AP STATISTICS
CHAPTER 4 REVIEW
created by
Daniel Ho and
Sachin Mehta
Betters
2 nd period
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
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
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
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)
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 of f 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
11.
PROBLEM ELEVEN
Gasoline. In June 2004, 16 gas stations in Ithaca, NY,
posted these prices for a gallon of regular gasoline.
2.029
2.119
2.259
2.049
2.079
2.089
2.079
2.039
2.069
2.269
2.099
2.129
2.169
2.189
2.039
2.079
a) 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.
b) Describe the shape, center, and spread of this
distribution.
c) What unusual feature do you see?
PROBLEM ELEVEN ANSWER
a) 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.
Stem
Leaves
2.2 6 5
2.2
2.1 6 8
2.1 1 2
2.0 7 6 8 7 9 7
2.0 2 3 4 3
2.1|7 = $2.179
b) 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.
c)
What unusual feature do you see?
There is a gap; no stations charge between $2.19 and $2.25 .
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:
a) Comment on this graph.
b) Create your own histogram of the data
PROBLEM FIFTEEN ANSWER
a) 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.
b) Create your own histogram of the data.
6
Frequency
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Home Runs
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