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- 1. Measures of Dispersion Prepared By: Dr. N.V. Ravi, Sr. Executive Officer, BOS, ICAI. Quantitative Aptitude & Business Statistics
- 2. Why Study Dispersion?An average, such as the meanor the median only locates thecentre of the data.An average does not tell usanything about the spread ofthe data. Quantitative Aptitude & Business Statistics: Measures of Dispersion 2
- 3. What is DispersionDispersion ( also known asScatter ,spread or variation )measures the items vary fromsome central value .It measures the degree ofvariation. Quantitative Aptitude & Business Statistics: Measures of Dispersion 3
- 4. Significance of Measuring DispersionTo determine the reliability ofan average.To facilitate comparison.To facilitate control.To facilitate the use of otherstatistical measures. Quantitative Aptitude & Business Statistics: Measures of Dispersion 4
- 5. Properties of Good Measure of Dispersion Simple to understand and easy to calculate Rigidly defined Based on all items A meanable to algebraic treatment Sampling stability Not unduly affected by Extreme items. Quantitative Aptitude & Business Statistics: Measures of Dispersion 5
- 6. Absolute Measure of Dispersion Based on selected Based on all items items 1.Range 1.Mean Deviation2.Inter Quartile Range 2.Standard Deviation Quantitative Aptitude & Business Statistics: Measures of Dispersion 6
- 7. Relative measures of DispersionBased on Based onSelected all itemsitems1.Coefficient of 1.Coefficient of MDRange 2.Coefficient of SD &2.Coefficient of Coefficient of Variation Quantitative Aptitude & Business Statistics:QD Measures of Dispersion 7
- 8. A small value for a measure ofdispersion indicates that the dataare clustered closely (the mean istherefore representative of the data).A large measure of dispersionindicates that the mean is notreliable (it is not representative ofthe data). Quantitative Aptitude & Business Statistics: Measures of Dispersion 8
- 9. The RangeThe simplest measure ofdispersion is the range.For ungrouped data, therange is the differencebetween the highest andlowest values in a set ofdata. Quantitative Aptitude & Business Statistics: Measures of Dispersion 9
- 10. RANGE = Highest Value -Lowest Value Quantitative Aptitude & Business Statistics: Measures of Dispersion 10
- 11. The range only takes intoaccount the most extremevalues.This may not berepresentative of thepopulation. Quantitative Aptitude & Business Statistics: Measures of Dispersion 11
- 12. The Range Example A sample of five accountinggraduates revealed thefollowing starting salaries:22,000,28,000, 31,000,23,000, 24,000.The range is 31,000 - 22,000= 9,000. Quantitative Aptitude & Business Statistics: Measures of Dispersion 12
- 13. Coefficient of RangeCoefficient of Range iscalculated as,Coefficient of Range = L − S L + S = 0 . 1698 Quantitative Aptitude & Business Statistics: Measures of Dispersion 13
- 14. From the following data calculate Range and Coefficient of RangeMarks 5 15 25 35 45 55No .of 10 20 30 50 40 30Students Quantitative Aptitude & Business Statistics: Measures of Dispersion 14
- 15. Largest term (L)=55,Smallest term (S)=5Range=L-S=55-5=50Coefficient of Range L − S 55 − 5 = = = 0.833 L + S 55 + 5 Quantitative Aptitude & Business Statistics: Measures of Dispersion 15
