Mathematics

Mathematics

Problem

Two cricket players, X and Y, scored runs in 10 innings each during a tournament. The data are summarised as follows: Player X: ∑x=380,∑x2=18 400\sum x = 380,\quad \sum x^{2} = 18\,400 Player Y: ∑y=400,∑y2=21 000\sum y = 400,\quad \sum y^{2} = 21\,000 Answer the following. a. (i) For each player, compute the mean runs per innings. b. (ii) For each player, compute the variance and the standard deviation of runs (correct to two decimal places). c. (iii) On the basis of your results, determine which player is more reliable in scoring runs and give a brief reason.
Intuitive explanation

Comparing two players' consistency requires looking beyond just their total runs—you need to measure how spread out their scores are. The key is calculating the variance or standard deviation for each player using the formulas Var=∑x2n−(∑xn)2\text{Var} = \frac{\sum x^2}{n} - \left(\frac{\sum x}{n}\right)^2. The player with lower variance is more consistent, while higher variance means more erratic performance. This tells you who's the more reliable scorer.

Intuitive explanation

Comparing two players' consistency requires looking beyond just their total runs—you need to measure how spread out their scores are. The key is calculating the variance or standard deviation for each player using the formulas Var=∑x2n−(∑xn)2\text{Var} = \frac{\sum x^2}{n} - \left(\frac{\sum x}{n}\right)^2. The player with lower variance is more consistent, while higher variance means more erratic performance. This tells you who's the more reliable scorer.

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