Multiple choice

The mean of twenty observations $\displaystyle { x }{ 1 },{ x }{ 2 },{ x }{ 3 },{ x }{ 4 },...{ x }_{ 20 }$ is $\displaystyle m$. If each of the first ten observations is increased by 8 and each of the next 10 observations is decreased by 8, then the new mean is $\displaystyle n$. The difference $\displaystyle m - n$ equals

  1. $16$
  2. $20$
  3. $0$
  4. $8$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial sum = 20 * m. New sum = (sum of first 10 + 80) + (sum of next 10 - 80) = original sum. New mean n = original sum / 20 = m. So m - n = 0.

AI explanation

Using the property of averages, the overall change in the total sum equals the change in the mean multiplied by the number of items. The total increase from the first ten observations is 10 times 8, giving 80, and the total decrease from the next ten is 10 times 8, also giving 80. Since the net change to the sum is 80 minus 80, which is 0, the new mean n remains exactly the same as the original mean m, making their difference 0.

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