1. Describing Data (Univariate Data) Ch. 1

2. Describe with S.O.C.S Shape: Overall appearance of distribution
Outliers: Any outliers and/or unusual gaps/features
Center: The value that divides the shape roughly in half
Spread: The minimum to the maximum (variability)

3. Histogram A example Shape: Mound Center: 35 Spread: 25 to 45
Outliers: None
Center: 35
Spread: 25 to 45

4. Histogram A practice Shape, Center, Outliers, Spread?

5. Histogram B example
Skewed Right

6. Histogram B example
Skewed left

7. Histogram B example Symmetrical, mound shaped

8. Histogram B example Shape: Uniform Center: 70
Outliers: None Spread:

9. Histogram B example Bimodal (two modes/two tall towers)

10. Histogram C example Shape: Roughly Symmetrical
Outliers: None, but gaps at 30 and 40
Center: 35
Spread:

11. Histogram C example Shape: Uniform Outliers: Possible at 5 Center: 40
Spread: 5 to 55

12. Displaying Distributions with Graphs
Categorical versus Quantitative
Categorical – Data that can not have values attached to it
Colors of cars, types of candy bars, etc.
Displayed in bar graphs and pie charts
Quantitative – Data that does have values attached to it
Weights, MPG of cars, income, etc.
Displayed in dotplots, histograms, stemplots, and boxplots

13. Categorical vs. Quantitative
Type of tree?
Ethnicity?
Blood pH?
Favorite Music?
Time to complete homework?
Mortality rates?

14. Example 1
The number of OU football wins since 1975 is listed below. Display in a dotplot
11, 9, 10, 11, 11, 10, 7, 8, 8, 9, 11, 11, 11, 9, 7, 8, 9, 5, 9, 6, 5, 3, 4, 5, 7, 13, 11, 12, 12, 12, 8, 11, 11, 12, 8, 12, 10, 10, 11
Shape: Skewed left
Outliers: None
Center: Between 9 and 10
Spread: 3 to 13

15. Typing Speeds Stemplot
Example 4
Typing Speeds Stemplot
Shape: Fairly
symmetrical 6 7 5 4 3 2 8 9 1 4
Outliers: No unusual features 2
8 5 2 6 1 5 8 3 5 2 5
Center: 62 7 5
Spread: from 22 to 91 5
Key: 2|2 means 22 wpm

16. Alfred Hitchcock Stemplot
Example 5
Alfred Hitchcock Stemplot
Shape: Slightly
skewed 13 12 11 10 9 8 1
Outliers: Gap in 90s 9
Center: 116 5
Spread: from 81 to 136
Key: 8|1 means 81 minutes

17. Back to Back Stemplots Example 6 9 3 8 4 1 6 5 4 3 2 1 4 1 6 7 6 9 6 1
9 3 8 4 1 6 5 4 3 2 1 4
5 4
5 2
Babe Ruth
Roger Maris 4 9 6 3 6 3
Key: 4 | 1 means 41

18. Babe Ruth vs. Roger Maris
Generally, we can see that Babe Ruth hit more home runs than Roger Maris.
The center of Babe Ruth is higher at 46 than Roger Maris at 24.5 home runs.
Roger Maris has a possible outlier at 61 yet Ruth has no outliers.
Maris has a larger spread from 8 to 61, but Ruth has a higher spread from 22 to 60; especially if we exclude the possible outlier.
Both distributions are fairly symmetrical.

19. Babe Ruth vs. Roger Maris
Generally, we can see that Babe Ruth hit more home runs than Roger Maris.
The center of Babe Ruth is higher at 46 than Roger Maris at 24.5 home runs.
Roger Maris has a possible outlier at 61 yet Ruth has no outliers.
Maris has a larger spread from 8 to 61, but Ruth has a higher spread from 22 to 60; especially if we exclude the possible outlier.
Both distributions are fairly symmetrical.

20. Example 2 continued Category Frequency Relative freq Cumulative
0 –<5 5
.1389
5 –<10 11
.3056
.4445
10 –<15 12
.3333
.7778
15 –<20 1
.0278
.8056
20 –<25 4
.1111
.9167
25 –<30 2
.0556
.9723
30 –<35

21. Example 3 .2
About .36 .4
Sixty percent of the teachers honored in Who’s Who were 50 years or younger.

22. Split Stemplot Similar to a histogram, we want to avoid too many
data points in a small range
ages of which a sample of 35 American mothers first gave birth 4 3 2 1
Key: 1|4 means 14 years old

23. Split Stemplot Split stemplot typically breaks each stem into
High (5-9) and Low(0-4) 3H 2H 1H 4L 3L 2L 1L 4
Key: 1|4 means 14 years old