Color and clarity of diamonds. Diamonds are categorized according to the “four C’s”: carats, clarity, color, and cut. Each diamond stone that is sold on the open market is provided a certificate by an independent diamond assessor that lists these characteristics. Data for 308 diamonds were extracted from Singapore’s Business Times (Journal of Statistics Education, Vol. 9, No. 1, 2001). Color is classified as D, E, F, G, H, or I, while clarity is classified as IF, VVS1, VVS2, VS1, or VS2. In addition to color and clarity, the independent certification group (GIA, HRD, or IGI), the number of carats and the asking price were recorded.

a. Use a graphical technique to summarize the color and clarity of the 308 diamond stones. What is the color and clarity that occurs most often? Least often?

b. Use a graphical method to describe the carat distribution of all 308 diamonds.

c. Use a graphical method to describe the carat distribution of diamonds certified by the GIA group.

d. Repeat part c for the HRD and IGI certification groups.

e. Compare the three carat distributions, parts c and

d. Is there one particular certification group that appears to be assessing diamonds with higher carats than the others?

f. Find and interpret the mean of the data set. g. Find and interpret the median of the data set. h. Find and interpret the mode of the data set. i. Which measure of central tendency best describes the 308 carat values? Explain. j. Use the mean and standard deviation to form an interval that will contain at least 75% of the carat values in the data set. DIAMND 20 sections of coated interior pipe. The data (in micrometers) are provided in the table. 1.72 2.50 2.16 2.13 1.06 2.24 2.31 2.03 1.09 1.40 2.57 2.64 1.26 2.05 1.19 2.13 1.27 1.51 2.41 1.95 Source: F. Farshed, & T. Pesacreta, “Coated Pipe Interior Surface Roughness as Measured by Three Scanning Probe Instruments,” Anti-corrosion Methods and Materials, Vol. 50, No. 1, 2003 (Table III).

a. Find and interpret the mean of the sample.

b. Find and interpret the median of the sample.

c. Which measure of central tendency—the mean or the median—best describes the surface roughness of the sampled pipe sections? Explain.