Describing Data (Univariate Data) Ch. 1

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)

Histogram A example Shape: Mound Center: 35 Spread: 25 to 45 Outliers: None Center: 35 Spread: 25 to 45 0 10 20 30 40 50 60 70 80 90 100

Histogram A practice Shape, Center, Outliers, Spread? 0 10 20 30 40 50 60 70 80 90 100

Histogram B example Skewed Right 0 10 20 30 40 50 60 70 80 90 100

Histogram B example Skewed left 0 10 20 30 40 50 60 70 80 90 100

Histogram B example Symmetrical, mound shaped 0 10 20 30 40 50 60 70 80 90 100

Histogram B example Shape: Uniform Center: 70 Outliers: None Spread: 55-80 0 10 20 30 40 50 60 70 80 90 100

Histogram B example Bimodal (two modes/two tall towers) 0 10 20 30 40 50 60 70 80 90 100

Histogram C example Shape: Roughly Symmetrical Outliers: None, but gaps at 30 and 40 Center: 35 Spread: 20-55 0 10 20 30 40 50 60 70 80 90 100

Histogram C example Shape: Uniform Outliers: Possible at 5 Center: 40 Spread: 5 to 55 0 10 20 30 40 50 60 70 80 90 100

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

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

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 3 4 5 6 7 8 9 10 11 12 13

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 1 9 6 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

Alfred Hitchcock Stemplot Example 5 Alfred Hitchcock Stemplot Shape: Slightly skewed 13 12 11 10 9 8 0 6 2 0 0 0 6 8 6 6 3 1 7 8 3 8 8 1 3 1 Outliers: Gap in 90s 9 Center: 116 5 Spread: from 81 to 136 Key: 8|1 means 81 minutes

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 1 6 7 6 9 6 1 5 4 5 2 Babe Ruth Roger Maris 4 9 6 3 6 3 Key: 4 | 1 means 41

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.

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.

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

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

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 1 2 3 2 0 0 0 0 1 1 1 2 3 3 4 4 4 4 6 7 8 8 1 4 6 6 6 7 7 8 8 8 9 9 9 Key: 1|4 means 14 years old

Split Stemplot Split stemplot typically breaks each stem into High (5-9) and Low(0-4) 3H 2H 1H 4L 3L 2L 1L 1 2 3 0 0 0 0 1 1 1 2 3 3 4 4 4 4 6 7 8 8 4 6 6 6 7 7 8 8 8 9 9 9 Key: 1|4 means 14 years old