- 16. From the following data ,calculate Range and Coefficient of RangeMarks 0-10 10-20 20-30 30-40 40-50 50-60No .of 10 20 30 50 40 30Students Quantitative Aptitude & Business Statistics: Measures of Dispersion 16
- 17. Lower limit of lowest class(S)=0Upper limit of highest class(L)=60Coefficient of Range L − S 60− 0 = = = 1.000 L + S 60+ 0 Quantitative Aptitude & Business Statistics: Measures of Dispersion 17
- 18. Merits Of Range1.Its easy to understand andeasy to calculate.2.It does not require anyspecial knowledge.3.It takes minimum time tocalculate the value of Range. Quantitative Aptitude & Business Statistics: Measures of Dispersion 18
- 19. Limitations of RangeIt does not take intoaccount of all items ofdistribution.Only two extreme values aretaken into consideration.It is affected by extremevalues. Quantitative Aptitude & Business Statistics: Measures of Dispersion 19
- 20. Limitations of RangeIt does not indicate thedirection of variability.It does not present veryaccurate picture of thevariability. Quantitative Aptitude & Business Statistics: Measures of Dispersion 20
- 21. Uses of RangeIt facilitates to study qualitycontrol.It facilitates to study variationsof prices on shares ,debentures,bonds and agriculturalcommodities.It facilitates weather forecasts. Quantitative Aptitude & Business Statistics: Measures of Dispersion 21
- 22. Interquartile RangeThe interquartile range isused to overcome theproblem of outlyingobservations.The interquartile rangemeasures the range of themiddle (50%) values only Quantitative Aptitude & Business Statistics: Measures of Dispersion 22
- 23. Inter quartile range = Q3 – Q1It is sometimes referred toas the quartile deviation orthe semi-inter quartilerange. Quantitative Aptitude & Business Statistics: Measures of Dispersion 23
- 24. ExerciseThe number of complaintsreceived by the manager ofa supermarket wasrecorded for each of thelast 10 working days.21, 15, 18, 5, 10, 17, 21,19, 25 & 28 Quantitative Aptitude & Business Statistics: Measures of Dispersion 24
- 25. Interquartile Range Example Sorted data5, 10, 15, 17, 18, 19, 21,21, 25 & 28 Quantitative Aptitude & Business Statistics: Measures of Dispersion 25
- 26. N +1Q1 = 4 11Q1 = 4Q1 = 2 .75= 2 item + 0 .75 (15 − 10 )= 10 + 3 .75 = 13 .75 Quantitative Aptitude & Business Statistics: Measures of Dispersion 26
- 27. 3( N + 1)Q3 = 4 33Q3 = 4Q3 = 8.25 = 8 + 0.25(9thitem − 8thitem)= 21 + 0.25(25 − 21)= 21 + 0.25(4) = 23 Quantitative Aptitude & Business Statistics: Measures of Dispersion 27
- 28. Inter quartile range = 23 – 13.75 = 9.25 Co-efficient of Quartile Deviation = Q3 − Q1 = Q3 + Q1 = 0.1979 Quantitative Aptitude & Business Statistics: Measures of Dispersion 28
- 29. From the following data ,calculate Inter Quartile Range and Coefficient of Quartile DeviationMarks 0- 10- 20- 30- 40- 50- 10 20 30 40 50 60No .ofStudents 10 20 30 50 40 30 Quantitative Aptitude & Business Statistics: Measures of Dispersion 29
- 30. Calculation of Cumulative frequencies Marks No. of Cumulative Students Frequencies 0-10 10 10 10-20 20 30 cf 20-30 30f 60Q1 ClassL1 30-40 50 110 cf 40-50 40 f 150Q3Class 50-60 30 180 L3 180 Quantitative Aptitude & Business Statistics: Measures of Dispersion 30
- 31. Q1= Size of N/4th item = Size of180/4th item = 45th itemThere fore Q1 lies in the Class20-30 ⎛N ⎞ ⎜ − c.f ⎟ Q1 = L + ⎜ 4 ⎟× C ⎜ f ⎟ ⎜ ⎟ ⎝ ⎠ Quantitative Aptitude & Business Statistics: Measures of Dispersion 31
