Multiple choice

The average weight of $14$ students was calculated as $71$. But it was later found that the weight of one student had been wrongly entered as $42$ instead of $56$ and of another as $74$ instead of $32$. The correct average is

  1. $75$
  2. $80$
  3. $68$
  4. $69$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The initial sum was 14 * 71 = 994. The errors were: 42 was written instead of 56 (add 14) and 74 was written instead of 32 (subtract 42). The net change is 14 - 42 = -28. The correct sum is 994 - 28 = 966. The correct average is 966 / 14 = 69.

AI explanation

The net error in the sum of the weights is the difference between the correct and incorrect values, calculated as (56 minus 42) plus (32 minus 74), which equals 14 minus 42, yielding a net decrease of 28. The correct average is found by dividing this net change by the number of students, so minus 28 divided by 14 gives a decrease of 2. Subtracting this 2 from the initial average gives the correct average of 71 minus 2, which is 69.

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