The number of observations in a group is $40$. If the average of first $10$ is $4.5$ and that of the remaining $30$ is $3.5$, then the average of the whole group is:

Using the weighted average method, the sum of the first 10 observations is 10 times 4.5, which is 45, and the sum of the remaining 30 is 30 times 3.5, which is 105. The total sum of all 40 observations is 45 plus 105, giving 150. Dividing this total by 40 gives the overall average, which is 150 divided by 40, equaling 15/4.

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