Multiple choice

The mean of 100 observations is 50. One observation is replaced by a new value and the mean becomes 50.5. The new value is greater than the old value by:

  1. 50

  2. 25

  3. 0.5

  4. 5
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A Correct answer
Explanation

The total sum of 100 observations increases by 100 * (50.5 - 50) = 50. Since one observation is replaced, the difference between the new value and the old value must equal this total increase of 50.

AI explanation

The original sum of the 100 observations is 100 multiplied by 50, which equals 5000. The new sum after the replacement is 100 multiplied by 50.5, resulting in 5050. The total increase in the sum is 5050 minus 5000, which is 50. Since the rest of the data is unchanged, the new value is greater than the old value by 50.

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