b) Two candidates X and Y at the B.A (Hons.) examination obtained the following marks in ten papers: Paper 1 2 3 4 5 6 7 8 9 10
X 58 49 76 80 47 72 61 59 77 48
Y 39 38 86 72 75 69 57 49 83 66
• Which of the candidate showed the more consistent performance?
• Which of the candidate has greater absolute dispersion?
Answers
Given : Two candidates X and Y at the B.A (Hons.) examination obtained the following marks in ten papers: Paper 1 2 3 4 5 6 7 8 9 10
X 58 49 76 80 47 72 61 59 77 48
Y 39 38 86 72 75 69 57 49 83 66
To Fin d: Which of the candidate showed the more consistent performance?
• Which of the candidate has greater absolute dispersion?
Solution:
X 58 49 76 80 47 72 61 59 77 48
arranging in order
47 48 49 58 59 61 72 76 77 80
Coefficient of dispersion in terms of range = ( Max _ Min ) / (Max + Min)
( 80 - 47)/(80 + 47)
= 33/127
= 0.26
Coefficient of dispersion in terms of Quartile = ( Q3 - Q1)/(Q3 + Q1)
(76 - 49)/(76 + 49)
= 27/125
= 0.216
Y 39 38 86 72 75 69 57 49 83 66
arranging in order
38 39 49 57 66 69 72 75 83 86
Coefficient of dispersion in terms of range = ( Max - Min ) / (Max + Min)
( 86 - 38)/(86 + 38)
= 48/124
= 0.387
Coefficient of dispersion in terms of Quartile = ( Q3 - Q1)/(Q3 + Q1)
(75 - 49)/(75 + 49)
= 26/124
= 0.209
based on range X shows consistent performance
based on Quartiles Y shows consistent performance
Similarly we can check for SD and Mean Absolute deviation
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