Problem 1. A study has been conducted to determine the distribution of the grades of In- troduction of Anthropology course at OU for last fall. A sample of 50 students who took Introduction of Anthropology last fall has been selected from several sections and their grades were determined. 7 students had an A, 12 had a B, 18 students had a C, 9 students had a D and 4 students had an F. (a). Construct a table of grades versus frequency, relative frequency and cumulative rela- tive frequency. (b). What is the percentage of students in the sample who had a B or a better grade ? Justify your answers. (c). What is the percentage of students in the sample who had a C or a lower grade ? Justify your answers. (d). Use Microsoft Excel to plot a pie chart of the grades of the 50 students selected for this study. To make a bar graph/ pie chart in Excel, (1) first input the data into Excel spreadsheet, make a table of four columns, Letter Grade, Count (or Frequency), Relative Frequency) and Cumulative Relative Frequency). Label the columns, Letter Grade, Frequency, Relative Frequency) and Cu- mulative Relative Frequency, respectively. (2) Select the relevant columns of the table and go to insert and you will see a number of plots (Bar graphs/ Pie Charts. If you click on the plot that looks like a Pie Chart, you will get a bunch of options. Pick the fist one, it will give you the Pie chart. Keep in mind that the Bar graphs/ Pie Charts may be constructed using Frequency or Relative Frequency, but not Cumulative Relative Frequency. Problem 2. Elias is a branch manager at a local bank. Recently, he has been receiving customer feedback saying that the wait times for a client to be served by a customer service representative are too long. Elias decides to observe and write down the time spent by each customer on waiting. Below are his findings from observing and writing down the wait times in seconds spent by N = 20 customers; 42.2, 45.5, 30.3, 31.4, 35.6, 45.2, 54.1, 45.6, 36.5, 43.1, 43.1, 35.6, 37.6, 36.5, 45.3, 43.5, 40.3, 50.2, 47.2, 31.2. Elias would like to analyze the data, by making a histogram and calculating some measures of center and spread for this dataset. 1. Sort that data from the smallest to the largest, and then decide the number of subintervals k to use for the histogram. Use the formula k = 1 + 3.3 log(N ) and round k to the nearest integer. 2. Choose a starting point for the first subinterval. The rule is to try a starting point that is slightly smaller than the smallest data point (after data have been ordered). For instance, if the smallest data point is 30.3, use the starting point {30.3 − 0.05 = 30.25}. The subintervals should 1 be consecutive, non-overlapping. The subintervals must be adjacent and are often of equal width. 3. Decide on the width of the subintervals. The width of bins or subintervals h can be assigned directly or can be calculated from a suggested number of bins k as: h = max x − min x , (1) k where max x is number that is slightly larger than the largest data point, and min x is the starting point from step 2. For instance, if the largest data point is 54.1 and the smallest data point is 30.3, max x = 54.1 + 0.05 = 54.15 and min x = 30.3 − 0.05 = 30.25. 4. Determine the subintervals and construct a table of subintervals of wait time versus frequency for the above data. 5. Construct the histogram of wait time classes (subintervals) versus frequency. 6. Based on the histogram in part 5, describe the shape of that data in terms of symme- try and the location of the peak. 7. Find the median, the first quartile and the third quartile of the wait time data. 8. Is the data point 54.1 a potential outlier?
