Read the given scenarios, and answer the accompanying questions.
Question 1: Statistics students were asked to fill a one-cup measure with raisin bran, then tap the cup lightly on the counter three times to settle the contents. If necessary, they were instructed to add more raisin bran to bring the contents exactly to the one-cup line, then spread the contents on a large plate, and count the raisins. The 13 students who chose Kellogg’s Raisin Bran obtained the results shown below:
23 33 44 36 29 42 31 33 61 36 34 23 24
a) Calculate the mean, median, and mode. Is the distribution skewed to the left or to the right?
b) Which is the best measure of central tendency and why?
c) Calculate the standard deviation. Why is there variation in the number of raisins in a cup of raisin bran? Why might it be difficult for Kellogg’s to reduce variation?
Question 2: The following are monthly rents paid by 30 students who live off-campus.
730 730 730 930 700 570
690 1030 740 620 720 670
560 740 650 660 850 930
600 620 760 690 710 500
730 800 820 840 720 700
a) Find the mean, median, mode, and standard deviation.
b) Describe the typical rent paid by a student.
c) Do the measures of central tendency agree? Explain.
d) Sort and standardize the data.
e) Are there outliers or unusual data values?
f) Do you think the data could come from a normal population?