1. Basic Practice of Statistics - 3rd Edition
Chapter 1
Picturing Distributions with Graphs
BPS - 5th Ed.
Chapter 1
Chapter 1

2. Statistics
Statistics is a science that involves the extraction of information from numerical data obtained during an experiment or from a sample. It involves the design of the experiment or sampling procedure, the collection and analysis of the data, and making inferences (statements) about the population based upon information in a sample.
BPS - 5th Ed.
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3. Individuals and Variables
the objects described by a set of data
may be people, animals, or things
Variable
any characteristic of an individual
can take different values for different individuals
BPS - 5th Ed.
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4. Basic Practice of Statistics - 3rd Edition
Variables
Categorical
Places an individual into one of several groups or categories
Quantitative (Numerical)
Takes numerical values for which arithmetic operations such as adding and averaging make sense
BPS - 5th Ed.
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Chapter 1

5. Distribution
Tells what values a variable takes and how often it takes these values
Can be a table, graph, or function
BPS - 5th Ed.
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6. Displaying Distributions
Categorical variables
Pie charts
Bar graphs
Quantitative variables
Histograms
Stemplots (stem-and-leaf plots)
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7. Histograms For quantitative variables that take many values
Divide the possible values into class intervals (we will only consider equal widths)
Count how many observations fall in each interval (may change to percents)
Draw picture representing distribution
BPS - 5th Ed.
Chapter 1

8. Histograms: Class Intervals
How many intervals?
One rule is to calculate the square root of the sample size, and round up.
Size of intervals?
Divide range of data (maxmin) by number of intervals desired, and round to convenient number
Pick intervals so each observation can only fall in exactly one interval (no overlap)
BPS - 5th Ed.
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9. Stemplots (Stem-and-Leaf Plots)
For quantitative variables
Separate each observation into a stem (first part of the number) and a leaf (the remaining part of the number)
Write the stems in a vertical column; draw a vertical line to the right of the stems
Write each leaf in the row to the right of its stem; order leaves if desired
BPS - 5th Ed.
Chapter 1

10. Weight Data 1 2
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11. Weight Data: Stemplot (Stem & Leaf Plot)
Basic Practice of Statistics - 3rd Edition 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Weight Data: Stemplot (Stem & Leaf Plot)
192 5
152 2
135
Key
20|3 means 203 pounds
Stems = 10’s Leaves = 1’s 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.
BPS - 5th Ed.
Chapter 1
Chapter 1

12. Weight Data: Stemplot (Stem & Leaf Plot)
Basic Practice of Statistics - 3rd Edition
11 009
14 08
16 555
19 245
20 3
21 025
22 0 23 24 25
26 0
Weight Data: Stemplot (Stem & Leaf Plot)
Key
20|3 means 203 pounds
Stems = 10’s Leaves = 1’s
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.
BPS - 5th Ed.
Chapter 1
Chapter 1

13. Extended Stem-and-Leaf Plots
If there are very few stems (when the data cover only a very small range of values), then we may want to create more stems by splitting the original stems.
BPS - 5th Ed.
Chapter 1

14. Extended Stem-and-Leaf Plots
Example: if all of the data values were between 150 and 179, then we may choose to use the following stems:
Leaves 0-4 would go on each upper stem (first “15”), and leaves 5-9 would go on each lower stem (second “15”).
BPS - 5th Ed.
Chapter 1

15. Examining the Distribution of Quantitative Data
Basic Practice of Statistics - 3rd Edition
Examining the Distribution of Quantitative Data
Overall pattern of graph
Deviations from overall pattern
Shape of the data
Center of the data
Spread of the data (Variation)
Outliers
BPS - 5th Ed.
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Chapter 1

16. Basic Practice of Statistics - 3rd Edition
Shape of the Data
Symmetric
bell shaped
other symmetric shapes
Asymmetric
right skewed
left skewed
Unimodal, bimodal
BPS - 5th Ed.
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Chapter 1

17. Symmetric Bell-Shaped
Basic Practice of Statistics - 3rd Edition
Symmetric Bell-Shaped
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18. Symmetric Mound-Shaped
Basic Practice of Statistics - 3rd Edition
Symmetric Mound-Shaped
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19. Basic Practice of Statistics - 3rd Edition
Symmetric Uniform
BPS - 5th Ed.
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20. Asymmetric Skewed to the Left
Basic Practice of Statistics - 3rd Edition
Asymmetric Skewed to the Left
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21. Asymmetric Skewed to the Right
Basic Practice of Statistics - 3rd Edition
Asymmetric Skewed to the Right
BPS - 5th Ed.
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22. Basic Practice of Statistics - 3rd Edition
Outliers
Extreme values that fall outside the overall pattern
May occur naturally
May occur due to error in recording
May occur due to error in measuring
Observational unit may be fundamentally different
BPS - 5th Ed.
Chapter 1
Chapter 1

23. Time Plots A time plot shows behavior over time.
Time is always on the horizontal axis, and the variable being measured is on the vertical axis.
Look for an overall pattern (trend), and deviations from this trend. Connecting the data points by lines may emphasize this trend.
Look for patterns that repeat at known regular intervals (seasonal variations).
BPS - 5th Ed.
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24. Average Tuition (Public vs. Private)
BPS - 5th Ed.
Chapter 1