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This pdf includes the following topics:-

Histogram with examples

The frequency polygon with examples

The Ogive

Cumulative Frequency

Histogram with examples

The frequency polygon with examples

The Ogive

Cumulative Frequency

1.
HISTOGRAMS,

FREQUENCY

POLYGONS, AND

OGIVES

FREQUENCY

POLYGONS, AND

OGIVES

2.
The histogram is a 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.

Example 1

Construct a histogram to represent the data shown for the record high

temperatures for each of the 50 states

bars (unless the frequency of a class is 0) of various heights to represent the

frequencies of the classes.

Example 1

Construct a histogram to represent the data shown for the record high

temperatures for each of the 50 states

3.

4.

5.
2- The Frequency Polygon

The frequency polygon is a graph that displays the data by using lines that

connect points plotted for the frequencies at the midpoints of the classes.

Example 2

Using the frequency distribution given in Example 1, construct a

frequency polygon.

Step 1 Find the midpoints of each class.

The frequency polygon is a graph that displays the data by using lines that

connect points plotted for the frequencies at the midpoints of the classes.

Example 2

Using the frequency distribution given in Example 1, construct a

frequency polygon.

Step 1 Find the midpoints of each class.

6.

7.
Step 4 Connect adjacent points with line segments. Draw a line back to the x

axis at the beginning and end of the graph, at the same distance that the

previous and next midpoints would be located

axis at the beginning and end of the graph, at the same distance that the

previous and next midpoints would be located

8.
3- The Ogive

This type of graph is called the cumulative frequency graph, or ogive.

The cumulative frequency is the sum of the frequencies accumulated

up to the upper boundary of a class in the distribution.

The ogive is a graph that represents the cumulative frequencies for the

classes in a frequency distribution.

This type of graph is called the cumulative frequency graph, or ogive.

The cumulative frequency is the sum of the frequencies accumulated

up to the upper boundary of a class in the distribution.

The ogive is a graph that represents the cumulative frequencies for the

classes in a frequency distribution.

9.
Example 3

Using the frequency distribution given in Example 1, construct an ogive.

Using the frequency distribution given in Example 1, construct an ogive.

10.
Step 3 Plot the cumulative frequency at each upper class boundary, as

shown in Figure a. Upper boundaries are used since the cumulative

frequencies represent the number of data values accumulated up to the

upper boundary of each class.

shown in Figure a. Upper boundaries are used since the cumulative

frequencies represent the number of data values accumulated up to the

upper boundary of each class.

11.
Fig. a

12.
Step 4 Starting with the first upper class boundary, 104.5, connect adjacent points

with line segments, as shown in Figure b. Then extend the graph to the first lower

class boundary, 99.5, on the x axis.

Fig. b

with line segments, as shown in Figure b. Then extend the graph to the first lower

class boundary, 99.5, on the x axis.

Fig. b

13.
Fig. c