Multiple choice

If all the class marks are reduced by 5 and divided by 10 and then the mean of the numbers so obtained is found out to be "x". How is "x" related to actual mean "m"?

  1. x = m

  2. x = 10 m - 5

  3. 10x = m - 5

  4. x = 50 m - 10
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C Correct answer
Explanation

Let the original values be xi. The new values are yi = (xi - 5) / 10. The mean x = (1/n) * sum(yi) = (1/n) * sum((xi - 5) / 10) = (1/10) * ((1/n) * sum(xi) - 5) = (m - 5) / 10. Therefore, 10x = m - 5.

AI explanation

When data is transformed by subtracting a constant and dividing by another constant, the new mean is found by applying the same operations to the original mean. This gives the equation x equals the quantity m minus 5 divided by 10. Multiplying both sides by 10 and rearranging the terms results in the relationship 10x equals m minus 5.

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