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Exercise 10.2 · Q10
Q.

ICC team ranking of men's Cricket for the month of May 2020 is given in following table. Calculate correlation coefficient for ODI and test rankings.

Sr. No.TeamRating of test matchesRating of ODI matches
1Australia116107
2New Zealand115116
3India114119
4England105127
5Sri Lanka9185
6South Africa90108
7Pakistan86102
8West Indies7976
9Bangladesh5588
10Zimbabwe1839

Source: https://www.icc-cricket.com/rankings/mens/team-rankings/test

Yanam CbseNCERTSubjective· 5mImportance★★★★★est
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Karl Pearson's correlation coefficient measures the strength/direction of the linear relationship between Test rating and ODI rating across the 10 teams; computing it from the raw ratings gives r≈0.89r\approx0.89, a strong positive correlation.

Karl Pearson's coefficient of correlation between two variables X,YX,Y over nn pairs:

r=n∑XY−(∑X)(∑Y)[n∑X2−(∑X)2][n∑Y2−(∑Y)2]r = \frac{n\sum XY - \left(\sum X\right)\left(\sum Y\right)}{\sqrt{\left[n\sum X^2-\left(\sum X\right)^2\right]\left[n\sum Y^2-\left(\sum Y\right)^2\right]}}

where XX = Test rating, YY = ODI rating, nn = number of pairs (teams).

  1. Tabulate XX (Test), YY (ODI), XYXY, X2X^2, Y2Y^2 for the 10 teams:
TeamXX (Test)YY (ODI)XYXYX2X^2Y2Y^2
Australia116107124121345611449
New Zealand115116133401322513456
India114119135661299614161
England105127133351102516129
Sri Lanka9185773582817225
South Africa901089720810011664
Pakistan861028772739610404
West Indies7976600462415776
Bangladesh5588484030257744
Zimbabwe18397023241521
Total869967904268406999529
  1. n=10n=10, ∑X=869\sum X=869, ∑Y=967\sum Y=967, ∑XY=90426\sum XY=90426, ∑X2=84069\sum X^2=84069, ∑Y2=99529\sum Y^2=99529.
  2. Numerator: n∑XY−∑X∑Y=10(90426)−(869)(967)=904260−840323=63937n\sum XY-\sum X\sum Y = 10(90426)-(869)(967) = 904260-840323=63937. …

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