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Runs scored by batsman in 5 one day matches are 50, 70, 82, 93, and 20. The standard deviation is ______

Question

Runs scored by batsman in 5 one day matches are 50, 70, 82, 93, and 20. The standard deviation is ______

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Solution

To calculate the standard deviation, follow these steps:

  1. Find the mean (average) of the scores. Add all the scores together and divide by the number of scores. In this case, (50 + 70 + 82 + 93 + 20) / 5 = 63.

  2. Subtract the mean from each score to get the deviation of each score. This gives you: -13, 7, 19, 30, -43.

  3. Square each deviation to get: 169, 49, 361, 900, 1849.

  4. Find the mean of these squared deviations. Add them all together and divide by the number of scores. (169 + 49 + 361 + 900 + 1849) / 5 = 665.6.

  5. Finally, take the square root of this mean squared deviation to get the standard deviation. The square root of 665.6 is approximately 25.8.

So, the standard deviation of the scores is approximately 25.8.

This problem has been solved

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