)Don t use counts (in a frequency table) or percents (in a relative frequency table) as data. 3)Use percents instead of counts on the vertical axis when comparing distributions with different numbers of observations. 4)Just because a graph looks nice, it s not necessarily a meaningful display of data. The Practice of Statistics, 5 th Edition 9
Exercise 56, page 45: Drive Time Professor Moore, who lives a few miles outside a college town, records the time he takes to drive to the college each morning. Here are the times (in minutes) for 42 consecutive weekdays: 8.25 7.83 8.30 8.42 8.50 8.67 8.17 9.00 9.00 8.17 7.92 9.00 8.50 9.00 7.75 7.92 8.00 8.08 8.42 8.75 8.08 9.75 8.33 7.83 7.92 8.58 7.83 8.42 7.75 7.42 6.75 7.42 8.50 8.67 10.17 8.75 8.58 8.67 9.17 9.08 8.83 8.67 Make a histogram to display the data. Write a paragraph describing the distribution of Professor Moore s drive times. Class Tallies Counts 6.75 to <7.25 7.25 to <7.75 7.75 to <8.25 8.25 to <8.75 8.75 to <9.25 9.25 to <9.75 9.75 to 10.25 The Practice of Statistics, 5 th Edition 10
Exercise 56, page 45: Drive Time Professor Moore, who lives a few miles outside a college town, records the time he takes to drive to the college each morning. Here are the times (in minutes) for 42 consecutive weekdays: 8.25 7.83 8.30 8.42 8.50 8.67 8.17 9.00 9.00 8.17 7.92 9.00 8.50 9.00 7.75 7.92 8.00 8.08 8.42 8.75 8.08 9.75 8.33 7.83 7.92 8.58 7.83 8.42 7.75 7.42 6.75 7.42 8.50 8.67 10.17 8.75 8.58 8.67 9.17 9.08 8.83 8.67 Make a histogram to display the data. Write a paragraph describing the distribution of Professor Moore s drive times. Class Tallies Counts 6.75 to <7.25 1 7.25 to <7.75 2 7.75 to <8.25 13 8.25 to <8.75 15 8.75 to <9.25 9 9.25 to <9.75 0 9.75 to 10.25 2 The Practice of Statistics, 5 th Edition 11
Exercise 56, page 45: Drive Time Make a histogram to display the data. Write a paragraph describing the distribution of Professor Moore s drive times. Class Counts 6.75 to <7.25 1 7.25 to <7.75 2 7.75 to <8.25 13 8.25 to <8.75 15 8.75 to <9.25 9 9.25 to <9.75 0 9.75 to 10.25 2 The Practice of Statistics, 5 th Edition 12
Data Analysis: Making Sense of Data Section Summary In this section, we learned how to MAKE and INTERPRET dotplots and stemplots of quantitative data DESCRIBE the overall pattern of a distribution IDENTIFY the shape of a distribution MAKE and INTERPRET histograms of quantitative data COMPARE distributions of quantitative data The Practice of Statistics, 5 th Edition 13
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