Graphing Data
Unit 2

Sometimes it is easier to identify patterns of a
data set by looking at a graph of the frequency
distribution. One such graph is a frequency
histogram.
◦ A frequency histogram is a bar graph that represents the
frequency distribution of a data set. A histogram has the
following properties.
◦
1. The horizontal scale is quantitative and measures the
data values
2. The vertical scale measures the frequencies of the
classes.
3. Consecutive bars must touch .
In a histogram the consecutive bars must touch, must
begin and end at class boundaries instead of the class
limits. Class boundaries are the numbers that
separate classes without forming gaps between them.
You can mark the horizontal scale either at the
midpoints or at the class boundaries.
Graphs of Frequency Distributions
Find the Class Boundaries
Class
Class
Boundaries
Frequency
7-18
19-30
6.5-18.5
18.5 – 30.5
6
10
31-42
43-54
55-66
67-78
79-90
30.5-42.5
42.5-54.5
54.5-66.5
66.5-78.5
78.5-90.5
13
8
5
6
2
To find the class boundaries, take the distance from the upper limit of
the first class and subtract it from the lower limit of the second class.
( 19-18=1) Half this distance is 0.5. So, the lower and upper
boundaries of the first class is 6.5 – 18.5
Constructing a Frequency
Histogram
Interpretation: From either histogram you can see that more than
half of the subscribers spent 19 and 54 minutes on the internet during
their most recent session.
Another way to graph a frequency
distribution is to use a frequency
polygon.
Because the graph should begin and end on the horizontal axis, extend the left side to
one class width before the first class midpoint and extend the right side to one class width
after the last class midpoint.
Other graphs

A cumulative frequency graph or ogive is a
line graph that displays the cumulative
frequency of each class at its upper class
boundary. The upper boundaries are marked
on the horizontal axis, and the cumulative
frequencies are marked on the vertical axis.
Step 1: Draw and label the x and y axis.
Step 2: Choose a suitable scale for the
frequencies or cumulative frequencies,
and label it on the y axis.
 Step 3: Represent the class boundaries
for the histogram or ogive, or the
midpoint for the frequency polygon, on
the x axis.
 Step 4: Plot the points and then draw the
bars or lines.


Constructing Statistical Graphs

The previous graphs were constructed by
using frequencies in terms of raw data.
These distributions can be converted to
distributions using proportions instead of
raw data as frequencies. These types of
graphs are called relative frequency
graphs.
Relative Frequency Graphs