Organizing Quantitative Data Section 2.2

1. Organizing Quantitative DataSection 2.2 Alan Craig 770-274-5242 acraig@gpc.edu

2. 2 Objectives 2.2 Summarize discrete data in tables. Construct histograms of discrete data. Summarize continuous data in tables. Construct histograms of continuous data. Draw stem-and-leaf plots. Identify the shape of a distribution. Draw time series graphs.

3. 3 Construct Table #6, p66 Number Free Relative Throws Frequency Frequency 1 16 .32 2 11 .22 3 9 .18 4 7 .14 (b) 5 2 .04 6 3 .06 7 0 .00 (d) 8 1 .02 9 0 .00 10 1 .02 (c)

4. 4 Definition Histogram A histogram is constructed by drawing rectangles for each class of data. The height of each rectangle is the frequency or relative frequency of the class. The width of each rectangle should be the same and the rectangles should touch each other.

5. 5 Histogram for #6, p66

6. 6 Using TI-84+ for a Histogram Enter number free throws in L1 and Frequency in L2 using STAT?1:Edit 2nd Y=?1:Plot1 ?On ?Enter Select histogram icon ?Enter Xlist ?L1 Freq ?2nd 2 to select L2 WINDOW ?Set Xmin, Xmax, Xscl (Note: Using ZOOM?9:ZoomStat lets the calculator set these values and automatically graphs the histogram.)

7. 7 Using TI-84+ for a Histogram For discrete data, set Xmin to lowest x value - � width of your bars and Xmax to the largest x value + � width. Set Xscl to the width of each bar. For our data, set Xscl to 1, Xmin to 0.5, and Xmax to 10.5 GRAPH

8. 8 �Free Throw� Histogram from TI-84+

9. 9 Tables & Histograms for Continuous Data Create classes�categories of data using intervals Lower class limit�smallest value in a class Upper class limit�largest value in a class Class width�difference between consecutive lower class limits Open ended�if the last class does not have an upper class limit

10. 10 Tables & Histograms for Continuous Data Example�see Tables 12 & 13, pp. 57-58. Arbitrarily set lower class limit to 10 and class width to 5 Classes must not overlap, so 10 � 14.9, 15 � 19.9,� For Histogram in Figure 9 (a), enter midpoints of each class in Table 13 in L1 and the corresponding frequency in L2

11. 11 Tables & Histograms for Continuous Data In STATPLOT, ensure Plot1 is ON, histogram is selected, Xlist = L1 and Freq = L2 In WINDOW, set Xmin = 10, Xmax = 50, Xscl = 5, Ymin = -1, Ymax =12 Now GRAPH

12. 12 Constructing Stem & Leaf Plots Step 1: Stem consists of the digits to the left of the rightmost digit. The leaf will be the rightmost digit. Step 2: Write the stems in a vertical column in increasing order. Draw a vertical line to the right of the stems. Step 3: Write each leaf corresponding to the stems to the right of the vertical line. Leaves must be written in ascending order.

13. 13 Example Stem & Leaf#26, p69 0 5 6 7 1 2 2 2 3 3 5 5 7 8 8 8 9 2 1 4 5 6 6 8 3 4 5 8 9 9 4 0 1 1 3 3 5 6 9 5 2 3 5 6 6 6 1 3 3 4 5 8

14. 14 Distribution Shapes Symmetric�right & left sides are mirror images Uniform�each class has same frequency Bell-shaped�highest in middle, equal tails Skewed Left�longer tail to left Skewed Right�longer tail to right See the histograms, top of p. 63

15. 15 Definition Time Series Plot Plot time on the horizontal axis (x-axis) and the corresponding value of the variable on the vertical axis (y-axis). Lines are then drawn connecting the points. Time series plots are very useful in identifying trends in the data.

16. 16 Time Series Plot

17. 17 Questions ???????????????