Measures of Dispersion and Variability: Range, QD, AD and SD
Mean
1. Seminar
on
‘Averages’
Presented by :-Presented by :-
Nirmal SinghNirmal Singh
M.A,M.ED,M.LIB. SC,M.Phil, UGC NETM.A,M.ED,M.LIB. SC,M.Phil, UGC NET
Dept. of Library & Information ScienceDept. of Library & Information Science
Kurukshetra University, KurukshetraKurukshetra University, Kurukshetra
3. INTRODUCTIONINTRODUCTION
One of the most important objective ofOne of the most important objective of
statistical analysis is to get one single valuestatistical analysis is to get one single value
that describes the characteristic of the entirethat describes the characteristic of the entire
mass of data. Such a value is called the centralmass of data. Such a value is called the central
value or an average or the expected value ofvalue or an average or the expected value of
the variable.the variable.
4. DEFINITIONSDEFINITIONS
”” Average is an attempt to find one single figure toAverage is an attempt to find one single figure to
describe whole of figures.”describe whole of figures.”
---According to Clark---According to Clark
““An average is a single value selected from a groupAn average is a single value selected from a group
of values to represent them in some way-a value which isof values to represent them in some way-a value which is
supposed to stand for whole group, of which it is a part ,supposed to stand for whole group, of which it is a part ,
as typical or all the values in the group.”as typical or all the values in the group.”
---According to A.E.Waugh---According to A.E.Waugh
5. MEANINGMEANING
It is clear from the above definitions that
an average is a single value that represents a
group of values. Such a value is of great
significance because it depicts the characteristic
of the whole group. Its value lies somewhere in
between the two extremes.
6. OBJECTIVESOBJECTIVES
There are two main objectives of theThere are two main objectives of the
study of averages:study of averages:
1. To get single value.1. To get single value.
2. To facilitate comparison.2. To facilitate comparison.
7. QUALITIES OF A GOODQUALITIES OF A GOOD
AVERAGEAVERAGE
It is desire that such a value satisfies the following
properties.
Easy to understand.Easy to understand.
Simple to compute.Simple to compute.
Based on all the items.Based on all the items.
Not to be unduly affected by extreme observations.Not to be unduly affected by extreme observations.
Rigidly defined.Rigidly defined.
Capable of further algebraic treatment.Capable of further algebraic treatment.
Simple stability.Simple stability.
8. TYPES OF AVERAGESTYPES OF AVERAGES
Arithmetic MeanArithmetic Mean
MedianMedian
ModeMode
Geometric MeanGeometric Mean
Harmonic MeanHarmonic Mean
13. MEDIANMEDIAN
The median by definition refers to theThe median by definition refers to the
middle value in a distribution.middle value in a distribution.
Med.= Size of N+1 th item.
2
14. MODEMODE
The mode or the modal value is that value inThe mode or the modal value is that value in
a series of observations which occurs with thea series of observations which occurs with the
greatest frequency.greatest frequency.
Mo = 3Median – 2mean
15. CONCLUSIONCONCLUSION
With the help of above discussionWith the help of above discussion
we can say that averages are help us towe can say that averages are help us to
interpret the data and find the relevantinterpret the data and find the relevant
result.result.
