1. HS 67 Lectue Notes Picturing Distributions with Graphs
Thursday, November 22, 2018
Chapter 1
Picturing Distributions with Graphs
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Chapter 1

2. What is Statistics?
Statistics is the science that involves the extraction of information from data.
It is a mistake to think of statistics as merely mathematical computations!
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3. Data Structure
Individuals = observations ≡ individual units (e.g., people, institutions) upon which measurements are made
rows in the data table
Variables ≡ characteristic that are measured
columns in the data table
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4. Types of Variables Categorical variables: named (“nominal”) categories
HS 67 Lectue Notes
Thursday, November 22, 2018
Types of Variables
Categorical variables: named (“nominal”) categories
Counts (frequencies), percentages
Quantitative variables: numerical scales
arithmetic operations such as means and standard deviations
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5. Types of Variables
Willet et al. (1995). Weight, weight change, and coronary heart disease in women. JAMA, 273(6).
Objective: to determine the effect weight gain on coronary heart disease (CHD) risk in women
Unit of observation: women between 30- to 55-years of age initially free of CHD.
Explanatory variable: body mass index (BMI) at age 18
Follow-up for 14 years (cohort study)
Response variable: fatal and nonfatal CHD
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6. Types of Variables Willet et al. (1995)
Explanatory variable
BMI at age 18
Weight / Height2
QUANTITATIVE
CHD occurrence
Yes or no
CATEGORICAL
Response variable
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7. Distributions
Distributions tell us how often a variable takes on various values (!)
Picture distributions with graphs
Categorical variables: pie charts, bar graphs
Quantitative variables: stemplots, histograms, (next chapter: boxplots)
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8. Types of Solid Waste (Categorical)
Material
Weight (million tons)
Percent
Food scraps
25.9
11.2 %
Glass
12.8
5.5 %
Metals
18.0
7.8 %
Paper, paperboard
86.7
37.4 %
Plastics
24.7
10.7 %
Rubber, leather, textiles
15.8
6.8 %
Wood
12.7
Yard trimmings
27.7
11.9 %
Other
7.5
3.2 %
Total
231.9
100.0 %
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9. Types of Solid Waste (Categorical)
Bar charts: bars do not touch (compare histograms)
Pie charts: Use Excel or Applet
Percentages must add to 100%
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10. Body Weight (Quantitative)
n = 53 students
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11. Body Weight (Quantitative) Histogram
HS 67 Lectue Notes
Thursday, November 22, 2018
Body Weight (Quantitative) Histogram
Create class interval frequency table
Approx 4 to 12 non-overlapping class-intervals
Tally frequencies and proportions
Wt. interval
Frequency %
100 – 119 7
13.5%
120 – 139 12
23.1
140 – 159
13.5
160 – 179 8
15.4
180 – 199
200 – 219 4
7.7
220 – 239 1
1.9
240 – 259
0.0
260 – 279
TOTAL 52
100%
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12. Body Weight (Quantitative) Histogram
HS 67 Lectue Notes
Thursday, November 22, 2018
Body Weight (Quantitative) Histogram
Draw histogram (frequencies and/or proportions) and label axes
Number of students
100
120
140
160
180
200
220
240
260
280
Weight (pounds)
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Chapter 1

13. Body Weight: Stem-and-Leaf
Separate each value into stem value (first one or two significant digits) and leaf value (next significant digit)
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14. Include “axis multiplier” Write leaf values next to stem
HS 67 Lectue Notes
Thursday, November 22, 2018 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Pounds(×10)
Draw “stem”
Label stem
Include “axis multiplier”
Write leaf values next to stem
192 5
152 2
135 2
The student should construct a stem & leaf plot here using the first two digits as the stem and the last digit as the leaf. The shape of the stem & leaf plot should look similar to the bar graph shown on an upcoming slide.
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Chapter 1

15. Plot one leaf per data point Then sort leaves in rank order
HS 67 Lectue Notes
Thursday, November 22, 2018
11 009
14 08
16 555
19 245
20 3
21 025
22 0 23 24 25
26 0
Pounds(×10)
Plot one leaf per data point Then sort leaves in rank order
The student should construct a stem & leaf plot here using the first two digits as the stem and the last digit as the leaf. The shape of the stem & leaf plot should look similar to the bar graph shown on an upcoming slide.
Chapter 1
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Chapter 1

16. Each Stemplot will differ!
Key: select the correct axis multiplier before breaking values in stem & leaf values
Think of the stemplot as a histogram with between 4 – 12 stem “bins”
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17. Second Example (n = 8)
Data (average coliform count): 1.47, 2.06, 2.36, 3.43, 3.74, 3.78, 3.94, 4.42
Stem = ones-place values
Leaves = tenths-place
Truncate extra digit (e.g., 1.47  1.4) The book rounds but we shall truncate
Do not plot the decimal
|1|4 |2|03 |3|4779 |4|4 (×1)Coliforms
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18. Third Example (n = 25) Data & stemplot Split stem values
|1|4789 |2| |3| (×1)
Too squished!
Split stem values
First “1” on stem holds leaves between 0 to 4
Second “1” on stem holds leaves between 5 to 9
Etc.
|1|4 |1|789 |2|2234 |2|66789 |3| |3|5678 (×1)
Notice shape (negative skew)
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19. Interpreting Stemplots
HS 67 Lectue Notes
Thursday, November 22, 2018
Interpreting Stemplots
Shape: Symmetrical? Mound(s)? Tails?
Central location (the book uses the midpoint)
Spread (for now use range; better methods next week)
Outliers: fall outside regular pattern
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Chapter 1

20. Interpreting Stemplots
10|0166
11|009
12|
13|00359
14|08
15|00257
16|555
17|000255
18|
19|245
20|3
21|025
22|0
23|
24|
25|
26|0
(×10)
Shape: tail toward larger numbers  positive skew
Center: n = 53  use the 26.5th ranked value  between 157 & 165
Spread: 100 to 260
Outlier: “260” seems out there
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21. Back-to-Back Stemplots
Women | | Men
|0|
|0|9
|1|
8|1|
|2|
|3|
minutes
(×100)
Data = Exercise 1.38 on page 35
I’ve plotted the first value for women (180 minutes) and the first value for men (90 minutes)
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22. Interpreting Histograms Example: 7th Grader Vocabulary Score
Shape: symmetrical
Center: around 7
Spread: from 2 to 12
Outlier: 12(?)
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