Grouped Frequency Distribution

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

1. Course Title: Business Statistics
BBA (Hons)
2
nd
Semester
Course Instructor: Atiq ur Rehman Shah
Lecturer, Federal Urdu University of Arts, Science &
Technology, Islamabad
[phone]
[email protected]

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

3. 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.

4. 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 value
1.85- 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

5. 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 = 3.65
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

6. 2.20- Upper Limit
1.85- Lower Limit

7. 2.20- Upper Limit
1.85- Lower Limit