This document provides information about calculating measures of central tendency - mean, median, and mode - for business statistics. It gives examples and explanations of how to calculate the mean by adding all values and dividing by the total number. The median is found by listing values in order and choosing the middle one. The mode is the value that occurs most often. It also shows how to calculate the mean, median, and mode for grouped data using specific formulas.

1. Course Title: Business Statistics
BBA (Hons)
2nd
Semester
Course Instructor: Atiq ur Rehman Shah
Lecturer, Federal Urdu University of Arts,
Science & Technology, Islamabad
+92-345-5271959
aatresh@gmail.com

2. Measure of Central tendency
• Mean
• Median
• Mode

3. The Mean
• It is defined as a value obtained by dividing
the sum of all observations by their number.

4. Example
• 2 Numbers
(With just 2 numbers the answer is easy: go half-way in-
between)
• what is the mean for 3 and 7?
You can calculate it by adding 3 and 7 and then dividing the
result by 2:
(3+7) / 2 = 10/2 = 5

5. • 3 or More Numbers
(You can use the same idea when you have 3 or more numbers)
Example: what is the central value of 3, 7 and 8?
• You calculate it by adding 3, 7 and 8 and then dividing the results by
3 (because there are 3 numbers):
(3+7+8) / 3 = 18/3 = 6

6. The Median
• List all numbers in order and choose the
middle one

7. Example
• Uncle Bob wants to know the median of age at the party, to
choose an activity.
• There will be 6 kids aged 13, and also 5 babies aged 1.
• List the ages in order:
1, 1, 1, 1, 1, 13, 13, 13, 13, 13, 13
• Choose the middle number:
1, 1, 1, 1, 1, , 13, 13, 13, 13, 13
So, the Median age is 13
13

8. • Sometimes there are two middle numbers. Just average
them:
• What is the Median of 3, 4, 7, 9, 12, 15
• There are two numbers in the middle:
3, 4, 7, 9, 12, 15
• So we average them:
(7+9) / 2 = 16/2 = 8
The Median is 8

9. The Mode
• The Mode is the value that occurs most often
• Example: Birthday Activities (continued)
• Group the numbers so we can count them:
1, 1, 1, 1, 1, 13, 13, 13, 13, 13, 13
"13" occurs 6 times, "1" occurs only 5 times, so the mode is 13

10. • Mode can be tricky, there can sometimes be more than one Mode.
• Example: What is the Mode of 3, 4, 4, 5, 6, 6, 7
4 occurs twice but 6 also occurs twice.
(So both 4 and 6 are modes.)
• When there are two modes it is called "bimodal", when there are three or
more modes we call it "multimodal".

11. Grouped Data: Arithmetic Mean
Arithmetic Mean = ΣfX/Σf
where
X = Individual score
f = Frequency

12. • From our previous example about CGPA of
MCS class students,

13. • Arithmetic Mean = ΣfX/Σf
ΣfX = 76.635
Σf = 27
• Arithmetic Mean = 76.635/27
= 2.838
Artimetic Mean for IT Department MCS = 2.838

14. Grouped Data: MODE
• Here,
l = lower limit of modal class
f1 = frequency of modal class
fo = frequency of class preceding the modal class.
f2 = frequency of class succeeding the modal class
h = size of class interval.

15. • Mode for IT Department:
l = 1.85, f1 = 6, fo = 0, f2 = 5, h = 0.35
• Mode = 1.85+[(6-0)/(6-0)+(6-5)](0.35)
= 1.85+(6/7)(0.35)
= 1.85 + 2.1/7
= 2.15
• Mode for IT Department MCS = 2.15

16. Grouped Data: Median
• Median= L + [(n/2-Cfp)/fmed]*W
• Where:
L = Lower limit of median class
Cfp= Cumulative frequency of class preceding the median
class
Fmed= Frequency of the median class
W= Width of the median class (interval)
N= Total number of frequencies
Median for IT department

17. • Median for IT department MCS:
• L = 2.57, Cfp= 11, Fmed= 3, W= 0.35, N= 27
Median=2.57+ [(27/2-11)/3)*0.35
= 2.57+ 13.5-11/3 *0.35
= 2.57+0.29166
= 2.861
Median for IT Department MCS = 2.86