Multiple choice

Mean of $31$ observation is $65$ .If mean of first $15$ observation is $64$ and that of last $15$ observation is $66$ ,then the sixteenth observation is

  1. $66$
  2. $65$
  3. $64.5$
  4. $62.55$
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B Correct answer
Explanation

Total sum = 31 * 65 = 2015. Sum of first 15 = 15 * 64 = 960. Sum of last 15 = 15 * 66 = 990. 16th observation = 2015 - (960 + 990) = 2015 - 1950 = 65.

AI explanation

The total sum of all 31 observations is 31 multiplied by 65, which equals 2015. The sum of the first 15 observations is 15 multiplied by 64 (960), and the sum of the last 15 observations is 15 multiplied by 66 (990). Adding these two partial sums gives a total of 1950. The 16th observation is the difference between the total sum and this partial sum, so 2015 minus 1950 equals 65.

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