Multiple choice

Out of $250$ observations, the first $100$ observations have mean $5$ and the average of the remaining $150$ observations is $25/3$. What is the average of the whole group of observations?

  1. $6$
  2. $7$
  3. $8$
  4. $9$
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B Correct answer
Explanation

Total sum = (100 * 5) + (150 * 25/3) = 500 + 1250 = 1750. Average = 1750 / 250 = 7.

AI explanation

Using the combined mean formula, the total sum of the first 100 observations is 100 multiplied by 5, giving 500. The sum of the remaining 150 observations is 150 multiplied by 25/3, giving 1250. The average of the whole group is the total sum divided by the total number of observations, so (500 + 1250) divided by 250 equals 1750 divided by 250, which is 7.

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