Course Title: Business Statistics

BBA (Hons)

2 nd Semester

Course Instructor: Atiq ur Rehman Shah

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

+92-345-5271959

aatresh@gmail.com

Learning Objective

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

Grouped Frequency Distribution

Raw Data: IT Department Graduate Level (MCS)

2.14 3.73 3.43 3.28

2.04 2.83 3.13 3.11

2.52 3.98 2.73 2.04

4.00 3.45 3.37 2.00

3.31 2.96 3.16 3.52

2.54 2.49 2.15 3.75

2.85 2.26 1.85

Total Number of Observations (N): 27

Minimum Value: 1.85

Maximum Value: 4

Range: 2.15

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

K- Number of classes

N- Total Number of observations.

In this project, 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 value

Range= 4 - 1.85 = 2.15

Range = 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

= 0.358333

The approximate class width that is therefore used is 0.35

Class Width = 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 were made like this:4- 0.35 = 3.653.65- Becomes the lower limit4- Is the upper limit

The next class is calculated by:3.64-0.35= 3.293.64- Upper limit3.29- Lower limit

The next class is calculated by:3.28-0.35 = 2.933.28- Upper limit2.93 Lower limit

This process is continued until the last class is made.2.20-0.35 = 1.852.20- Upper Limit1.85- Lower Limit