Measure of central tendency

1. MEASURE OF CENTRAL
TENDANCY
By Saim waheed and Muqadas Fatima

2. PARTS
MEASURE OF CENTRAL TENDANCY
MEAN MODE MEDIAN

3. MEAN
•. The mean is simply the sum of the values
divided by the total number of items in the
set.

4. Advantages
•It is easy to understand and easy to
calculate.
•It is capable of further mathematical
treatment.

5. Disadvantages
•mean cannot be obtained if a single
observation is missing or lost.

6. UNGROUPED DATA
Mean =
Xn
n

7. Example of Ungrouped Data
• Numbers = 6, 11, 7
• Add the numbers: 6 + 11 + 7 = 24
• Divide by how many numbers (there are 3 numbers): 24 / 3 = 8
The mean is 8

8. GROUPED DATA
Mean =
𝑓𝑥
n
• To calculate the mean of grouped data, the first step is to determine
the midpoint. (Midpoint formula L.L+U.L/2) These midpoints must
then be multiplied by the frequencies of the corresponding classes.
The sum of the products divided by the total number of values will
be the value of the mean

9. Example of Grouped Data
Class X (L.L+U.L/2) f fX
1-5 3 3 3x3=9
6-10 8 2 2x8=16
11-15 13 8 8x13=104
16-20 18 7 7x18=126
21-25 23 4 4x23=92
∑f=24 ∑Fx=347

10. Calculation
= 14.458
X =
∑fX
n
=
347
24

11. Uses of Mean
•It use for making decisions about wages,
production and purchasing.
• It can also be valuable in day-to-day
operations that involve data

12. Mode
•The mode is the most frequently occurring
value.

13. Advantages
Mode is easy to calculate.
Mode can be conveniently located.

14. Disadvantages
 It is not capable of further mathematical
treatment.

15. UNGROUPED DATA
The most frequent and repeated numbers or
values is mode in ungrouped data

16. Example of Ungrouped data
Numbers = 12,13,12,113,12,1,1,3,4.
The Mode is 12

17. GROUPED DATA
•The maximum frequency is mode in
grouped data.

18. Formula of Grouped Data
Mode = l +
fm−f1
2fm−f1−f2
× h
• l = lower class boundary of modal class.
• h = class interval of modal class.
• fm = frequency of modal class.
• f1 = frequency of the class preceding modal class.
• f2 = frequency of the class succeeding the modal class

19. Example of Grouped data.
Class interval Frequency Class boundaries
1-3 2 0.5-3.5
4-6 3 3.5-6.5
7-9 5 6.5-9.5
10-12 4 f1 9.5-12.5
13-15 6 f 12.5-15.5
16-18 2 f2 15.5-18.5
19-21 1 18.5-21.5

20. Calculation
l=12.5, h=3, f=6, f1=4, f2=2
Mode = l +
fm−f1
2fm−f1−f2
× h
Mode = 12.5 +
6−4
2(6)−4−2
× 3
Mode = 12.5 +
2
12−6
× 3
Mode = 13.5

21. Uses
•It is used in models of cars or
flavours of soda (beverages
company).

22. Median
•The median is the value in the middle of a
data set, For a small data set, first you count
the number of data points (n) and arrange
the data points in increasing order.

23. Advantages
• It is easy to understand and easy to
calculate.
•Can be determined graphically.

24. Disadvantages
•In case of even number of observations
median cannot be determined exactly.
•It is not capable of further mathematical
treatment.

25. If Two Numbers or even numbers in the
middle
•In that case we find the middle pair of
numbers, & then find the value that is half
way between them. This is easily done by
adding them together and dividing by 2 .

26. Example.
3, 13, 7, 5, 21, 23, 23, 40, 23, 14, 12, 56, 23, 29
In order
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56
21 + 23 = 44
Then 44 ÷ 2 = 22

27. Uses
•Median helps the employees to
know the middle point of their
salaries in their careers