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Young World
WORLD OF SCIENCE
Variation in batting skills
DR. T. V. PADMA
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How do we measure variation in a set of numbers?
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Let's look at one way to measure variation in a set of numbers, using the example from last week — a consistent batsman and an inconsistent batsman, both of whom have an average of 50, after their first six matches. The consistent batsman scored 50 runs in his first test, then 55, 45, 52, 50 and 48 in the sixth. The inconsistent batsman scored 10 runs in his first match, 90 in his second test, then 95, 5, 100 and a duck in his sixth. Both batsmen ended up with the same average — 50 runs.
The method
One way to look at variation is to calculate the average, and then look at how different each actual score is from the average. The average is 50 in both cases. Now, let's look at the difference between 50 and each of the six scores made by the consistent batsman. That means, we have to look at the difference between the average of 50 and the first real score the batsman made, which was 50, so the difference in this case is 0. Next, we look at the difference between the average and the second score the batsman made, so in this case, the difference is five runs. In the third test, the difference between the average and the actual runs scored is once again five runs. In the fourth match, the difference between average and runs scored is two, just as in the sixth match. And in the fifth match, since the average is 50 and the batsman actually scored 50, the difference is 0. Already, we can see that the difference between the average and the actual scores is very small, for our consistent batsman. It ranges, in our case, between 0 and five runs — so he usually scores very close to his average. Our next step is to square the differences, which in order of the matches, would be: 0, 25, 25, 4, 0, 4. Then, we can average the numbers 0, 25, 25, 4, 0, 4. If we do this, we get (0+25+25+4+0+4)/6 = 9.7, or approximately 10. This is sometimes known as the variance, as it measures the variability in a set of numbers — in this case, the data set is the batting scores. We have now a number that gives an idea of the variability around the average score.
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