Multiple choice

The mean of first $8$ observations is $18$ and last $8$ observations is $20$. If the mean of all $15$ observations is $19$, find the $8^{th}$ observation

  1. $18$
  2. $12$
  3. $19$
  4. $20$
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C Correct answer
Explanation

The sum of the first 8 observations is 8 * 18 = 144, and the sum of the last 8 observations is 8 * 20 = 160. The sum of all 15 observations is 15 * 19 = 285. The 8th observation is counted twice in the sum of the first and last 8, so it is equal to 144 + 160 - 285 = 19.

AI explanation

The sum of the first 8 observations is 8 multiplied by 18, giving 144, and the sum of the last 8 observations is 8 multiplied by 20, giving 160. Adding these two sums results in 304, but this double counts the 8th observation. The actual sum of all 15 observations is 15 multiplied by 19, which equals 285, so the 8th observation is 304 minus 285, resulting in 19.

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