AP Statistics
CH. 4 Displaying Quantitative Data
By. Jamie Morreale and Thulasi Thiviyanathan
What is a Histogram?
● Histograms plot the bin counts
as the height of bars
● The bins and the counts in each
bin give the distribution of the
quantitative variable
● Relative Frequency Histogram- displays
the percentage of cases in each bin
instead of the count
How to make a Histogram
•Used with numerical data
•The Bars touch
•There are two types
–Discrete-bars which are centered over discrete values
–Continuous-bars cover a class (interval) of values
What is a Stem-and-Leaf Display?
Stem-and-leaf displays- contain all the information found in a histogram and,
when carefully drawn, satisfy the area principle and show the distribution. In
addition, stem-and-leaf displays preserve the individual data values.
What are Dotplots?
● Dotplot is a simple display. It just places a dot along an axis for each case
in the data
● They may be displayed vertically or horizontally
CUSS
Center
Unusual Points
Shape
Spread
Use CUSS when describing a distribution.
Humps and Bumps
Identify if the Histogram has a single, central, or several humps.
Modes are humps
Unimodal- a histogram with one main peak
Bimodal- histograms with two peaks
Multimodal- histograms with three or more peaks
Uniform- a histogram distribution that is roughly flat
Symmetry
Identify if the Histogram is Symmetric
Tails- are the parts that typically trail off on either side. They can be identified
as having long tails or short tails.
Skewed- a distribution is skewed if it’s not symmetric and one tail stretches
out farther than the other.
Skewed Left- when the longer tail stretches to the left
Skewed Right- when the longer tail stretches to the right
Unusual
Outliers- extreme values that don’t appear to belong with the rest of the data.
They may be unusual values that deserve further investigation. or just
mistakes.
Compare the graphs
Compare the two graphs on the number of
male and female patients
What is a timeplot?
Timeplot- displays data that change over time. Often, successive values are
connected with lines to show trends more clearly.
What can go Wrong?
-
Don’t make a histogram of a categorical variable
-
Don’t look for shape, center, and spread of a bar chart
-
Don’t use bars in every display- save them for histograms and bar charts
-
Choose a bin width appropriate to the data
-
Avoid inconsistent scales
-
Label Clearly
HW Problem #35
7
3
45
3
222
10
3
01
98
3
8
777
2
7
2
2
222
11
2
0
999888
1
77776
1
U.S. Cars
44
67
According to the data U.S. car milage have
a lower center and is skewed to the right.
The mode is near 19 mpg. Others have
more cars in their category with a mode at
32 mpg and another mode at 22 mpg.
Others
3
1 l 6 means 16 mpg
HW Problem #37
8
0148
7
9
6
02 3
5
6
4
3
25
2
8
2 l 8 means $28
thousand/mW
b. The graph is
skewed to the left
and also has
some gaps.
d. According to the
timeplot, the cost is
generally
increasing
overtime.