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

““Averages”Averages”

INTRODUCTIONINTRODUCTION

One of the most important objective of One of the most important objective of statistical analysis is to get one single value statistical analysis is to get one single value that describes the characteristic of the entire that describes the characteristic of the entire mass of data. Such a value is called the central mass of data. Such a value is called the central value or an average or the expected value of value or an average or the expected value of the variable.the variable.

DEFINITIONSDEFINITIONS

” ” Average is an attempt to find one single figure to Average 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 group An average is a single value selected from a group of values to represent them in some way-a value which is of 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

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.

OBJECTIVESOBJECTIVES

There are two main objectives of There are two main objectives of the study of averages:the study of averages:

1. To get single value.1. To get single value.

2. To facilitate comparison.2. To facilitate comparison.

QUALITIES OF A GOOD QUALITIES 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.

TYPES OF AVERAGESTYPES OF AVERAGES Arithmetic MeanArithmetic Mean

MedianMedian

Mode Mode

Geometric MeanGeometric Mean

Harmonic MeanHarmonic Mean

MONTHSMONTHS E&CE&C MECH.MECH. COM. ENGCOM. ENG ITIT GTGT

JANJAN 122122 156156 162162 104104 544544

FEBFEB 106106 125125 119119 9494 444444

MARMAR 9696 135135 125125 8080 436436

APRAPR 112112 109109 9696 103103 420420

MAYMAY 127127 9494 8282 7474 377377

JUNJUN 8686 4848 7373 5656 263263

JULJUL 5252 156156 6262 4646 316316

AUGAUG 175175 117117 109109 138138 539539

SEPSEP 135135 138138 9898 123123 494494

OCTOCT 150150 108108 107107 8484 449449

TOTALTOTAL 11411141 11861186 10331033 902902 42624262

CIRCULATION DATA OF SKIT MAIN LIBRARY

ARITHMETIC MEANARITHMETIC MEAN

X =X =

OrOr

X =X = ∑∑

−− X1+X2+X3+………………………………….Xn

N

−−X

N

X−−=

MONTHSMONTHS GTGT

JANJAN 544544

FEBFEB 444444

MARMAR 436436

APRAPR 420420

MAYMAY 377377

JUNJUN 263263

JULJUL 316316

AUGAUG 539539

SEPSEP 494494

OCTOCT 449449

TOTALTOTAL 42624262

426210

= 426.2

Circulation Data of Ten Months of SKIT Main Library

Calculation of Mean by Simple Methods

Short Cut MethodsShort Cut Methods

X−−= A +

∑∑dN

MONTHSMONTHS GTGT d= X-Ad= X-A

A=377A=377

JANJAN 544544 167167

FEBFEB 444444 6767

MARMAR 436436 5959

APRAPR 420420 4343

MAYMAY 377377 00

JUNJUN 263263 -114-114

JULJUL 316316 -61-61

AUGAUG 539539 162162

SEPSEP 494494 117117

OCTOCT 449449 7272

512512

=377+ 51210

=428.2

MEDIANMEDIAN The median by definition refers to the The median by definition refers to the

middle value in a distribution.middle value in a distribution.

Med.= Size of N+1 th item.2

MODEMODE The mode or the modal value is that value in The mode or the modal value is that value in

a series of observations which occurs with the a series of observations which occurs with the greatest frequency.greatest frequency.

Mo = 3Median – 2mean

CONCLUSIONCONCLUSION

With the help of above With the help of above discussion we can say that averages discussion we can say that averages are help us to interpret the data and are help us to interpret the data and find the relevant result.find the relevant result.