1. A sample of 400 visitors to an exhibition was timed to determine how long each took to view the exhibit. Three samples were taken: one in the morning, the second in the afternoon and the third in the evening (use data set XR04-57 and Excel).
a. Determine the mean and the median of each sample.
b. Determine the range, the variance and the standard deviation of each sample.
c. Discuss the similarities and differences among samples.
d. Interpret your findings.
2. The set of data below is from a sample of n = 5
7, -5, -8, 7, 9
a. Calculate the mean, median, and mode
b. Calculate the range and interquartile range
c. Calculate the variance, standard deviation, and coefficient of variation
3. The Excel spreadsheet Investment.xls contains data on daily rate of returns (percentages) on three different investment options (A, B and C) over the past three years. Use these data to answer the following questions. When necessary use Excel's "Data Analysis" tool to generate graphs and statistics.
(a) Construct a histogram of the percentage returns for the data on Type A. (Note: Allow Excel to automatically select the number of ‘Bins' or classes. You may wish to reduce the number of decimal places in the ‘Bin' column of the output to 2 decimal places to keep the x axis tidy).
(b) In general, what do we mean if we say that a histogram is (i) symmetric, (iii) positively skewed, or (iii) negatively skewed?
(c) Would you describe the histogram for invest option A as symmetric, positively skewed or negatively skewed? Explain your answer.
(d) Use Excel to calculate the descriptive statistics for the percentage returns on investment Option A.
(e) Now use Excel to calculate the descriptive statistics for the percentage returns on investment options B and C given in the spreadsheet Investments.xls.
(f) Which investment option do you think has the highest expected returns? Use descriptive statistics to answer this question.
(g) Identify the investment option with the largest variation or ‘spread' in returns. Use available information to justify your answer.
(h) If you are an investor, who would like to invest in one of these options, which type of option you would rather invest in? Explain the reasoning behind your choice.