Multiple choice

The mean of $12$ observations is $14$. By an error one observation is registered as $ 24$ instead of $-24$. Find the actual mean.

  1. $10$
  2. $20$
  3. $30$
  4. $40$
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A Correct answer
Explanation

Original sum = 12 * 14 = 168. The error was adding 24 instead of -24, a difference of 48. Correct sum = 168 - 48 = 120. Correct mean = 120 / 12 = 10.

AI explanation

The original sum of the 12 observations is 12 times 14, which equals 168. The error involves registering 24 instead of negative 24, meaning the sum is too high by 24 minus (negative 24), which is 48. The correct sum is found by subtracting this difference from the original sum: 168 minus 48 equals 120. Dividing this correct sum by 12 gives the actual mean of 10.

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