- 32. ⎛ 180 ⎞ ⎜ − 30 ⎟Q 1 = 20 + ⎜ 4 ⎟ × 10 ⎜ 30 ⎟ ⎜ ⎟ ⎝ ⎠ ⎛ 15 ⎞= 20 + ⎜ ⎟ × 10 ⎝ 30 ⎠= 25 Quantitative Aptitude & Business Statistics: Measures of Dispersion 32
- 33. Q3= Size of 3.N/4th item = Size of3.180/4th item = 135th itemThere fore Q3 lies in the Class40-50 ⎛ N ⎞ ⎜ 3. − c. f ⎟ Q3 = L + ⎜ 4 ⎟×C ⎜ ⎜ f ⎟ ⎟ ⎝ ⎠ Quantitative Aptitude & Business Statistics: Measures of Dispersion 33
- 34. ⎛ 180 ⎞ ⎜ 3. − 110 ⎟Q 3 = 40 + ⎜ 4 ⎟ × 10 ⎜ 40 ⎟ ⎜ ⎟ ⎝ ⎠ ⎛ 25 ⎞= 40 + ⎜ ⎟ × 10 ⎝ 10 ⎠= 46.25 Quantitative Aptitude & Business Statistics: Measures of Dispersion 34
- 35. Inter Quartile Range=Q3-Q1 =46.25-25=21.25Coefficient of Quartile Deviation Q 3 − Q1 = =0.2982 Q 3 + Q1 Quantitative Aptitude & Business Statistics: Measures of Dispersion 35
- 36. Merits Of Quartile DeviationIts easy to understand and easyto calculate.It is least affected by extremevalues.It can be used in open-endfrequency distribution. Quantitative Aptitude & Business Statistics: Measures of Dispersion 36
- 37. Limitations of Quartile DeviationIt is not suited to algebraictreatmentIt is very much affected by samplingfluctuationsThe method of Dispersion is notbased on all the items of the series .It ignores the 50% of thedistribution. Quantitative Aptitude & Business Statistics: Measures of Dispersion 37
- 38. Mean DeviationThe mean deviation takes intoconsideration all of the valuesMean Deviation: The arithmeticmean of the absolute values ofthe deviations from thearithmetic mean Quantitative Aptitude & Business Statistics: Measures of Dispersion 38
- 39. MD = ∑ x− x nWhere: X = the value of eachobservation X = the arithmeticmean of the valuesn = the number of observations|| = the absolute value (the signs ofthe deviations are disregarded) Quantitative Aptitude & Business Statistics: Measures of Dispersion 39
- 40. Mean Deviation ExampleThe weights of a sample of cratescontaining books for the bookstore are(in kgs.) 103, 97, 101, 106, 103.X = 510/5 = 102 kgs.Σ |x-x| = 1+5+1+4+1=12MD = 12/5 = 2.4Typically, the weights of the crates are2.4 kgs. from the mean weight of 102 kgs. Quantitative Aptitude & Business Statistics: Measures of Dispersion 40
- 41. Frequency Distribution Mean Deviation If the data are in the form of a frequency distribution, the mean deviation can be calculated using the following formula: _ MD = ∑ f |x−x| ∑ fWhere f = the frequency of an observation xn = Σf = the sum of the frequencies Quantitative Aptitude & Business Statistics: Measures of Dispersion 41
- 42. Frequency Distribution MD Example Number ofoutstanding Frequency fx |x-x| f|x-x| accounts 0 1 0 2 2 1 9 9 1 9 2 7 14 0 0 3 3 9 1 3 4 4 16 2 8 Total: 24 Σfx Σ f|x-x| = = 48 22 Quantitative Aptitude & Business Statistics: Measures of Dispersion 42
- 43. _ x= ∑ fx ∑f mean = 48/24 = 2 _MD = ∑ f |x−x| ∑ fMD = 22/24 = 0.92 Quantitative Aptitude & Business Statistics: Measures of Dispersion 43
- 44. Calculate Mean Deviation and Coefficient of Mean Deviation Marks No. of Cumulative (X) Students Frequencies 0-10 10 10 10-20 20 30 20-30 30 60 cf 30-40 50 f 110 40-50 40 150 Median 50-60 30 180 ClassL 180 Quantitative Aptitude & Business Statistics: Measures of Dispersion 44
- 45. Calculation of Mean deviations from Median N 180 = 2 2 =90th itemMedian in Class =30-40,L=30,c.f=60,f=50 and c=10 Quantitative Aptitude & Business Statistics: Measures of Dispersion 45
- 46. ⎛ N ⎞ ⎜ − c .f ⎟M =L+ ⎜ 2 ⎟×c ⎜ f ⎟ ⎜ ⎟ ⎝ ⎠ ⎛ 180 ⎞ ⎜ − 30 ⎟= 30 + ⎜ 2 ⎟ × 10 ⎜ 50 ⎟ ⎜ ⎟ ⎝ ⎠= 30 + 6 = 36 Quantitative Aptitude & Business Statistics: Measures of Dispersion 46
