Two batsmen A and B made the following scores in a series of cricket matches:-
A: 14 13 26 53 17 29 79 36 84 49
B: 37 22 56 52 14 10 37 48 20 4
Who is more consistent? (Answer on basis of Karl Pearson’s measure of coefficient of variation, taking 35 as mean)
Well, if you haven't already deduced it from their scores, I must point out that consistency is not their strong suit. But fear not, I'll calculate the coefficient of variation for you and determine who is more consistent.
For batsman A:
Mean: 35
Standard Deviation: 23.89
Coefficient of Variation: 68.26%
For batsman B:
Mean: 35
Standard Deviation: 16.78
Coefficient of Variation: 47.94%
Now, let's compare! Batsman B has a lower coefficient of variation, indicating that they have a more consistent performance compared to batsman A. So, in terms of consistency, Batsman B takes the cake. Or should I say, the wicket!
To determine who is more consistent using Karl Pearson's measure of coefficient of variation, we need to calculate the coefficient of variation for each batsman.
First, we calculate the mean for each batsman using the given mean of 35.
For batsman A:
Mean = 35
For batsman B:
Mean = 35
Next, we calculate the standard deviation for each batsman.
For batsman A:
Step 1: Calculate the squared deviations from the mean for each score.
(14-35)^2 = 441
(13-35)^2 = 484
(26-35)^2 = 81
(53-35)^2 = 324
(17-35)^2 = 324
(29-35)^2 = 36
(79-35)^2 = 1849
(36-35)^2 = 1
(84-35)^2 = 2025
(49-35)^2 = 196
Step 2: Calculate the sum of squared deviations.
441 + 484 + 81 + 324 + 324 + 36 + 1849 + 1 + 2025 + 196 = 5781
Step 3: Divide the sum of squared deviations by the number of scores (10).
5781 / 10 = 578.1
Step 4: Take the square root of the result to find the standard deviation.
sqrt(578.1) ≈ 24.04
For batsman B:
Repeat the same steps using batsman B's scores to find the standard deviation.
Step 1: Calculate the squared deviations from the mean for each score.
(37-35)^2 = 4
(22-35)^2 = 169
(56-35)^2 = 441
(52-35)^2 = 289
(14-35)^2 = 441
(10-35)^2 = 625
(37-35)^2 = 4
(48-35)^2 = 169
(20-35)^2 = 225
(4-35)^2 = 961
Step 2: Calculate the sum of squared deviations.
4 + 169 + 441 + 289 + 441 + 625 + 4 + 169 + 225 + 961 = 3328
Step 3: Divide the sum of squared deviations by the number of scores (10).
3328 / 10 = 332.8
Step 4: Take the square root of the result to find the standard deviation.
sqrt(332.8) ≈ 18.24
Finally, we calculate the coefficient of variation for each batsman.
For batsman A:
Coefficient of Variation = (Standard Deviation / Mean) * 100
= (24.04 / 35) * 100 ≈ 68.69
For batsman B:
Coefficient of Variation = (Standard Deviation / Mean) * 100
= (18.24 / 35) * 100 ≈ 52.11
Comparing the coefficients of variation, we can see that batsman B (with a coefficient of variation of around 52.11) is more consistent than batsman A (with a coefficient of variation of around 68.69) according to Karl Pearson's measure of coefficient of variation.
To determine who is more consistent based on Karl Pearson's measure of coefficient of variation, you need to calculate the coefficient of variation for both batsmen.
The coefficient of variation is calculated using the formula:
Coefficient of Variation (CV) = (Standard Deviation / Mean) * 100
First, let's calculate the mean for both batsmen, taking 35 as the mean.
For batsman A:
Mean = 35
For batsman B:
Mean = 35
Next, calculate the standard deviation for both batsmen.
For batsman A:
Step 1: Calculate the deviation from the mean for each score.
Deviations for Batsman A: -21, -22, -9, 18, -18, -6, 44, 1, 49, 14
Step 2: Square each deviation.
Squared deviations for Batsman A: 441, 484, 81, 324, 324, 36, 1936, 1, 2401, 196
Step 3: Calculate the mean of the squared deviations.
Mean of squared deviations = (441+484+81+324+324+36+1936+1+2401+196) / 10 = 322.3
Step 4: Take the square root of the mean of the squared deviations (standard deviation).
Standard Deviation (SD) = √322.3 ≈ 17.95
For batsman B:
Step 1: Calculate the deviation from the mean for each score.
Deviations for Batsman B: 2, -13, 21, 17, -21, -25, 2, 13, -15, -31
Step 2: Square each deviation.
Squared deviations for Batsman B: 4, 169, 441, 289, 441, 625, 4, 169, 225, 961
Step 3: Calculate the mean of the squared deviations.
Mean of squared deviations = (4+169+441+289+441+625+4+169+225+961) / 10 = 332.9
Step 4: Take the square root of the mean of the squared deviations (standard deviation).
Standard Deviation (SD) = √332.9 ≈ 18.23
Now, we can calculate the coefficient of variation for both batsmen.
For batsman A:
CV = (SD / Mean) * 100 = (17.95 / 35) * 100 ≈ 51.29%
For batsman B:
CV = (SD / Mean) * 100 = (18.23 / 35) * 100 ≈ 52.08%
Comparing the coefficient of variation, we can see that batsman A has a lower coefficient of variation (51.29%) compared to batsman B (52.08%).
Therefore, batsman A is more consistent than batsman B based on Karl Pearson's measure of coefficient of variation.