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

Download Course for Statstics and Probability and more Schemes and Mind Maps Probability and Statistics in PDF only on Docsity!

Frequency Distributions

and Graphs

Dr. Nadeem Shaukat

Part-

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

 Each raw data value is placed into a quantitative or

qualitative category called a class.

 A class then is the number of data values contained in

a specific class called frequency.



A frequency distribution is the organization of raw data in

table form, using classes and frequencies.

Two types of frequency distribution Categorical Frequency Distributions Grouped Frequency Distributions Used for data that can be placed in specific categories (nominal or ordinal level data). When the range of the data is large data is grouped into classes that are more than one unit in width

Grouped Frequency Distributions

 Class limits

 Lower class limit

Upper class limit

Class limits Class boundaries Tally Frequency 24-30 23. 5 -30. 5 /// 3 31-37 30. 5 -37. 5 / 1 38-44 37. 5 -44. 5 //// 5 45-51 44. 5 -51. 5 //////// 9 52-58 51. 5 -58. 5 ///// 6 59-65 58. 5 -65. 5 / 1

Class boundaries

Upper class boundaries

Lower class boundaries

First class second class Lower class Upper class

• In this distribution, the values 24 and 30 of the first class are called “class limits”.
• (^) 24 is the “lower class limit” and 30 is the “upper class limit.”
• (^) The numbers in the second column are called class boundaries.
• (^) The class boundaries are used to separate the class so that there is no gap in frequency distribution. Lower boundary= lower limit - 0. Upper boundary= upper limit + 0.



The lower class limit represents the smallest data value that

can be included in the class.



The upper class limit represents the largest data value that

can be included in the class.

 (^) The class width is found by subtracting the lower (or upper) class limit of one class from the lower (or upper) class limit of the next class. For example: Class limits Class boundaries 24 -30 23.5-30. 31 -37 30.5-37.  (^) Class width=lower of second class limit-lower of first class limit  (^) Class width=upper of first class boundary -lower of first class boundary class width : 31-24 = 7 class width class width

Rules for Classes in Grouped Frequency Distributions

1. There should be 5-20 classes.

2. The class width should be an odd number.

3. The classes must be mutually exclusive.

4 .The classes must be continuous.

5 .The classes must be exhaustive.

6. The classes must be equal in width

(except in open-ended distributions).

Age 10- 20- 30- 40- 50- Age 10- 21- 32- 43- 54- Better way to construct a frequency distribution

Constructing a Grouped Frequency Distribution

1- The following data represent the record high

temperatures for each of the 50 states. Construct a grouped

frequency distribution for the data using 7 classes.

Step 2 : Tally the data.

Step 3 : Find the frequencies.

Class Limits Class Boundaries Frequency Cumulative Frequency 100 - 104 105 - 109 110 - 114 115 - 119 120 - 124 125 - 129 130 - 134

2- The data shown here represent the number of miles per

gallon that 30 selected four-wheel- drive sports utility

vehicles obtained in city driving.

Class Limits Class Boundaries Frequency Cumulative Frequency 12 13 14 15 16 17 18 19

Class Frequency 4-9 2 10-15 4 16-21 3 22-27 8 28-33 5

Find the class boundary , midpoint of the last class

and the class width?