2. Chapter 01 – Section 04 Stem-and-Leaf Plots

3. © William James Calhoun To display and interpret data on a stem-and-leaf plot. Statistics is a branch of mathematics which focuses on collecting, organizing, and interpreting various forms of data. data – numerical information For most of us, seeing long lists of numbers in random order is confusing. We need to have order arise from the chaos of random lists. Just look at the list of miles per gallon (mpg) ratios from cars on the next slide.

4. © William James Calhoun 313028262231263447 321833262318291340 31421722501241 These mpg ratios are called a set of data – a listing of numbers. Sets of numbers can be listed in many ways. One way is in the rows and columns above. A second way is in what we call set notation: {12, 13, 17, 18, 18, 22, 22, 23, 26, 26, 26, 28, 29, 30, 31, 31, 31, 32, 33, 34, 40, 41, 42, 47, 50} Set of Data

5. © William James Calhoun The representation of data for today is a third way: via a stem-and-leaf plot. Making a stem-and-leaf plot is a four step process. 1) Choose your stems and leaves. 2) Fill in a Stem | Leaf t-chart, keeping all the same stems on the same line. 3) Reorganize the leaves from lowest to highest. 4) Add a key to the bottom. Now to do this for our data.

6. © William James Calhoun 1) Stem and leaf dividing: In a stem-and-leaf plot, the data is divided across digits and organized in a t-chart by the higher place-value positions. For example, the number 51 becomes 5 | 1, where “5” is the tens-value and “1” is the ones-value. So, from our list of mpg, 31 becomes 30 becomes 28 becomes 26 becomes Do you get the picture? 3 | 1 3 | 0 2 | 8 2 | 6

7. © William James Calhoun 2) Data into the t-chart. Take the divided numbers and place them in a chart, like so… 313028262231263447 321833262318291340 31421722501241 StemLeaf Get it? Fill it up! 3 2 no repeats in the stemslist all leaves – worry about order later 1 4 5 10 862 1 4 2 3 1 6 6 3 9 2 8 8 3 7 2 7 0 2 1 0

8. © William James Calhoun 3) Reorganize the leaves from lowest to highest. StemLeaf 1234512345 8 8 3 7 2 8 6 2 6 6 3 9 2 1 0 1 4 2 3 1 7 0 2 1 0 StemLeaf 1234512345 8 8 8 3 7 2 8372 2 3 7 8 8 8 6 2 6 6 3 9 2 86266392 2 2 3 6 6 6 8 9 1 0 1 4 2 3 1 1014231 0 1 1 1 2 3 4 7 0 2 1 7021 0 1 2 7 0 0

9. © William James Calhoun 4) Add a key to the bottom. StemLeaf 12 3 7 8 8 22 2 3 6 6 6 8 9 30 1 1 1 2 3 4 40 1 2 7 50 3 | 1 = 31

10. © William James Calhoun EXAMPLE 1α: Use the information in the stem-and-leaf plot shown below to answer each question. Stem Leaf 1 2 3 7 8 8 2 2 2 3 6 6 6 8 9 3 0 1 1 1 2 3 4 4 0 1 2 7 5 0 3 | 1 = 31 a. Which mpg ratio occurs most often? b. What are the highest and lowest mpg ratios? c. Each line of the stem-and-leaf plot represents an interval of the data. In which mileage interval did most cars fall? d. How many cars have a ratio of between 20 and 39 mpg? Answering these questions is much easier when in a stem-and-leaf plot. 2631both appear three times& 1250& between 20 and 29 mpg 15 cars

11. © William James Calhoun EXAMPLE 1β: Lori sells tickets at a movie theater. Her sales for week 1 were $173, $160, $182, $183, and $247. Sales for week 2 were $137, $182, $151, $193, $199, and $194. a. Make a stem-and-leaf plot of two weeks’ sales. Round the data to the nearest $10. (We sometimes round the data before plotting.) b. What is the most amount of money made in one day during the two week period?

12. © William James Calhoun PAGE 29 #11 – 21 odd #21 – Make the stem-and-leaf plot