1. Honors Statistics Chapter 4 Part 2
Displaying and Summarizing Quantitative Data

2. Learning Goals
Know how to display the distribution of a quantitative variable with a histogram, a stem-and-leaf display, or a dotplot.
Know how to display the relative position of quantitative variable with a Cumulative Frequency Curve and analysis the Cumulative Frequency Curve.
Be able to describe the distribution of a quantitative variable in terms of its shape.
Be able to describe any anomalies or extraordinary features revealed by the display of a variable.

3. Learning Goals
Be able to determine the shape of the distribution of a variable by knowing something about the data.
Know the basic properties and how to compute the mean and median of a set of data.
Understand the properties of a skewed distribution.
Know the basic properties and how to compute the standard deviation and IQR of a set of data.

4. Learning Goals
Understand which measures of center and spread are resistant and which are not.
Be able to select a suitable measure of center and a suitable measure of spread for a variable based on information about its distribution.
Be able to describe the distribution of a quantitative variable in terms of its shape, center, and spread.

5. Quantitative Data
Stem and leaf Plot

6. Learning Goal 1: Stem-and-Leaf Plots
What is a stem-and-leaf plot? A stem-and-leaf plot is a data plot that uses part of a data value as the stem to form groups or classes and part of the data value as the leaf.
Most often used for small or medium sized data sets. For larger data sets, histograms do a better job.
Note: A stem-and-leaf plot has an advantage over a grouped frequency table or histogram, since a stem-and-leaf plot retains the actual data by showing them in graphic form.

7. Learning Goal 1: Stem-and-Leaf Plots
Stem-and-leaf plots are used for summarizing quantitative variables.
Separate each observation into a stem (first part of the number) and a leaf (typically the last digit of the number).
Write the stems in a vertical column ordered from smallest to largest, including empty stems; draw a vertical line to the right of the stems.
Write each leaf in the row to the right of its stem in order.

8. Learning Goal 1: Stem and Leaf Plot Construction

9. Learning Goal 1: Stem-and-Leaf Plots
How to make a stemplot:
Separate each observation into a stem, consisting of all but the final (rightmost) digit, and a leaf, which is that remaining final digit. Stems may have as many digits as needed. Use only one digit for each leaf—either round or truncate the data values to one decimal place after the stem.
Write the stems in a vertical column with the smallest value at the top, and draw a vertical line at the right of this column.
Write each leaf in the row to the right of its stem, in increasing order out from the stem. Title and include key.Original data: 9, 9, 22, 32, 33, 39, 39, 42, 49, 52, 58, 70.
STEM
LEAVES
Include key – how to read the stemplot.
0|9 = 9

10. Learning Goal 1: Stem-and-Leaf Plots – Picking Stems
Data in ordered array:
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Here, use the 10’s digit for the stem unit:
Stem Leaf
21 is shown as
38 is shown as
41 is shown as

11. Learning Goal 1: Stem-and-Leaf Plots – Picking Stems
(continued)
Completed stem-and-leaf diagram:
Data in ordered array:
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Stem
Leaves 2 3 4 1
Key
3⃓ 0 = 30

12. Learning Goal 1: Stem-and-Leaf Plots - Using Other Stem Units
Using the 100’s digit as the stem:
Round off the 10’s digit to form the leaves
613 would become (610)
776 would become (780)
. . .
1224 becomes (1220)
Stem Leaf

13. Learning Goal 1: Stem-and-Leaf Plots - Using Other Stem Units
(continued)
Using the 100’s digit as the stem:
The completed stem-and-leaf display:
Key
6⃓ 3 = 630
Data:
613, 632, 658, 717,
722, 750, 776, 827,
841, 859, 863, 891,
894, 906, 928, 933,
955, 982, 1034, 1047,1056, 1140, 1169, 1224
Stem Leaves

14. Learning Goal 1: Stem-and-Leaf Plots - Example
Construct a stem-and-leaf diagram, which simultaneously groups the data and provides a graphical display similar to a histogram.
Change to page 68
Insert Table 2.17 above figure 2.6

15. Learning Goal 1: Stem-and-Leaf Plots - Example
Put the data in a List in the TI – 84 (STAT/EDIT/L1).
Order the data using sort ascending function (STAT/EDIT/2:SortA(… ) and List 1.

16. Learning Goal 1: Stem-and-Leaf Plots - Example
Return to the list (STAT/EDIT) to view ordered data.

17. Learning Goal 1: Stem-and-Leaf Plots - Example
First, list the leading digits of the numbers in the table (3, 4, , 9) in a column, as shown to the left of the vertical rule.
Next, write the final digit of each number from the table to the right of the vertical rule in the row containing the appropriate leading digit.
Do not forget the title and key.

18. Learning Goal 1: Stem-and-Leaf Plots - Variation
Splitting Stems – (too few stems or classes) Split stems to double the number of stems when all the leaves would otherwise fall on just a few stems.
Each stem appears twice.
Leaves 0-4 go on the 1st stem.
Leaves 5-9 go on the 2nd stem.

19. Learning Goal 1: Stem-and-Leaf Plots – Split Stems Example
A pediatrician tested the cholesterol levels of several young patients and was alarmed to find that many had levels higher than 200 mg per 100 mL. The table below presents the readings of 20 patients with high levels. Construct a stem-and-leaf diagram for these data by using
a. one line per stem b. Split Stems - two lines per stem.
Change to page 69
Insert Table 2.18 above figure 2.7

20. Learning Goal 1: Stem-and-Leaf Plots – Split Stems Example
The stem-and-leaf diagram in (a) is only moderately helpful because there are so few stems. (b) is a better stem-and-leaf diagram for these data. It uses Split Stems - two lines for each stem, with the first line for the leaf digits 0-4 and the second line for the leaf digits 5-9.
Cholesterol Levels
Key
19⃓ 9 = 199
Cholesterol Levels
Change to page 69
Insert Table 2.18 above figure 2.7
Key
19⃓ 9 = 199

21. Learning Goal 1: Stem-and-Leaf Plots - Your Turn
A sample of the number of admissions to a psychiatric ward at a local hospital during the full phases of the moon is as follows: 22, 30, 21, 27, 31, 36, 20, 28, 25, 33, 21, 38, 32, 35, 26, 19, 43, 30, 30, 34, 27, and 41.
Display the data in an appropriate stem-and-leaf plot.

22. Learning Goal 1: Stemplots versus Histograms
Stemplots are quick and dirty histograms that can easily be done by hand, therefore, very convenient for back of the envelope calculations. However, they are rarely found in scientific or laymen publications.

23. Learning Goal 1: Stemplots versus Histograms
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.