easy and quick access

2. Presentation Topic
MEASURE OF CENTRAL
TENDENCY
o Name of Presenters
 Hafiz Sikander Hayat

3. MEASURE OF CENTRAL
TENDENCY
Introduction
A measure of central tendency is a single value that attempts to describe a set of data
by identifying the central position within that set of data. As such, measures of central
tendency are sometimes called measures of central location. They are also classed as
summary statistics. The mean (often called the average) is most likely the measure of
central tendency that you are most familiar with, but there are others, such as the
median and the mode.
The mean, median and mode are all valid measures of central tendency, but under
different conditions, some measures of central tendency become more appropriate to
use than others. In the following sections, we will look at the mean, mode and median,
and learn how to calculate them and under what conditions they are most appropriate
to be used.

4. MEASURE OF CENTRAL
TENDENCY
 TYPES
1. MEAN
2. MEDIAN
3. MODE

5. MEASURE OF CENTRAL
TENDENCY
 MEAN
The mean (or average) is the most popular and well known
measure of central tendency if we have ‘n’values in a data set they
have values x1,x2…..;xn mean is use for ungroup and group data
MEAN=µ=(X1+X2+….,Xn)/n
 Types
1. Geometric mean
2. Hormonic mean
3. Arithmetic mean

6. MEASURE OF CENTRAL
TENDENCY
 ARITHMETIC MEAN(ungroup data)
o MEAN=µ=µx/n
Example
µ=µx/n
n=5
µ=29/5
MEAN=µ=5.8
X
5
6
9
7
2
TOTAL =29

7. Measures of Central Tendency
ARITHMETIC Mean (GROUP DATA)
MEAN=µ=µFX/µf
MEAN=µ=191/56
MEAN=µ=3.41
X F FX
0 2 0
1 5 5
2 7 14
3 14 42
4 15 60
5 8 40
6 5 30
TOTAL 56 191

8. Measures of Central Tendency
GEOMETRIC MEAN(UNGROUP DATA)
 G.M=antilog(logx)/n
n=4=total number of observation
g.m=antilog(5.3467)/4
g.m=antilog(1.3366)
X LOG (X)
57 1.7558
65 1.8129
12 1.0791
5 0.6989
µx=139 µ(logx)=5.3467
G.M=21.7107

9. MEASURE OF CENTRAL TENDENCY
GEOMETRIC MEAN(GROUP DATA)
G.M=ANTILOG(FLOGX)/µf
G.M=ANTILOG(34.8184)/33
G.M=ANTILOG(1.0551)
CLASS
BOUNDRY
MID POINT
X
F LOG X F(LOGX)
0-4 2 2 0.3010 0.6021
4-8 6 5 0.7781 3.8908
8-12 10 7 1.0000 7.0000
12-16 14 8 1.1461 9.1690
16-20 18 7 1.2552 8.7869
20-24 22 4 1.3424 5.3697
µx=72 µf-33 µ=34.8184
G.M=11.3528

10. MEASURE OF CENTRAL TENDENCY
HORMONIC MEAN(UNGROUP DATA)
H.M=n/µ(1/X)
n=5
H.M=5/0.3031
X 1/X
5 0.2
65 0.0153
29 0.0344
32 0.0312
45 0.0222
µ(1/X)=0.3031
H.M=16.4962

11. MEASURE OF CENTRAL TENDENCY
HORMONIC MEAN(GROUP DATA)
H.M=µf/µ(1/f(1/x))
H.M=22/3.1047 Class
bondry
MID
POINT
X
F 1/X F(1/X)
0-4 2 2 0.5 1.0000
4-8 6 5 0.2 0.8333
8-12 10 7 0.14 0.7000
12-16 14 8 0.125 0.5714
µf=22 µ(F(1/X)
=3.1047
H.M=7.0860

12. MEASURE OF CENTRAL TENDENCY
 MEDIAN(UNGROUP DATA)
The median is the middle score for a set of data that has been
arranged in order of magnitude. The median is less affected by
outliers and skewed data. In order to calculate the median,
suppose we have the data below:
EXAMPLE
65 85 95 75 55
MEDIAN
45 35 25 15

13. MEASURE OF CENTRAL TENDENCY
 MEDIAN(UNGROUP DATA)
 Formula for even numbers
median= n+1/2
Median=39+1/2=20
x
5
6
9
4
8
7
µx=39
Median=9

14. MEASURE OF CENTRAL TENDENCY
 Median(group data)
Median=L+h/f(n/2-c) n=30
Median=n/2=30/2=15
L=95.5,h=5,C=10
Median=95.5+5/10(30/2-10)
CLASS
BOUNDRY
MID POINT
X
F C.F
85.5-90.5 87 6 6
90.5-95.5 93 4 10
95.5-100.5 98 10 20
100.5-105.5 103 6 26
105.5-110.5 108 3 29
110.5-115.5 113 1 30
MEDIAN=98.0

15. MEASURE OF CENTRAL TENDENCY
 MODE
Mode is defined as the most frequent value in a data set
MODE=L+(FM-F1)/(FM-F1)+(FM-F2)XH
MODE=10.25=L=LOWER CLASS LIMIT
FM=17=FREQUENCY OF MODE
F1=12=THE UPPER FREQUENCY VALUE OF MODE
F2=14=THE LOWER FREQUENCY VALUE OF MODE
H=5=CLASS INERVEL
MODE=10.25+(17-12)(17-12)+(17-14)X5
Class boundary F C.B
9.3-9.7 2 9.25-9.75
9.8-10.2 5 9.75-10.25
10.3-10.7 12 10.25-10.75
10.8-11.2 17 10.75-11.25
11.3-11.7 14 11.25-11.75
11.8-12.2 6 1.75-12.25
12.3-12.7 3 12.25-12.75
12.8-13.2 1 12.75-13.25
MODE=11.06

16. MEASURE OF CENTRAL
TENDENCY
ANY
Questions