# Module On Measures Of Central Tendency

Topics: Mean, Mode, Median Pages: 39 (1996 words) Published: February 9, 2015
Module on Measures of
Central Tendency

Measures of Central
Tendency
There are many ways of describing of a
given set of data. A good number of descriptive
measures exist in statistics whose use depends
largely on the nature of data and the intended
purpose of the description. This measure is the
measures of position or central tendency, it is
use to see how a large set of raw materials can
be summarized so that the meaningful essential
can be extracted from it.
The most commonly measures of central
tendency are the mean, median, and mode.

Properties of the Arithmetic Mean

easy to compute
easy to understand
valuable in statistical tool
strongly influence by extreme values,
this is particularly true when the number
of cases is small
cannot be compute when distribution
contains open-ended intervals

Uses of Mean

for interval and ratio measurement
when greatest sampling stability is
desired
when the distribution is symmetrical
when we want to know the “center of
gravity” of a sample

The Arithmetic Mean (X)
The most popular and useful measure of central tendency is the arithmetic mean, which simply refer to as the mean. Widely referred to in everyday usage as the average.
The mean of a set of measurement is defined as,
sum of measurements
mean = -----------------------------------number of measurements In formula form,
 Xi
X = --------N
Where:

N = total number of measurements
X = represent the mean
Xi = represents the individual scores

The symbol  is a Greek letter sigma, which means sum of. In plain language, the arithmetic is obtained merely by adding the individual scores and dividing the sum by the number of scores.

Mean (ungrouped data)
 Xi

X1 + X2 + X3 + X4 +

X5 + … + Xn

X = ---------------=
-----------------------------------------------------N

N

Raw data: 15
Xi
X = ------------------- =
N

16

19

20

18

15 + 16 + 19 + 20 + 18
--------------------------------------------------------------5

= 17.6

Some values sometimes are given
importance than others. In such instance, the
weighted mean is computed.
The formula in computing the weighted
mean is,
WX
X = ----------n
where: W = weight of each item or
value
X
= represent each of the
items
n
= total number of
weights

Example: Determine the weighted mean if,
500 bags were sold at P250.00 each, 350
bags at P200.00 each , 200 bags at P150.00
each , 150 bags at P100.00 each and 50 bags
at
P80.00 each.
Solution:
[500 x 250] + [350 x 200] + [200 x 150] + [150 x 100] + [50 x 80]
X = --------------------------------------------------------------------------------500 + 350 + 200 + 150 + 50 P 244,000.00
X = -------------------1250
X = P195.20

Methods of Computing Mean of
a Grouped Distribution
There are two methods that can
be used in calculating the mean of
a grouped distribution. One
method is called the long method
and the other is called the short or
coded deviation method

Long Method
 f midpoint
X = ------------------N

Where:
 f midpoint = algebraic sum of all the
product of frequency and the midpoint
N = number of cases or
observations

Example: Find the mean of the following distribution.

X
50
47
44
41
38
35
32
29
26
23

f
52
49
46
43
40
37
34
31
28
25

2
2
1
1
5
8
5
1
4
2
N = 31

midpoint
50 – 52
47 – 49

2
2

44 – 46
41 – 43

1
1

38
35
32
29

– 40
– 37
– 34
– 31

5
8
5
1

26 – 28

4

51
4
8
45
42
39
36
33
30
2
2
74

X
fmidpoint
50
47
44
41
38
35
32
29
26
23

52
49
46
43
40
37
34
31
28
25

f
2
2
1
1
5
8
5
1
4
2
N = 31

midpoint
51
48
45
42
39
36
33
30
27
24

102
96
45
42
195
288
165
30
108
48
 f midpt = 1119

By long method;
 f midpoint
X =...