2.2 Graphical Displays of Distributions
Recall from the last section that there are two types of data: _____________ (categorical) and
______________ (numerical). It is important that you can differentiate between these types of
variables.
Quantitative variables can be further classified as either _______________ or _________. If the
numerical data can take on any value on a given interval, the variable is _______________. Examples
are height, weight, inflation rate, and _________________.
If the numerical data cannot take on every value within their range, the variable is ___________.
Examples are the number of cylinders in a car and the sizes of a collection of wrenches (only values that
are a multiple of
1
16
of an inch).
On the AP Statistics exam, interpretation of graphical display is crucial, but occasionally you are asked to
make a plot as well as interpret it. Always remember to include scales and labels on all graphs.
These are the standard plots used to display a single variable:
Qualitative Variables
Bar chart
Quantitative Variables
Dot Plot
Stemplot (stem-and-leaf plot)
Histogram
Cumulative frequency plot (section 2.4)
Boxplot (box-and-whiskers plot) (section 2.3)
Bar Charts
When to use: categorical data
How to draw:
1. Write the category names below the horizontal axis at regularly spaced intervals.
2. Label the scale on the vertical axis using either frequency or relative frequency.
3. Center each bar over the category labels. Draw each bar with a blank space between it. All bars
should have the same width so that the height and the area of the bar are proportional to
frequency and relative frequency. The order of the bars, technically, is irrelevant.
Example: page 53, P13
Dot Plots
When to use: small numerical data sets
How to Construct:
1. Draw a horizontal axis and mark it with an appropriate measurement scale.
2. Locate each value in the data set along the scale, and represent it by a dot. If there are two or
more observations with the same value, stack the dots vertically.
Example: page 52, P7.
Stemplots
When to use: numerical data sets with a small to moderate number of observations.
How to construct:
1. Select one or more leading digits for the stem values. The trailing digits become the leaves.
2. List possible stem values in a vertical column.
3. Record the leaf for every observation as they appear beside the corresponding stem value.
4. Redo the plot, ordering the leaves.
5. Indicate the units for stems and leaves someplace in the display.
Example: page 52, P11.
Histogram
When to use: continuous numerical data. Even works well for large data sets.
How to construct:
1. Draw a horizontal scale, and mark the boundaries of the class intervals on the scale.
2. Draw a vertical scale, and mark it with either frequency or relative frequency.
3. Draw a rectangle for each class directly above the corresponding interval (so the edges are at
the class boundaries).
4. The height of each rectangle is the corresponding frequency or relative frequency.
Example: page 52, P8.
Comparison of Graphical Displays
These plots all give some indication of the shape, center, and spread of the data. You should choose the
one that best meets the needs of the situation.
Plot Type
Bar Chart
Dot Plot
Stemplot
Histogram
Cumulative Frequency Plot
Boxplot
Advantages
 Only way to display categorical
data (besides a pie chart)
 Shows the shape of the distribution
nicely
 Can be used for large or small data
sets
 Preserves at least two digits of the
actual numerical values of the data
 Can be used for small to moderate
data sets
 Can be made quickly by hand
 Most useful for moderate to large
data sets
 Shows the relative standing of an
individual observation
 Provides a quick summary of
location, spread, and possible
skewness
Disadvantages
 Does not preserve the exact
numerical values in the data
set
 Best made by a computer or
calculator
 Does not give detailed
information on shape
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How to construct