1. The midrange of a data set is defined as the average of the maximum and the minimum of that dataset. Is this statistic robust (Le "resistant") to the effect of outliers? A. No, it is not robust to outliers. The maximum and minimum are particularly affected byoutliers, so any statistic calculated using them will also be affected by outliers. B. Yes, it is robust to outliers. The maximum and minimum are not strongly affected byoutliers, so any statistic calculated using them will not be affected by outliers either. 2. The first histogram below [noted as (1)] shows the distribution of the yearly incomes of 40 customersat a college coffee shop. Suppose two new people walk into the coffee shop: one making $225,000 and the other $250,000. The second histogram [noted as (2)] shows the new income distribution among the coffee shop customers after the two new people enter. Summary statistics are also provided. 12- (1) (2) 0- 40 42 $60k $62.5k $65k $67.5k $70k Min. 60,680 60,680 (1) 1st Qu. 63,620 63,710 Median 65,240 65,350 12- Mean 65,090 73,300 3rd Qu. 66,160 66.540 Max. 69,890 250,000 A SD 2,122 37,321 $60k $110k $160k $210k $260k (2) Would the mean or median best represent what we might think of as a typical income for the 42 customers (i.e. including the two new customers) at this coffee shop? . O A. The mean would be a better choice. It is important to include every customer's income if we want to calculate a single value that represents the typical income of all customers. . O B. The median would be a better choice. The two new customers have unusually large incomes relative to the other customers and would distort the mean. 6. 910 randomly sampled registered voters from Tampa, FL were asked if they thought workers who have illegally entered the US should be (i) allowed to keep their jobs and apply for US citizenship, (ii) allowed to keep their jobs as temporary guest workers but not allowed to apply for US citizenship, or (iii) lose their jobs and have to leave the country. The results of the survey by political ideology are shown below. Political ideology Conservative Moderate Liberal Total (i) Apply for citizenship 57 120 101 278 Response (ii) Guest worker 121 113 28 262 (iii) Leave the country 179 126 45 350 (iv) Not sure 15 4 1 20 Total 372 363 175 910 Of the Tampa, FL voters who identify themselves as conservatives, what percent are in favor of the guest worker option? . O A. 28.8% . O B. 32.5% . O C. 40.96 . O D. 46.2%
