Multiple choice

Mean of 199 observations is 40. If mean of first 100 observations is 42.5 and that of last 100 observations is 39.5 then the hundredth observation is

  1. 120

  2. 200

  3. 240

  4. 100
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sum of 199 = 199 * 40 = 7960. Sum of first 100 = 100 * 42.5 = 4250. Sum of last 100 = 100 * 39.5 = 3950. The 100th observation is counted twice. (4250 + 3950) - 7960 = 8200 - 7960 = 240.

AI explanation

The total sum of all 199 observations is 199 multiplied by 40, which equals 7960. The sum of the first 100 observations is 100 multiplied by 42.5 (4250), and the sum of the last 100 observations is 100 multiplied by 39.5 (3950). Adding these two partial sums gives 8200, which counts the 100th observation twice. The value of the 100th observation is the difference between this combined sum and the actual total sum, so 8200 minus 7960 equals 240.

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