- 47. Calculation of Mean Deviation of MedianMean Deviation from Median = ∑f x−M N 2040 = = 11 . 333 180 Quantitative Aptitude & Business Statistics: Measures of Dispersion 47
- 48. Coefficient of MeanDeviation MeanDeviat ion = Median 11.333 = = 0.3148 36 Quantitative Aptitude & Business Statistics: Measures of Dispersion 48
- 49. Merits of Mean DeviationIt is easy to understandIt is based on all items of theseriesIt is less affected by extremevaluesIt is useful small samples whenno detailed analysis is required. Quantitative Aptitude & Business Statistics: Measures of Dispersion 49
- 50. Limitations of Mean DeviationIt lacks properties such that(+) and(-)signs which are nottaken into consideration.It is not suitable formathematical treatment. Quantitative Aptitude & Business Statistics: Measures of Dispersion 50
- 51. It may not give accurateresults when the degree ofvariability in a series is veryhigh. Quantitative Aptitude & Business Statistics: Measures of Dispersion 51
- 52. Standard DeviationStandard deviation is the mostcommonly used measure ofdispersionSimilar to the mean deviation,the standard deviation takesinto account the value of everyobservation Quantitative Aptitude & Business Statistics: Measures of Dispersion 52
- 53. The values of the meandeviation and the standarddeviation should be relativelysimilar. Quantitative Aptitude & Business Statistics: Measures of Dispersion 53
- 54. Standard DeviationThe standard deviation uses thesquares of the residualsSteps; Find the sum of the squares of the residuals Find the mean Then take the square root of the mean Quantitative Aptitude & Business Statistics: Measures of Dispersion 54
- 55. 2 ⎛ ⎞ _ ∑⎜ x − x ⎟ ⎝ ⎠σ= N Quantitative Aptitude & Business Statistics: Measures of Dispersion 55
- 56. From the following data calculateStandard Deviation5,15,25,35,45 and 55 X= ∑X X= 180 = 30 N 6 Quantitative Aptitude & Business Statistics: Measures of Dispersion 56
- 57. σ= ∑ (X − X ) 2 N 1750= = 17 .078 6 Quantitative Aptitude & Business Statistics: Measures of Dispersion 57
- 58. Frequency Distribution SDIf the data are in the form of a frequencydistribution the standard deviation is given by σ= ∑ f.(X − X) 2 N ∑ ∑ 2 f .x 2 ⎛ f .x ⎞ = −⎜ ⎟ N ⎜ N ⎟ ⎝ ⎠ Quantitative Aptitude & Business Statistics: Measures of Dispersion 58
- 59. From the following data ,calculate Standard Deviation . Marks 5 15 25 35 45 55 (X) No. of 10 20 30 50 40 30Students (f) Quantitative Aptitude & Business Statistics: Measures of Dispersion 59
- 60. Mean = X= ∑f.x = 6300= 35 N 180 Quantitative Aptitude & Business Statistics: Measures of Dispersion 60
- 61. Marks No. of (X- fx2(X) Students 35)=x (f) 5 10 -30 9000 15 20 -20 8000 25 30 -10 3000 35 50 0 0 45 40 10 4000 55 30 20 12000 N=180 ∑fx2 Quantitative Aptitude & Business Statistics: Measures of Dispersion =3600061
- 62. ∑ ∑ 2 f.x 2 ⎛ f.x ⎞σ= −⎜ ⎟ N ⎜ N ⎟ ⎝ ⎠= ∑ f.x − (X ) 2 2 =14.142 N Quantitative Aptitude & Business Statistics: Measures of Dispersion 62
- 63. Properties of Standard DeviationIndependent of change of originNot independent of change of Scale.Fixed Relationship among measuresof Dispersion. Quantitative Aptitude & Business Statistics: Measures of Dispersion 63
- 64. In a normal distribution there is fixed relationship 2 QD = σ 3 4 MD = σ 5 Thus SD is neverAptitude & Business Statistics: and MD Quantitative less than QD Measures of Dispersion 64
