Final answer:
The combined mean of the whole set of observations, with the mean of 25 observations at 80 and another 55 observations at 60, is 66.25.
Step-by-step explanation:
The student asks to determine the mean of the whole set of observations, given that the mean of 25 observations is 80 and the mean of another 55 observations is 60. To calculate this, we'll use the formula for the combined mean of two groups:
Overall Mean = (Sum of Observations of Group A + Sum of Observations of Group B) / Total Number of Observations.
For the first group of 25 observations, the total sum is 25 × 80 = 2000. For the second group of 55 observations, the total sum is 55 × 60 = 3300. The combined total sum is 2000 + 3300 = 5300, and the number of observations is 25 + 55 = 80. Therefore, the overall mean is:
Overall Mean = 5300 / 80 = 66.25
So, the mean of the whole set of observations is 66.25.