2.3 Stats

1. SECTION 2-3
Histograms, Frequency Polygons, and
Ogives

2. 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?

3. 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

4. Three Most Common Types of
Graphs
 Histogram
 Frequency Polygon
 Cumulative Frequency Graph (Ogive)

5. 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.

6. Histogram Example

7. Histogram Example
Example 2-4 on p.48

8. 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)

9. Frequency Polygon Example
0
2
4
6
8
10
12
14
16
18
20
102 107 112 117 122 127 132 137

10. Frequency Polygon Example
Example 2-5 on p.50

11. 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.

12. 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.

13. 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

14. 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

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

16. #1 - Histogram

17. #1 – Frequency Polygon

18. #1 - Ogive

19. #3 - Histogram

20. #3 – Frequency Polygon

21. #3 - Ogive

22. #7 – Histogram 1

23. #7 – Hisotgram 2

24. #15 – Frequency Table

25. #15 - Histogram

26. #15 – Frequency Polygon

27. #15 – Ogive