SECTION 2-3Histograms, Frequency Polygons, and Ogives

Objective: To represent data in frequency

distributions graphically using histograms, frequency polygons, and ogives.

a] What % of Americans find life dull?b] What % of Americans are color blind?c] How many gallons of soda does the average American drink during a year?

Graphs Purpose: To display data to viewer in

pictorial form Used to: Describe or analyze data

Discuss an issue Reinforce a critical point Summarize a data set Discover a pattern or trend over time

Useful in getting the attention of the audience

Three Most Common Types of Graphs

Histogram Frequency Polygon Cumulative Frequency Graph (Ogive)

Histogram histogram: graph that displays the data by

using contiguous vertical bars (unless the frequency of a class is 0) of various heights to represent the frequencies of the classes

To construct a histogram: Draw and label the x and y axes. Represent the frequency on the y-axis and the

class boundaries on the x-axis. Using the frequencies as heights, draw vertical

bars for each class.

Histogram Example

Histogram Example

Example 2-4 on p.48

Frequency Polygon frequency polygon: graph that uses lines that connect

points plotted for the frequencies at the midpoints of the classes; frequencies are represented by the heights of the points

To construct a frequency polygon: Find the midpoints of each class Draw the x and y axes. Label the x-axis with the midpoint of

each class then use a suitable scale for the frequencies on the y-axis.

Using the midpoints for the x values and the frequencies as the y values, plot the points.

Connect adjacent points with line segments. Draw a line back to the x-axis at the beginning and end of the graph (where the next midpoints would be located)

Frequency Polygon Example

102 107 112 117 122 127 132 13702468

101214161820

Frequency Polygon Example

Example 2-5 on p.50

The Ogive (Cumulative Frequency Polygon)

ogive: graph that represents the cumulative frequencies for the classes in a frequency distribution

To construct an ogive: Find the cumulative frequency for each class Draw the x and y axes. Label the x-axis with the class

boundaries. Label the y-axis with an appropriate frequency (don’t use actual frequency numbers-yields uneven intervals or classes)

Plot the cumulative frequency at each upper class boundary

Starting with the first upper class boundary, connect adjacent points with line segments. Extend the graph to the first lower class boundary on the x-axis.

Constructing Statistical Graphs- General Procedures

Draw and label the x and y-axes Choose a suitable scale for the

frequencies or cumulative frequencies, and label it on the y-axis.

Represent the class boundaries for the histogram or ogive, or the midpoint for the frequency polygon, on the x-axis.

Plot the points and then draw the bars or lines.

Relative Frequency Graphs Thus far, frequencies have been used in

terms of raw data. Relative Frequency Graphs convert raw

data to proportions or percentages.

Relative Frequency example on p.54

Distribution Shapes

Bell-shaped: single peak and tapers off at either end Uniform: basically flat or rectangular J-Shaped: Few data values on the left side and increases

as one moves to the right Reverse J-Shaped: Opposite of J-Shaped Right-Skewed: Peak of the distribution is to the left and

the data values taper off to the right (Positively skewed) Left-Skewed: Data values are clustered to the right and

taper off to the left (Negatively skewed) Bimodal: Two peaks of the same height U-Shaped: Peaks at both ends and decreases toward

middle

Assignment: pp. 58-59 # 1,3, 7, 15

#1 - Histogram

#1 – Frequency Polygon

#1 - Ogive

#3 - Histogram

#3 – Frequency Polygon

#3 - Ogive

#7 – Histogram 1

#7 – Hisotgram 2

#15 – Frequency Table

#15 - Histogram

#15 – Frequency Polygon

#15 – Ogive