one of the important topic of statistics "Measure of central tendency"

1. PRESENATION ON MEAN,
MEDIAN & MODE
Presented By: Muhammad Raza

2. INTRODUCTION TO MEASURE OF CENTRAL
TENDENCY:
 In Statistics measure of central tendency is
a central value for a probability distribution of the
given data:
 There are two type of Data:
Ungroup
Group

3. INTRODUCTION TO MEASURE OF
CENTRAL TENDENCY:
 Measure of central Tendency includes three
measurements.
Mean
Median
Mode

4. Mean:
 In statistics Mean refers to the “Average” that is used to
derive the central tendency of the given data. We use
Mean where the data is less scattered.
 Formula: (For Ungroup Data)
X=x
 Formula: (For Group Data)
X=fx
n
n
X = observation
N=number of observations
F= frequecy

5. Median:
 Median is the “middle” value in the list of numbers. To
find the Median, we arrange the observations in
ascending order. If there is odd number of
observations, the Median is the middle value. If the
observations are in even numbers, the Median is the
average of two middle values.
Median is used when the data is more scattered.

6. Median Ungrouped Data(ODD number of
observations):
 Formula:
Median = n+1 e.g. 5,10,15,20,25
2
Median Ungrouped Data(Even number of observation)
 Formula:
Median= n/2 + (n/2+1) e.g. 5,10,15,20,25,30
2

7. Median (Group Data):
 Formula:
l + h f - c.f
f 2
Where;
l= lower class boundary
h= size of class boundary
f= median frequency
c.f= cumulative frequency of preceding value
Class Interval Frequency
10 14 6
15 19 8
20 24 10
25 29 12
30 34 18

8. MODE:
 Most repeated value in a set of data is said as Mode.
There may two or more than two modes in a data.
Example:
7,8,6,7,84,7,3,2,7,8

9. MODE: (Group Data)
 Formula:
l + h (fm-f1) Where;
2fm-f1-f2 l= lower class boundary
of modal group.
 Example: h=size of class boundary.
fm=frequency of modal group.
f1= proceeding value of modal
group.
f2= preceding frequency of
modal group.
Class Interval Frequency
11 20 2
21 30 4
31 40 6
41 50 8
51 60 10

10. .
Thank You