- 65. Bell - Shaped Curve showing the relationship between σ and μ . 68.27% 95.45% 99.73% μ−3σ μ−2σ μ−1σ μ μ+1σ μ+2σ μ+ 3σ Quantitative Aptitude & Business Statistics: Measures of Dispersion 65
- 66. Minimum sum of Squares; The Sum ofSquares of Deviations of items in theseries from their arithmetic mean isminimum.Standard Deviation of n natural numbers 2 N −1 = 12 Quantitative Aptitude & Business Statistics: Measures of Dispersion 66
- 67. Combined standard deviation 2 2 2 2 N1σ1 +N2σ2 +N1d1 +N2d2 σ12 = N1 +N2 Quantitative Aptitude & Business Statistics: Measures of Dispersion 67
- 68. Where σ12 =Combined standard Deviation oftwo groups σ 1 =Standard Deviation of first groupN1=No. of items of First groupN2=No. of items of Second group σ2 = Standard deviation of Second group Quantitative Aptitude & Business Statistics: Measures of Dispersion 68
- 69. d1 = X 1 − X 12d2 = X2 − X12 Where X 12 is the combined mean of two groups Quantitative Aptitude & Business Statistics: Measures of Dispersion 69
- 70. Merits of Standard DeviationIt is based on all the items ofthe distribution.it is a meanable to algebraictreatment since actual + or –signs deviations are taken intoconsideration.It is least affected byfluctuations of sampling Quantitative Aptitude & Business Statistics: Measures of Dispersion 70
- 71. Merits of Standard DeviationIt facilitates the calculation ofcombined standard Deviation andCoefficient of Variation ,which isused to compare the variability oftwo or more distributionsIt facilitates the other statisticalcalculations like skewness,correlation.it provides a unit of measurement forthe normal distribution. Quantitative Aptitude & Business Statistics: Measures of Dispersion 71
- 72. Limitations of Standard DeviationIt can’t be used for comparingthe variability of two or moreseries of observations given indifferent units. A coefficient ofStandard deviation is to becalculated for this purpose.It is difficult to compute andcompared Quantitative Aptitude & Business Statistics: Measures of Dispersion 72
- 73. Limitations of Standard Deviation It is very much affected by the extreme values. The standard deviation can not be computed for a distribution with open-end classes. Quantitative Aptitude & Business Statistics: Measures of Dispersion 73
- 74. VarianceVariance is the arithmetic mean ofthe squares of deviations of all theitems of the distributions fromarithmetic mean .In other words,variance is the square of theStandard deviation= 2 σVariance= σ= var iance Quantitative Aptitude & Business Statistics: Measures of Dispersion 74
- 75. Interpretation of VarianceSmaller the variance,greater the uniformity inpopulation.Larger the variance ,greaterthe variability Quantitative Aptitude & Business Statistics: Measures of Dispersion 75
- 76. The Coefficient of VariationThe coefficient of variation is ameasure of relative variability It is used to measure the changes that have taken place in a population over time Quantitative Aptitude & Business Statistics: Measures of Dispersion 76
- 77. To compare the variability oftwo populations that areexpressed in different units ofmeasurementIt is expressed as apercentage Quantitative Aptitude & Business Statistics: Measures of Dispersion 77
- 78. Formula: σ Where: CV = × 100 X X = meanσ = standard deviation Quantitative Aptitude & Business Statistics: Measures of Dispersion 78
