Displaying Quantitative (Numerical) Data with Graphs DOTPLOTS: One of the simplest graphs to construct and interpret is a dotplot. Each data value is shown as a dot above its location on a number line. Total goals scored by individual teams in the 2014 World Cup 1 : 18 15 12 11 8 7 7 7 5 6 6 5 5 5 5 4 4 4 4 4 3 3 3 3 3 3 2 2 2 2 1 1 1 Examining the Distribution of a Quantitative Variable: Describe the overall pattern of a distribution by its: 1. When you describe a distribution s shape, concentrate on the main features. Look for rough or clear. A distribution is roughly: if the right and left sides of the graph are approximately mirror images of each other. if the right side of the graph (containing the half of the observations with larger values) is much longer than the left side. if the left side of the graph is much longer than the right side. 1 http://www.fifa.com/worldcup/statistics/teams/goal-scored.html
2. 3. 4. (individual values that fall outside the overall pattern) Stemplots (Stem-and-Leaf Plots) 1. Separate each observation into a stem (all but the final digit) and a leaf (the final digit). 2. Write all possible stems from the smallest to the largest in a vertical column and draw a vertical line to the right of the column. 3. Write each leaf in the row to the right of its stem. 4. Arrange the leaves in increasing order out from the stem. 5. Provide a key that explains in context what the stems and leaves represent. These data represent the responses of 20 female AP Statistics students to the question, How many pairs of shoes do you have? Construct a stemplot. Splitting stems and Back-to-Back Stemplots Females Males What is the problem with using the ones digit as the stem? Which group has more shoes?
Practice: 1. The following table displays the number of gold medals won by a sample of countries in the 2012 Summer Olympic Games in London. Country Gold Medals Country Gold Medals USA 46 New Zealand 6 Jamaica 4 Cypress 0 France 11 Poland 2 Belarus 6 South Korea 13 Indonesia 0 Argentina 1 Turkey 2 Estonia 0 Latvia 1 Gabon 0 Brazil 3 Romania 2 Guatemala 0 Bahamas 1 Kenya 2 Ukraine 6 Ireland 1 Egypt 0 a) Make a dotplot to display these data. Describe the overall pattern of the distribution and any deviations from that pattern. b) Overall, 205 countries participated in the Games in 2012, of which 50 won at least one gold medal. Do you believe the sample of countries I chose to list in the table is representative of the larger population? Why or why not?
2. The dotplot below shows the difference (highway-city) in EPA mileage ratings for each of 24 model year 2009 midsize cars. 2009 Midsize Cars 4 5 6 7 8 9 Difference (Highway- City) 10 11 a) Explain what the dot above 6 represents. b) What does the graph tell us about the fuel economy in the city versus on the highway for these car models? Be specific. 3. It appears that El Nino affects the monsoon rains that are essential for agriculture in India. Here are the monsoon rains (in mm) for the 23 strongest El Nino years between 1871 and 2004: 628 669 740 651 710 736 717 957 698 653 604 781 784 790 811 872 830 858 858 896 806 790 792 a) Round each number to the nearest 10 and make two stemplots, with and without splitting the stems. Which plot do you prefer? b) Describe the shape of the graph. c) The average monsoon rainfall for all years from 1871 to 2004 is about 850 mm. What effect does El Nino appear to have on monsoon rains?
4. The total points scored by MHS in its football games in both 2012 and 2013 are recorded below. 2 2012 43 0 20 61 63 45 27 21 33 6 2013 21 6 19 63 76 41 22 13 10 60 20 a) Construct a back-to-back stemplot to compare the points scored by MHS in the two years. b) Write a few sentences comparing the distributions. 5. Describe the shape of the distributions. 2 http://www.maxpreps.com/high-schools/manhattan-indians-%28manhattan,ks%29/football/home.htm