This document discusses measures of central tendency, which summarize a data set with a single value representing the center or typical value. There are three main types of measures: the arithmetic mean, which is the sum of all values divided by the number of values; the median, which is the middle value when data is ordered from lowest to highest; and the mode, which is the most frequently occurring value. The document provides formulas for calculating each of these measures and explains their properties and uses for summarizing and comparing data sets.

1. For practical purpose the condensation of data
set into a frequency distribution and the visual
presentation are not enough particularly when two
or more different data sets are to be compared. A
data set can be summarized in a single value. Such a
value usually where in the center and representing
the entire data set is a value at which the data have
a tendency to concentrate.

2. The tendency of the observation to cluster in the
central part of the data is called Central Tendency and
the summary values as a measure of central tendency.
Since a measure of central tendency indicates the
location or general position of the distribution or the
data set in range of observations it is also known as
measure of location or position. The measure of central
tendency or location are generally known as Average,
but in everyday language the average is often
understood to refer to the arithmetic mean it is for this
reason that when anyone speaks of the average.

3.  Rigorously defined.
 Based on all observation made.
 Simple to understand and easy to interpret.
 Quickly and easily calculated.
 Amenable to mathematical treatment.
 Relatively stable in repeated sampling experiment.
 Not unduly influenced by abnormally large or small
observation.

4. There are five types of averages.
oThe Arithmetic Mean.
oThe Median.
oThe Mode.
oThe Geometric Mean.
oThe Harmonic Mean.

5. The arithmetic mean or simply the mean is the most
familiar average. It is defined as the value obtained by
dividing the sum of all the observation by their number ,
that is
Formula x
X
n



6. The median is defined as a value which divides a data
set that have been ordered, into two equals parts, one
part comparing of observation greater than and the
other part smaller than it, or more precisely the median
is a value at or below 50% of the ordered data lie.
Formula
2
h n
Median l C
f
 
   
 

7. The mode is defined as a value which occurs most
frequent in a set of data , that is it indicates the most
common results. A set of data may have more than one
mode or no mode at all when each observation occurs
the same number of times.
Formula
 
1
1 2( )
m
m m
f f
Mode l h
f f f f

  
  

8. MUHAMMAD IRFAN HUSSAIN
Bs 3rd Semester (Regular)
Roll # 39