Frequency
Distribution Graphs (Visualizations)
Numeric and Ordinal Variables

 Histograms
 A histogram is used to portray the (grouped) frequency
distribution of a variable at the interval or ratio level
of measurement. It consists of vertical bars drawn above
scores (or score intevals) so that
 The height of the bar corresponds to the frequency
 The width of the bar extends to the real limits
of the score (interval)
In ViSta, these intervals are called "BINS".
Example: Data and frequencies for example given
by Gravetter & Wallnau on page 39.
Scores on a 10point quiz. 
Frequency Table 


Here is one of the histograms produced by ViSta of these
data. This histogram is based on the frequency table given
above.
Histogram 

Note that the histogram shown here (which is produced
by ViSta) does not have exactly the same intervals as
the table, although the frequencies are the same.
This is because the histogram follows somewhat different
rules for constructing intervals than those given above
(which are used for the table).
Since the rules are somewhat arbitrary, neither the
plot nor the table are "wrong". They're just different.
However, for homework problems from the book we should
follow the rules given in the book.
Also, recall the fact that different intervals (bins)
produce histograms that can look very different. Some
may be misleading, but we don't really know which.
The BinWidth button lets you change the intervals
dynamically to see what other histograms look like.
Here is ViSta's help information for Histograms:
 Hollow Histograms
 A Hollow Histogram shows the same information
as a histogram or a frequency polygon. It
is simply the histogram drawn without including the sides
of the bars.
Here is the hollow histogram for the data given above:
Hollow Histogram 

ViSta 5.2 can do hollow histograms. They are produced
by clicking on the Plots button at the bottom of
the window.
 Frequency Polygons
 A frequency distribution graph pictures the (grouped)
frequency distribution of a variable at the interval or
ratio level of measurement, using a line connecting dots
rather than bars. It is drawn by locating dots and connecting
them so that
 The dot is centered above the score (the center
of the bin)
 The height of the dot corresponds to the frequency.
 A continuous line is drawn connecting the dots.
 Gravetter and Wallnau suggest that the line be drawn
down to the xaxis (at zero) at each end of the range
of scores. This is not done here, as it can be very
misleading.
 Example: The same data are used here as for the
histogram.
Frequency Polygon 

This frequency plot shows the same data as used for
the histogram (and has the same intervals).
ViSta 5.2 can do frequency plots. They are
produced by clicking on the Plots button at the
bottom of the window.
 Dotplots
 A dotplot uses dots to show where the scores in a distribution
are. This does not portray frequencies, but the actual
observations, although by observing the density of thge
dots one can see the frequency distribution. The dots
are plotted against their actual data values on a vertical
(sometimes horizontal) scale. Sometimes the dots are "jittered"
by adding a small random value to the horizontal axis
so that the dots don't overlap. A sidebyside dot plot
shows two or more dotplots sidebyside.
Sidebyside Dot Plot
Psych 30 GPA by Gender 

This sidebyside dot plot uses data gathered in this
class. It shows the GPA of the students in the class
for both previous years, classified by Gender. We can
see that the Males tend to have a higher GPA than the
Females.
 Boxplots
 A boxplot (also called a boxandwhisker plot) pictures
the (grouped) frequency distribution of a variable at
the interval or ratio level of measurement. It uses a
box and lines to create a schematic of the frequency distribution.
The box shows the main "clump" of scores, the dots show
where the actual data are, and the horizontal lines show
the scores at the middle, the upper and lower quarters
of the distributions, and the upper and lower tenths of
the distribution. Shown here is a boxandwhisker plot,
since it has a vertical line (whisker) connecting the
upper and lower horizontal lines. This is also a sidebyside
boxandwhisker plot, since it shows two or more boxplots
sidebyside.
SidebySide Box and Dot Plot
Psych 30 GPA by Gender 

 The box covers the middle half of the data (the
upper and lower edges of the box lie at the upper
and lower quarters (called upper and lower quartiles).
 The line inside the box is at the middle score (called
the median).
 The lines outside the box show the upper and lower
10% (called upper and lower deciles).
 The width of the box is proportional to the number
of scores in the distribution. There are more females
than males, so the female box is wider.
This boxplot shows the Psych 30 GPA by Gender data
that we used for the dot plot.
 Diamond Plots
 A Diamond Plot is similar to a boxplot. It pictures
the (grouped) frequency distribution of a variable at
the interval or ratio level of measurement. It uses a
diamond, dots and a line to create a schematic of the
frequency distribution. The diamond shows the main "clump"
of scores, the dots show where the actual data are, and
the line show the middle of the distribution is.
Sidebyside Diamond and Dot Plot
Psych 30 GPA by Gender 

 The diamond covers the data between plus and minus
one standard deviation.
 The line inside the box is at the average score
(called the mean).
This boxplot shows the same data as used for the histogram
and frequency plot.
Here is ViSta's help information for Box, Diamond
and Dot plots:
 Quantile Plots
 A Quantile Plot (QPlot) pictures the (grouped) frequency
distribution of a variable at the interval or ratio level
of measurement. It represents a variable's distribution
by plotting each observed value against the fraction of
the data that is smaller than the observed value. The
fractions are called quantiles. The jagged line represents
the variable's distribution.
Quantile Plot
Psych 30 GPA for Females 

Here is ViSta's help information for Quantile plots:
 Normal Probability Plots
 A Normal Probability Plot (NPPlot) pictures the (grouped)
frequency distribution of a variable at the interval or
ratio level of measurement. It represents a variable's
distribution by plotting each observed value against the
Zscore that would be obtained for the value under the
assumption of normality. This is done by using the QPlot's
"fraction of data" as a probability under the assumption
of normality to obtain a normallydistributed Zscore.
The jagged line represents the variable's distribution,
and the straight line represents a normal distribution.
Normal Probability Plot
Psych 30 GPA for Females 

Here is ViSta's help information for Normal Probability
plots:
 QuantileQuantile Plots
 A QuantileQuantile Plot (QQPlot) represents the relationship
between the distributions of two variables, each at the
interval or ratio level of measurement. The jagged line
represents the relationship between the two variables'
distributions. The line is constructed by plotting the
quantiles of one variable versus those of the other. The
quantiles of a variable are the fraction of the data that
is smaller than each observed value. The two variables
do not have to have the same number of observations. If
they dont, interpolation is used.
QuantileQuantile Plot
Psych 30 GPAMales and Females 

Here is ViSta's help information for QuantileQuantile
plots:

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