Question 5 Buying a year's worth of textbooks for college can be expensive! Consider a large population of college students for whom the distribution of the annual cost of textbooks is slightly skewed to the left. Here is the five-number summary for the annual cost of textbooks for this population: Minimum 80 Quartile 1 215 Median 335 Quartile 3380 Maximum 440 Suppose we take random samples of size 32 from this population and calculate the interquartile range (IQR) for each of our samples. Below is a dotplot of the IQR from 50 such samples. 60 80 100 120 140 160 180 200 220 240 280 Sample IQR A) Briefly explain what the dot at 240 represents. (3 points) B) Is the sample IQR is an unbiased estimator of the population IQR? Justify your answer.(5 points)

Describe how the presence of possible outliers might be identified on the following. (a) histograms gap between the first bar and the rest of bars or between the last bar and the rest of bars large group of bars to the left or right of a gap higher center bar than surrounding bars gap around the center of the histogram higher far left or right bar than surrounding bars (b) dotplots large gap around the center of the data large gap between data on the far left side or the far right side and the rest of the data large groups of data to the left or right of a gap large group of data in the center of the dotplot large group of data on the left or right of the dotplot (c) stem-and-leaf displays several empty stems in the center of the stem-and-leaf display large group of data in stems on one of the far sides of the stem-and-leaf display large group of data near a gap several empty stems after stem including the lowest values or before stem including the highest values large group of data in the center stems (d) box-and-whisker plots data within the fences placed at q1 â’ 1.5(iqr) and at q3 + 1.5(iqr) data beyond the fences placed at q1 â’ 2(iqr) and at q3 + 2(iqr) data within the fences placed at q1 â’ 2(iqr) and at q3 + 2(iqr) data beyond the fences placed at q1 â’ 1.5(iqr) and at q3 + 1.5(iqr) data beyond the fences placed at q1 â’ 1(iqr) and at q3 + 1(iqr)