Final answer:
The mean is affected by changes in the scale but not the origin. Since the mean is an average of all values, multiplying or dividing these by a constant will change the mean. The scale change is analogous to altering the scale units on a graph, which can make data fluctuations appear different in size.
Step-by-step explanation:
The question is examining the impact of changing the origin and scale on the calculation of the mean. In mathematics, particularly in the field of statistics, the mean is a measure of central tendency and is calculated as the sum of all the values in a data set, divided by the number of values in that set.
When it comes to the change of origin, this means adding or subtracting a constant from each value in the set. This operation affects the location or position of the data but does not affect the mean. On the other hand, changing the scale involves multiplying or dividing all values in the set by a constant. This operation actually changes the mean because the average value will be multiplied or divided by that same constant. Therefore, changing the scale will have a direct impact on the mean, as it is proportional to all the values in the dataset.
It's similar to the comparison of fluctuation in unemployment based on different scales on the vertical axis. If the scale units are changed, the representation of data changes as well, making fluctuations seem smaller or larger as illustrated previously. Thus, the mean is affected by the change in scale, but not the origin.