for statistics The chemicals in clay used to make pottery can differ depending o
ID: 3069089 • Letter: F
Question
for statistics
The chemicals in clay used to make pottery can differ depending on the geographical region where the clay originated. Sometimes, archaeologists use a chemical analysis of clay to help identify where a piece of pottery originated. Such an analysis measures the amount of a chemical in the clay as a percent of the total weight of the piece of pottery. The boxplots below summarize analyses done for three chemicals-X, Y, and Z--on pieces of pottery that originated at one of three sites: I, I or III Site I Site II Site III 16 16 Site ! Site 11 Site 111 14 121--- 12 --TE 4. 4 0 0 X Y Z Chemical X Y Z Chemical XY ChemicalExplanation / Answer
(a) For chemical Z, mean value of the percentage weight found in pottery is almost same (approximately equal to 7%) across three sites. But, the range of the weight percentage is different across 3 sites. For eg. range at site 1 is between 4 and 10%, at site 2, it is between 6 to 8; at site 3, it is between 3 and 11%.
(b) (i) Among the 3 sites, only at site 3, we observe that the sum of the mean weight percentage for the 3 chemicals is approximately equal to 20%. Hence, the most likely site of origination is 3.
(ii) Clearly, chemical Y will be most useful for site identification. Because among the 3 chemicals, only Y has both mean value and range of the weight percentage significantly different as we go from one site to another. So, Y is the most useful in identifying the site.
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