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Chapter 1 Section 7 Displaying and Interpreting Data

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Example 1 The number of annual visitors to the Grand Canyon is given in the table below. Construct a line graph to predict the number of annual visitors to the Grand Canyon in the year 2010. YearGrand Canyon Visitors (million) 19601.0 19702.2 19802.5 19903.5 20005.0

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Grand Canyon Visitors 19601970198019902000 0 1 4 3 2 5 Step 1: Draw a horizontal axis and a vertical axis and label them as shown to the right. Include a title Step 2: Plot the Points Step 3: Draw a line by connecting the points Number Of People (Millions) Year You can see from the graph that the general trend is that the number of visitors to the Grand Canyon increases steadily every ten years. A good prediction for the year 2010 might be about 6 or 6.5 million people.

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Your Turn The table below shows the approximate U.S. consumption of bottled water per person. Construct a line graph of the data. Then use it to predict the amount of bottled water each person will drink in the year 2005. YearBottle Water (Gallons) 19751 19802.5 19855 19907 199512 200016

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Another type of graph that is used to display data is a histogram. A histogram uses data from a frequency table and displays it over equal intervals. To construct a histogram, include the same three items as the line graph: title, axes labels, and equal intervals. In the histogram, all of the bars should be the same width with no spaces between them.

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Example 2 The frequency table shows the various time intervals that “charged” balloons remained stuck to the wall. Construct a histogram of the data. Step 1: Draw a horizontal axis and a vertical axis and label them as shown to the right. Include a title. Step 2: Show equal intervals given in the frequency table on the horizontal axis. Show equal intervals of 1 on the vertical axis. Step 3: For each time interval, draw a bar Whose height is given by the frequency. Static Electricity Time(s)TallyFrequency 15-24IIIII III8 25-34IIIII IIII9 35-44IIIII II7 45-54I1

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Construct Bar Graph For Example 2

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The histogram gives a better visual display of the data than the frequency table. In lesson 1-6 we used cumulative frequency tables to organize data. Likewise, we can construct cumulative frequency histograms.

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Example 3 The ages of people who participated in a recent survey are shown in the table below. Construct a cumulative frequency histogram to display the data. Survey AgeTallyFrequency 1-10IIIII III8 11-20IIIII IIII9 21-30IIIII5 31-40IIIII IIIII II12 41-50IIIII III8

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First Step First make a cumulative frequency table. Survey AgeFrequencyCumulative Frequency 1-1088 11-20917 21-30522 31-401234 41-50842

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Second Step Then construct a histogram using the cumulative frequencies for the bar heights. Remember to label the axes and include the title. (Construct as a class)

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Your Turn Construct a cumulative histogram of the data below. Static Electricity Time(s)TallyFrequency 15-24IIIII III8 25-34IIIII IIII9 35-44IIIII II7 45-54I1

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Example 4 The table shows the class results on a 50- question test. Make a stem-and-leaf plot of the grades. Class Scores 293748401734 284337354929 132942453746

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The tens digits are the stems, so the stems are 1,2,3, and 4. The ones digits are the leaves. Stem Leaf 1 7 3 2 9 8 9 9 3 7 4 7 5 7 4 8 0 3 9 2 5 6 3 7 = 37

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Now arrange the leaves in numerical order to make the results easier to observe and analyze. Stem Leaf 1 3 7 2 8 9 9 9 3 4 5 7 7 7 4 0 2 3 5 6 8 9

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Stem Leaf 1 3 7 2 8 9 9 9 3 4 5 7 7 7 4 0 2 3 5 6 8 9 What were the highest scores? 49 and 13 Which scores occurred most frequently? 29 and 37, three times each How many students received a Score of 35 or better? 11 students

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Your Turn Make a stem and leaf plot of the quiz grades below. 54, 55, 60, 42, 41, 75, 50, 68, 62, 54, 70, 50

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Stem Leaf 4 1 2 5 0 0 4 4 5 6 0 2 8 7 0 5

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