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Following are the runs scored by two batsmen in 5 cricket matches. Who is more consistent in scoring runs?
Batsman A3847341833
Batsman B3735412735


Answer
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Hint: In this question, we are given scores of two batsmen and we have to find who is more consistent. For this, we have to find coefficient of variation for both data and then compare it to find who have less coefficient of variation and that batsman will be more consistent. For calculating coefficient of variation we will use formula given by CV=σX×100 where, σ is standard deviation and X is the mean of data. For mean X we will divide the sum of the terms by the number of terms. For standard deviation we will use formula σ=x2N where, x is deviation from mean and N is the number of terms.

Complete step-by-step answer:
Let us calculate coefficient of variation for both data one by one:
For batsman A, data is as follows:
38, 47, 34, 18, 33.
Let us first find the mean of the data for which we can see the number of terms are 5 and sum of terms is 38+47+34+18+33=170. Hence,
Mean XA=1705=34.
For calculating standard deviation let us draw table with columns: Runs (X), deviation from mean (x=XX) and x2 is square of deviation.
Runs (X)(x=XX)X=34x2=(XX)2
38416
4713169
3400
18-16256
33-11


Now, let us calculate sum of x2 terms which becomes
x2=16+169+256+1=442.
Standard deviation for batsman A becomes
σA=x2N=4425=88.49.4.
Coefficient of variation for batsman A becomes
CVA=σAXA×100=9.434×100=27.65.
Hence, coefficient of variation for batsman A is equal to 27.65.
For batman B, data is as follows:
37, 35, 41, 27, 35
Let us find the mean of the data for which we can see the number of terms are 5 and sum of terms is 37+35+41+27+35=175. Hence,
Mean XB=1755=35.
For calculating standard deviation let us draw table with columns: Runs (X), deviation from mean (x=XX) and x2 is square of deviation
Runs (X)(x=XX)X=35x2=(XX)2
3724
3500
41636
27-864
3500


Now, let us calculate sum of x2 terms which becomes
x2=4+36+64=104.
Standard deviation for batsman B becomes
σB=x2N=1045=20.84.6.
Coefficient of variation for batsman B becomes
CVB=σBXB×100=4.635×100=13.14.
Hence, coefficient of variation for batsman B is equal to 13.14.
As we can see CVA=27.65 and CVB=13.14 therefore, coefficient of variation for batsman B is less than coefficient of variation for batsman A.
Therefore, batsman B is more consistent than batsman A in scoring the runs.

Note: Students should note that, sum of deviation from mean is always zero. Students should carefully apply the formula for calculating standard deviation and coefficient of variation. Squares and square roots must be calculated carefully. We have used coefficient of variation for comparing because coefficient of variation measures how consistent the different values of the set are from the mean of the data set. The lesser the variation the more is the consistency.