Class 3 Measures central tendency 2024.pptx

1. Measures of Central Tendency
Several statistics can be used to represent the
"center" of the distribution. These statistics
are commonly referred to as measures of
central tendency (They are sometimes called
Measures of location).
We shall look at three measures of location and
then discuss their relative merits

2. 1. Arithmetic Mean
The arithmetic mean, or simply called mean, is the
most common measure of central tendency and
the one that can be mathematically
manipulated. It is defined as the average of a set
of measurements.
To distinguish between the mean for the sample
and the mean for the population, we will use the
symbol (x-bar) for a sample mean and the
symbol U ( mu) for the mean of a population

3. Arithmetic Mean for Raw Data
It is always obtained by adding together all of
the measurements and dividing by the total
number of measurements taken.
Mathematically it is given as

4. Examples:
Calculate the arithmetic mean of the following
sample data:
1, 3, 4, 4, 5, 6, 3, 7
Solution:

5. 8
7
3
6
5
4
4
3
1 






8
33
= 4.125

6. 2) 650, 675, 700, 725, 800, 900, 1050, 1125,
1200, 575
Solution:

7. Arithmetic Mean for Grouped Data:
It is always obtained by adding together all of
frequency distribution of the measurements
and dividing by the total frequency of the
measurements taken. Mathematically it is
given as
Examples:

8. Wage in $ 220 250 300 350 375
No. of
Workers
12 15 18 20 5
Find the mean wage of the workers:

9. Wage in $ No. of Workers f x
220 12 2640
250 15 3750
300 18 5400
350 20 7000
375 5 1875
TOTAL 70 20665

10. 5
20
18
15
12
)
5
(
375
)
20
(
350
)
18
(
300
)
15
(
250
)
12
(
220








70
20665
Solution:
=
= $ 295.214
70
20665
= $ 295.214

11. Number of
accidents, xi
Frequency
Fi
f x
0 55 0
1 14 14
2 5 10
3 2 6
4 0 0
5 2 10
6 1 6
7 0 0
8 1 8
TOTAL 80 54
Find the sample mean of the following accidents data.
Solution:
=
= 0.675

12. The mean for Class-interval data
•
Examples

13. The weights of milk deliveries to a processing plant
are shown below (use 5 classes):
45 49 50 46 48 42 39 47 42 51
48 45 45 41 46 37 46 47 43 33
56 36 42 39 52 46 43 51 46 54
39 47 46 45 35 44 45 46 40 47

14. Solution
Class Tally Frequency
(f)
Mid-point
(x)
Fx
33- 37 //// 4 33+37/2=35 35 * 4 =
140
38-42 ///// /// 8 40 320
43-47 //// //// ////
///
19 45 855
48-52 //// // 7 50 350
53-57 // 2 55 110
Total 40 1775

15. 375
.
44
40
1775




f
fx

16. 500<600
400<500
300<400
200<300
100 < 200
Salaries
15
30
25
17
13
Workers
The following table represents the salaries (in dollars) of a group of workers in a company.

17. Solution
Class Frequency(f) Mid-point (x) Fx
100 < 200 13 150 1950
200<300 17 250 4250
300<400 25 350 8750
400<500 30 450 13500
500<600 15 550 8250
Total 80 36700
375
.
44
40
1775




f
fx
(
) =
Mean =36700 / 80 = 458.75