- 79. 1. Dispersion measures(a) The scatter ness of a set of observations(b) The concentration of set of observations( c) The Peaked ness of distribution (d) None Quantitative Aptitude & Business Statistics: Measures of Dispersion 79
- 80. 1. Dispersion measures(a) The scatter ness of a set of observations(b) The concentration of set of observations( c) The Peaked ness of distribution (d) None Quantitative Aptitude & Business Statistics: Measures of Dispersion 80
- 81. 2. Which one is an absolute measure of Dispersion? (a) Range (b) Mean Deviation ( c) Quartile Deviation( d) all these measures Quantitative Aptitude & Business Statistics: Measures of Dispersion 81
- 82. 2. Which one is an absolute measure of Dispersion? (a) Range (b) Mean Deviation ( c) Quartile Deviation( d) all these measures Quantitative Aptitude & Business Statistics: Measures of Dispersion 82
- 83. 3.Which measures of Dispersion is not affected by the presence of extreme observations (a) deviation (b) Quartile Deviation (C) Mean Deviation(d) Range Quantitative Aptitude & Business Statistics: Measures of Dispersion 83
- 84. 3.Which measures of Dispersion is not affected by the presence of extreme observations (a) deviation (b) Quartile Deviation (C) Mean Deviation(d) Range Quantitative Aptitude & Business Statistics: Measures of Dispersion 84
- 85. 3.Which measures of Dispersion is not affected by the presence of extreme observations (a) deviation (b) Quartile Deviation (C) Mean Deviation(d) Range Quantitative Aptitude & Business Statistics: Measures of Dispersion 85
- 86. 4.which measures of Dispersion is based on all the items of observations(a) Mean Deviation(b) Standard Deviation(C) Quartile Deviation(d) a and b but not c Quantitative Aptitude & Business Statistics: Measures of Dispersion 86
- 87. 4.which measures of Dispersion is based on all the items of observations(a) Mean Deviation(b) Standard Deviation(C) Quartile Deviation(d) a and b but not c Quantitative Aptitude & Business Statistics: Measures of Dispersion 87
- 88. 5.Standard Deviation is(a) absolute measure(b) relative measure(c) both(d) none Quantitative Aptitude & Business Statistics: Measures of Dispersion 88
- 89. 5.Standard Deviation is(a) absolute measure(b) relative measure(c) both(d) none Quantitative Aptitude & Business Statistics: Measures of Dispersion 89
- 90. 6.Coefficient of standard deviation is(a) SD/mean(b) SD/Median(c) SD/Mode (d) Mean/SD Quantitative Aptitude & Business Statistics: Measures of Dispersion 90
- 91. 6.Coefficient of standard deviation is(a) SD/mean(b) SD/Median(c) SD/Mode (d) Mean/SD Quantitative Aptitude & Business Statistics: Measures of Dispersion 91
- 92. 7.Coefficient of Quartile Deviation iscalculated by formula(a)(Q3-Q1)/4(b) (Q3-Q1)/2 (c) (Q3-Q1)/(Q3+Q1)(d) (Q3+Q1)/(Q3-Q1 Quantitative Aptitude & Business Statistics: Measures of Dispersion 92
- 93. 7.Coefficient of Quartile Deviation iscalculated by formula(a)(Q3-Q1)/4(b) (Q3-Q1)/2 (c) (Q3-Q1)/(Q3+Q1)(d) (Q3+Q1)/(Q3-Q1 Quantitative Aptitude & Business Statistics: Measures of Dispersion 93
- 94. 8.The standard Deviation of5,8,5,5,5,8and 8 is(a) 4(b) 6(C) 3(d) 0 Quantitative Aptitude & Business Statistics: Measures of Dispersion 94
- 95. 8.The standard Deviation of5,8,5,5,5,8and 8 is(a) 4(b) 6(C) 3(d) 0 Quantitative Aptitude & Business Statistics: Measures of Dispersion 95
