Final answer:
The real mean of the observations is calculated by adjusting the supposed mean with the sum of the deviations divided by the number of observations. In this case, the real mean is 31.
Step-by-step explanation:
The sum of the deviations from the mean (30) for 50 observations is given as 50. In statistics, the sum of the deviations from the mean is usually zero as the total distance of values above the mean equals the total distance below. If sum is non-zero, it indicates the mean used for deviations is not actual mean of the data.
Here, the sum of deviations is not zero, which means 30 is not the real mean of the data. To find the mean, you need to adjust the supposed mean (30) by the sum of deviations divided by the number of observations. The adjustment is thus 50/50 = 1.
So, the real mean of the observations is 30 (supposed mean) + 1 (adjustment) = 31.
Learn more about Mean of Observations