Question

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)

Answer 1

a)

Here dot plot shows the sampling distribution of IQR from the given population. So 240 shows the interquartile range of one of the 50 samples.

b)

Since sampling distribution is approximately symmetric so center of dot plot should be approximately at 165. Since IQR of population is 380 -215 = 165 so we can say IQR is unbiased estimator of population IQR.