The percentage of foreign-born population for each of the 50 states is represented below. Do you think the mean is the best average for this set of data? Explain.
Percentage
Frequency
0.8----4.4
26
4.5----8.1
11
8.2----11.8
4
11.9---15.5
5
15.6---19.2
2
19.3---22.9
1
23----26.6
1
In this case, the mean may not be the best average for this set of data. The reason is that the distribution of the data is not symmetrical. There is a higher concentration of frequencies in the lower range of percentages (0.8-8.1), and then the frequencies decrease for the higher ranges of percentages.
The mean is influenced by extreme values, and in this case, there are very few instances of higher percentages (19.3-26.6). These extreme values could skew the mean towards a higher value, even though the majority of the data is concentrated in the lower range of percentages.
To better represent the average percentage of foreign-born population for each state, it might be better to consider using a median. The median represents the middle value of a data set when arranged in ascending order, and it is not as affected by extreme values as the mean. This would provide a more representative average that aligns with the majority of the data.