How do I find the mean in statistical surveys?

Question

I have this question on my math homework and I would really like to understand how to solve a problem like this.

In a statistics survey, several measurements were taken and the mean of the measurements was 10.2. In a new survey, twice as many measurements were taken and the mean of these measurements was 10.8. What is the average of all the measurements?

What I don't understand is how to solve it, since I know that the mean is all the values added together and then divided on the number of values I use. But I am not told how many values or which values are used in these surveys. Or am I missing something?

Answer 1

Hint:

• Suppose there were $n$ measurements in the first survey
• What was the sum of the measurements in the first survey?
• How many measurements were there in the second survey?
• What was the sum of the measurements in the second survey?
• How many measurements were there altogether?
• What was the sum of the measurements altogether?
• What was the average of the measurements altogether?