1. AP Statistics chapter 4 review
created by Daniel Ho and Sachin Mehta
Betters
2nd period

2. Displaying quantitative data
Large groups of data are difficult to comprehend without summarization…
visual aids such as pie and bar charts provide a solution, but are for categorical data...
THUS, we explore various graphs that can effectively display quantitative data in this chapter

3. Histogram data should be divided into equal width groups, or bins
bins and count of data presents distribution
a histogram plots the counts in each bin as height on a graph
a relative frequency histogram displays the percentage of each bin instead of the exact amount
percentiles are the percent of data that is at or below a certain value.
quartiles are located every
25% of the data.
interquartile range is the range of the
middle half of the data.
bars on a histogram touch
discrete – bars are centered over
distinct values
continuous – bars cover an interval
of values

4. Stem and leaf displays
stem and leaf displays, like a histogram, show distribution, but present individual data as well
each value is cut into leading digits (stems) and following digits (leaves)
the bins are labeled by the stems
each leaf can only be one digit

5. Dot plots
a dot plot is a display where a dot represents a case along an axis (can be both vertical or horizontal)
shows both data distribution and individual cases of data in each bin
-- TIME PLOTS --
although not a dot plot, time plots show data and trends over time (see above)

6. Shape, center, and spread
distribution of data is described by CUSS – center, unusual points, shape, and spread
humps in the graphs are called modes, and are specified by classic prefixes such as unimodal, bimodal, etc. no humps is called uniform
symmetry is important to describing data; graph is symmetric if it can be mirrored across a vertical line
If the data tapers off to a side, it is referred to as skewed in the direction of the taper (the narrow side is called the tail)
unusual points to look out for are outliers, points that stand far away from distribution, and gaps

7. Problem eleven
11.
Gasoline. In June 2004, 16 gas stations in Ithaca, NY, posted these prices for a gallon of regular gasoline.
Make a stem-and-leaf display of these gas prices. Use split stems; for example, use two 2.1 stems. One for prices between $2.10 and $2.149, the other for prices $2.15 to $2.199.
Describe the shape, center, and spread of this distribution.
What unusual feature do you see?
2.029
2.119
2.259
2.049
2.079
2.089
2.039
2.069
2.269
2.099
2.129
2.169
2.189

8. Problem eleven ANSWER
Make a stem-and-leaf display of these gas prices. Use split stems; for example, use two 2.1 stems. One for prices between $2.10 and $2.149, the other for prices $2.15 to $2.199.
Describe the shape, center, and spread of this distribution.
The distribution of gas prices is skewed to the right, centered around $2.10 per gallon, with most stations charging between $2.05 and $2.13. The lowest and highest prices were $2.03 and $2.27.
What unusual feature do you see?
There is a gap; no stations charge between $2.19 and $2.25.
Stem
Leaves
2.2 6 5
2.1 8 1 2
2.0 7 9 3 4
2.1|7 = $2.179

9. Problem FIfteen
15. Home runs, again. Students were asked to make a histogram of the number of home runs hit by Mark McGwire from 1986 to 2001 (see Exercise 13). One student submitted the following display:
Comment on this graph.
Create your own histogram of the data

10. Problem Fifteen ANSWER
Comment on this graph.
This is not a histogram. The horizontal axis should split the number of home runs hit in each year into bins. The vertical axis should show the number of years in each bin.
Create your own histogram of the data.