Section 2-2
Histograms,
Frequency Polygons
Ogives
Histograms
 The histogram is a graph
that displays data by
using contiguous vertical
bars of various heights to
represent the frequencies
of the classes.
 the x-axis of a histogram
represents quantitative
i.e. numerical values
that are organized in
intervals.
Frequency Histogram
Side by side
Histograms
Side by side Histograms
Bar graph
• A Bar Graph (also called Bar Chart) is a
graphical display of data using bars of different
heights.
• The x-axis will display qualitative i.e. categorical
data.
Bar graph
Histograms
Please refer to the states temperatures
data from section 2-2.
Use your ruler and draw the x and y
axes.
Label each of the axes.
Scale each axes carefully.
Represent the class boundaries on the
x axis.
Represent the frequency on the y axis.
Using the frequencies as the heights, draw
vertical bars for each class.
The Frequency Polygon
The frequency polygon is a graph that
displays the data by using lines to
connect points plotted for the frequencies
at the midpoints of the classes. The
frequencies are represented by the
heights of the points.
Frequency Polygon
Frequency Polygon Superimposed on a Histogram
Constructing a frequency polygon
Step1: Find the midpoints of each class.
Step 2: Draw the x and y axes. Label the x
axis with the midpoint of each class. Scale y
axis appropriately to plot the frequencies.
Step 3: Using the midpoints for the x values
and the frequencies for the y values, plot the
points.
Step 4: Connect the plotted points with line
segments.
The Ogive (pronounced o-jive)
The ogive is a graph that represents the
cumulative frequencies for the classes in a
frequency distribution.
Ogive frequency graphs are constructed
similar to a histogram, with one
exception. In this case the y axis
represents the cumulative frequency.
Cumulative Frequency
Relative frequency graphs
Relative frequency graphs are
constructed similar to a histogram,
with one exception. In this case the
y axis represents the relative
frequency.
Relative Frequency Histogram
Cumulative Relative frequency graphs
Relative cumulative frequency
graphs are constructed similar to a
histogram, with one exception. In
this case the y axis represents the
cumulative relative frequency.
Cumulative Relative Frequency
Graphing Calculator
• Page 61
– Constructing histograms from raw data
• Page 62
– Constructing a Histogram from a
frequency distribution table
Homework:
Read pages 51-60.
Applying Concepts 2-2 page 60
Make sure to answer all questions
completely.
Graphs must be done on graph paper;
make sure to use a ruler.
Homework
Exercises 2-2, page 61 starting
with # 1 every other odd problem.