Multiple choice

Mean of twenty observations is $15$. It two observations $3$ and $14$ are replaced by $8$ and $9$ respectively, then the new mean will be

  1. $14$
  2. $15$
  3. $16$
  4. $17$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The original total is 20 x 15 = 300. Replacing 3 and 14 by 8 and 9 changes the total by -3 - 14 + 8 + 9 = 0. The total and number of observations remain unchanged, so the new mean is 15.

AI explanation

The original sum of the twenty observations is 20 multiplied by 15, which equals 300. When observations 3 and 14 are replaced by 8 and 9, the net change in the sum is 8 plus 9 minus 3 minus 14, which equals 0, keeping the sum at 300. Dividing this sum by 20 gives the new mean as 15.