2. Suppose you study family income in a random sample of 300 families. You find that the mean family income is $41,000; the median is $35,000; and the highest and lowest incomes are $250,000 and $2,400, respectively. (a) Is the distribution of income symmetric, right-skewed or left-skewed? How many families in the sample earned less than $35,000? Explain how you know. (b) Based on the given information, can you determine how many families earned more than $41,000? Why or why not? 3. Forbes magazine published data on the best small firms in 1993. These were firms with annual sales of more than five and less than $350 million. Firms were ranked by five-year average return on investment. The data extracted are the age and annual salary of the chief executive officer for the first 60 ranked firms. Histograms of the data are shown below. How would you describe the distribution in terms of its symmetry, modality and outliers for the ages and the salaries of CEO? Which measure of central tendency should be used? Give a brief reason and interpret this value. 39 CEO Age Histogram of CEO age for best small Mean 51.46667 companies 16 Standard Error 1.151876 Median 50 Mode 50 12 Standard Deviation 8.92239 Sample Variance 79.60904 Frequency Kurtosis 0.093062 Skewness 0.199901 A Range 42 Minimum 32 O 30 35 40 45 50 55 60 65 70 75 Maximum 74 CEO age Sum 3088 Count 60 CEO Salary Histogram of CEO salary for best Mean 404.1695 Standard Error 28.71102 20 small companies Median 350 16 Mode 291 HHHHHHHHH Standard Deviation 220.5335 12 Sample Variance 48635.04 Frequency Kurtosis 0.658471 8 Skewness 0.939667 Range 1082 Minimum 21 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 Maximum 1103 Sum 23846 CEO salary ($1000s) Count 59 4. (Use Excel) How many days in advance do travellers purchase their airline tickets? Below are data showing the advance days for a sample of 28 passengers on a particular flight