Statistical Methods I FA_15_291 531_01 Kowski Homework Week 2 (14 points) Section 1.3 Section 1.3 (14 points) 1) (4 points) Examining boxplots. A sample of people were surveyed and asked their favorite genre of reading (nonfiction, novels, poems), as well as their age. A boxplot showing the results of ages for each genre is depicted in the graph above. Refer to the graph of below to answer the following. 100 - Favorite Non-Fiction Genre Age (years) 50 40 - 110 20 Nonfiction Novels Poems Type Note: 1 10 represents the data entry number, i.e. the 1 10" person. + represents the mean a) Determine the five-number summary for each reading genre b) Comparing the mean and the median, describe the distribution shape with respect using symmetrical, right skewed, left skewed 2) (1 point) Median versus mean for net worth. A report on the assets of American households says that the median net worth of U.S. families is $77,300. The mean net worth of these families is $498,800. What explains the difference between these two measures of center? Statistical Methods I FA_15_291_531_01 Kowski 3) (1 point) Based on the median and mean from the previous question, which choice below explains how the relationship between the mean and the median reflects the shape of the distribution. a) Since the mean is smaller, the distribution is skewed to the right. b) Since the mean is larger, the distribution is skewed to the right. c) Since the mean is larger, the distribution is skewed to the left. d) Since the mean is smaller, the distribution is skewed to the left. 4) (8 points) Business start times. An entrepreneur faces many bureaucratic and legal hurdles when starting a new business. The following is sample of 25 countries from data on the time, in days, to complete all the procedures required to start a business. 13 66 36 12 8 27 6 7 52 48 15 94 28 5 13 60 S 18 18 294 Use the data above to answer the following questions. a) Calculate the sample mean b) Calculate the sample standard deviation c) Determine the five-number summary d) Use the IQR to determine if there are any potential outliers e) Sketch a modified boxplot. Be sure to give your graph a title and label the axis f) Recalculate the mean and median with the removal of any outliers. g) Circle the correct answers (in bold) to complete the sentence: The [mean or median] changed by a larger amount as a result of removing the outlier. This implies that [mean or median] is a more resistant measure of center to the outlier