Chapter 4 Displaying Quantitative Data

1. Chapter 4Displaying Quantitative Data • Summarizing the data will help us when we look at large sets of quantitative data. • Without summaries of the data, it’s hard to grasp what the data tell us. • The best thing to do is to make a picture… • We can’t use bar charts or pie charts for quantitative data, since those displays are for categorical variables. Quantitative Variables:

2. Quantitative Variables • Can be sorted into two types - discrete & continuous

3. Discrete • listable set of values • usually counts of items

4. Continuous • data can take on any values in the domain of the variable • usually measurements of something

5. Dotplot • Used with quantitative data (either discrete or continuous) • Made by putting dots (or X’s) on a number line • Can make comparative dotplots by using the same axis for multiple groups

6. A histogramplots the bin counts as the heights of bars (like a bar chart, except the bars touch). • Here is a histogram of the monthly price changes in Enron stock: Min=-20 Max<-15

7. A company has 24 sales representatives who sold the following number of units during the first quarter of 2007.

8. Stem-and-Leaf Displays • Stem-and-leaf displays show the distribution of a quantitative variable, like histograms do, while preserving the individual values. • Stem-and-leaf displays contain all the information found in a histogram and, when carefully drawn, satisfy the area principle and show the distribution.

9. Constructing a Stem-and-Leaf Display • First, cut each data value into leading digits (“stems”) and trailing digits (“leaves”). • Use the stems to label the bins. • Use only one digit for each leaf—either round or truncate the data values to one decimal place after the stem. • Make a “key” or “legend” Students quiz scores: 100 83 91 71 93 88 85 88 76 79 97 90

10. Variations of a stem-and-leaf plot: • If you have a large number of observations in each row, it may be helpful to divide the leaves into Low (0-4) and High (5-9) Example: Several states reported the median age at which their residents were “mostly gray”. 41 33 39 29 37 36 44 41 34 39 38 38 42 39 40 39 47 38

11. Frequently we want to see whether two groups of data differ in some fundamental way. A comparative stem-and-leaf display (sometimes called “back-to-back”) is useful for comparing the distributions of two sets of quantitative data.

12. Percentage of primary school aged children enrolled in school (UNICEF, April 2005) Northern African countries: 55 34 49 78 60 89 97 93 84 87 97 89 99 92 98 96 92 95 99 Central African countries: 58 35 36 45 39 64 54 62 70 43 85 63 58 62 41 74 35 74 97 61

13. Homework Use your class survey data. Construct a histogram that displays the heights of the students in your class. (use calc & sketch) Construct a stemplot (high/low) that displays the number of states visited by students in your class. Construct TWO dotplots that display the amount of sleep students in your class got the night before the first day of school --- one for males and one for females.