- 96. 9.If all the observations are increased by 10,then(a) SD would be increased by 10(b)Mean deviation would be increased by 10 ( c) Quartile Deviation would be increased by 10 (d) all these remain unchanged Quantitative Aptitude & Business Statistics: Measures of Dispersion 96
- 97. 9.If all the observations are increased by 10,then(a) SD would be increased by 10(b)Mean deviation would be increased by 10 ( c) Quartile Deviation would be increased by 10 (d) all these remain unchanged Quantitative Aptitude & Business Statistics: Measures of Dispersion 97
- 98. 10.For any two numbers SD is always(a) Twice the range(b) Half of the range© Square of range(d) none of these Quantitative Aptitude & Business Statistics: Measures of Dispersion 98
- 99. 10.For any two numbers SD is always(a) Twice the range(b) Half of the range© Square of range(d) none of these Quantitative Aptitude & Business Statistics: Measures of Dispersion 99
- 100. 11Mean deviation is minimum whendeviations are taken about(a) Arithmetic Mean(b) Geometric Mean© Harmonic Mean(d) Median Quantitative Aptitude & Business Statistics: Measures of Dispersion 100
- 101. 11.Mean deviation is minimum whendeviations are taken about(a) Arithmetic Mean(b) Geometric Mean© Harmonic Mean(d) Median Quantitative Aptitude & Business Statistics: Measures of Dispersion 101
- 102. 12.Root mean square deviation is(a) Standard Deviation(b) Quartile Deviation© both(d) none Quantitative Aptitude & Business Statistics: Measures of Dispersion 102
- 103. 12.Root mean square deviation frommean is(a) Standard Deviation(b) Quartile Deviation© both(d) none Quantitative Aptitude & Business Statistics: Measures of Dispersion 103
- 104. 13.Standard Deviation is(a) Smaller than mean deviation aboutmean(b) Smaller than mean deviation aboutmedian© Larger than mean deviation about mean(d) none of these Quantitative Aptitude & Business Statistics: Measures of Dispersion 104
- 105. 13.Standard Deviation is(a) Smaller than mean deviation aboutmean(b) Smaller than mean deviation aboutmedian© Larger than mean deviation about mean(d) none of these Quantitative Aptitude & Business Statistics: Measures of Dispersion 105
- 106. 14.Is least affected by samplingfluctuationsa) Standard Deviation(b) Quartile Deviation© both(d) none Quantitative Aptitude & Business Statistics: Measures of Dispersion 106
- 107. 14.Is least affected by samplingfluctuationsa) Standard Deviation(b) Quartile Deviation© both(d) none Quantitative Aptitude & Business Statistics: Measures of Dispersion 107
- 108. 15. Coefficient of variation of two series is 60%and 80% respectively. Their standard deviationsare 20 and 16 respectively, what is their A.MA) 15 and 20B) 33.3 and 20C) 33.3 and 15D) 12 and 12.8 Quantitative Aptitude & Business Statistics: Measures of Dispersion 108
- 109. 15. Coefficient of variation of two series is 60%and 80% respectively. Their standard deviationsare 20 and 16 respectively, what is their A.MA) 15 and 20B) 33.3 and 20C) 33.3 and 15D) 12 and 12.8 Quantitative Aptitude & Business Statistics: Measures of Dispersion 109
- 110. 16. For the numbers 1, 2, 3, 4, 5, 6, 7 standarddeviation is:A) 3B) 4C) 2D) None of these Quantitative Aptitude & Business Statistics: Measures of Dispersion 110
- 111. 16. For the numbers 1, 2, 3, 4, 5, 6, 7 standarddeviation is:A) 3B) 4C) 2D) None of these Quantitative Aptitude & Business Statistics: Measures of Dispersion 111
- 112. THE ENDMeasures of Dispersion

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