Course Title: Business StatisticsBBA (Hons)

2nd SemesterCourse Instructor: Atiq ur Rehman Shah

Lecturer, Federal Urdu University of Arts, Science & Technology, Islamabad

+92-345-5271959aatresh@gmail.com

Learning Objective

• Concept about No of observations, Maximum and minimum value,• Frequency distribution and cumulative Frequency distribution • Determine the range of variation• Class width determination• Location of class limit

Raw Data: IT Department Graduate Level (MCS)

Maximum Minimum

Number of observations = 27

Frequency Distribution

• A representation, either in a graphical or tabular format, which displays the number of observations within a given interval.

• The intervals must be mutually exclusive.

Steps:

1. Deciding number of classes into which the data are to be grouped

• This is done with a simple formula.K = 1 + 3.3Log N

• Where K is Number of classes and N is the Total Number of observations.

• In this example, the classes were found using this formula.

K= 1 + 3.3 Log (27)K= 5.7

• Rounding that off to the next whole number got the number of classes. Which is 6.

• Therefore Number of Classes = 6

2. Determine the range of variation• “This is the difference between the largest

and the smallest value in the data.”4- Largest value1.85- Smallest valueSo, Range= 4 - 1.85Range = 2.15

3. Class width determination• Determining the approximate width of the classes can be

done by dividing the Range by Number of Classes.

Range- 2.15, Number of Classes- 6 Class width(Approximate) = 2.15/6

= 0.35The approximate class width therefore used is 0.35

4. Location of class limit• The largest value in the data is 4, and therefore that is the upper limit of

the last class in the data. The class width can then be subtracted from each limit until the minimum value is accommodated in the first class.

The classes are made like this:4- 0.35 = 3.65

» 3.65- Becomes the lower limit» 4- Is the upper limit

• The next class is calculated by:3.64-0.35= 3.29

» 3.64- Upper limit» 3.29- Lower limit

• The next class is calculated by:3.28-0.35 = 2.93

» 3.28- Upper limit» 2.93 Lower limit

• This process is continued until the last class is made.

2.20-0.35 = 1.85» 2.20- Upper Limit» 1.85- Lower Limit

5. Distributing data into appropriate classes