Course for Statstics and Probability, Schemes and Mind Maps of Probability and Statistics

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Frequency Distributions

and Graphs

Dr. Nadeem Shaukat

Part-

Organizing Data  Histograms, Frequency Polygons, and Ogives  Other Types of Graphs Introduction

The three most commonly used graphs in research are as follows:

1. The histogram
2. The frequency polygon
3. The cumulative frequency graph, or Ogive For ContinuousData

The histogram is a graph that displays the data by using continuous vertical bars (unless the frequency of a class is 0) of various heights to represent the frequencies of the classes. Histogram The class boundaries are represented on the horizontal axis ( On x-axis ,put class boundaries .On y-axis ,put frequency ).

 (^) Histograms use class boundaries and frequencies of the classes.

Frequency polygons

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. The frequencies are

represented by the heights of the points.

 The class midpoints are represented on the horizontal axis. ( On x-axis ,put class midpoints .On y- axis ,put frequency ).

 Frequency polygons use class midpoints and frequencies

of the classes.

A frequency polygon is anchored on the x-axis before the first class and after the last class.

Cumulative Frequency Graphs Or Ogives

 The ogive is a graph that represents the cumulative

frequencies for the classes in a frequency distribution

 The upper class boundaries are represented on the horizontal axis ( On x-axis ,putupper class boundaries .On y- axis ,put cumulative frequency ).

 Cumulative frequency distribution is a distribution that

shows the number of data values less than or equal t a specific

value.

Class Limits Class Boundaries Frequency 100 - 104 105 - 109 110 - 114 115 - 119 120 - 124 125 - 129 130 - 134 99.5 - 104. 104.5 - 109. 109.5 - 114. 114.5 - 119. 119.5 - 124. 124.5 - 129. 129.5 - 134. 2 8 18 13 7 1 1 Class Boundaries Cumulative Frequency Less than 99. Less than 104. Less than 109. Less than 114. Less than 119. Less than 124. Less than 129. Less than 134.

 (^) Ogives use upper class boundaries and cumulative frequencies of the classes.

Example 2-7:

Construct a histogram, frequency polygon, and ogive using

relative frequencies for the distribution (shown here) of the

miles that 20 randomly selected runners ran during a given

week.

Class

Boundaries

Frequency

Histograms Class Boundaries Frequency ( f ) Relative Frequency 5.5 - 10. 10.5 - 15. 15.5 - 20. 20.5 - 25. 25.5 - 30. 30.5 - 35. 35.5 - 40.

The following is a frequency distribution of miles run per week by 20 selected runners.

 f = 20  rf = 1.

The sum of the relative frequencies will always be 1

Frequency Polygons Class Boundaries Class Midpoints Relative Frequency 5.5 - 10. 10.5 - 15. 15.5 - 20. 20.5 - 25. 25.5 - 30. 30.5 - 35. 35.5 - 40.

The following is a frequency distribution of miles run per week by 20 selected runners.

Use the class midpoints and the relative frequencies of the classes.