1.Suppose that a state introduces a state income tax which will be at a flat rate. The state legislature wishes to estimate how much money they will receive in taxes, and to do this they need to know the average income of residents of the state. Which information would be most useful, the mean income, the median income, or the mode of the incomes? Why?
2.Dave is a college student contemplating a possible career option. One factor that will influence his decision is the amount of money he is likely to make. He decides to look up the average salary of graduates in that profession. Which information would be more useful to him, the mean salary or the median salary? Why?
3.The 10% trimmed mean of a data set is found by arranging the data in order, deleting the bottom 10% of the values and the top 10% of the values and then calculating the mean of the remaining values. What advantages do you think that the trimmed mean has as compared to the mean?
4. Boxplots are graphs that are useful for revealing central tendency, the spread of the data, the distribution of the data and the presence of outliers. Draw an example of a box plot and comment on each of these characteristics as shown by your boxplot.
5. Without calculating the standard deviation, compare the standard deviation for the following three data sets. (Note: All data sets have a mean of 30.) Which do you expect to have the largest standard deviation and which do you expect to have the smallest standard deviation? Explain your answers in terms of the formula s =[sum(x - x)
2]/（n - 1）
Set A: 30 30 30 30 30 30 30 30 30 30
Set B: 20 25 25 30 30 30 30 35 35 40
Set C: 20 20 20 25 25 35 35 40 40 40
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