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- 1. Seminar on ‘Averages’ Presented by :-Presentedby :- 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
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- 3. INTRODUCTIONINTRODUCTION One of themost 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 isan 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 clearfrom 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 twomain 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 AGOODQUALITIES 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 AVERAGESTYPESOF AVERAGES Arithmetic MeanArithmetic Mean MedianMedian ModeMode Geometric MeanGeometric Mean Harmonic MeanHarmonic Mean
- 9. 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
- 10. ARITHMETIC MEANARITHMETIC MEAN X=X = OrOr X =X = ∑∑ −− X1+X2+X3+………………………………….Xn N −− X N
- 11. X −− = MONTHSMONTHS GTGT JANJAN 544544 FEBFEB444444 MARMAR 436436 APRAPR 420420 MAYMAY 377377 JUNJUN 263263 JULJUL 316316 AUGAUG 539539 SEPSEP 494494 OCTOCT 449449 TOTALTOTAL 42624262 4262 10 = 426.2 Circulation Data of Ten Months of SKIT Main Library Calculation of Mean by Simple Methods
- 12. Short Cut MethodsShortCut Methods X −− = A + ∑∑d N 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 + 512 10 =428.2
- 13. MEDIANMEDIAN The median bydefinition 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 orthe 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 helpof 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.