Question: 51. Mandarin or Cantonese 2011 Below are data on Canadian cities showing mother-tongue counts from the 2011 census: a) Find the correlation between these two

51. Mandarin or Cantonese 2011 Below are data on Canadian cities showing mother-tongue counts from the 2011 census:

Urban Centre Cantonese Mandarin Abbotsford (BC) 310 400 Barrie (ON) 215 295Brantford (ON) 125 90 Calgary (AB) 20 175 11 380 Edmonton (AB)

a) Find the correlation between these two mother-tongue counts. Are you surprised that the correlation is so high? Explain.

b) Plot Cantonese speaker count versus Mandarin speaker count. Describe the relationship. Is a correlation a useful and appropriate summary measure here?

c) Take the log (base 10) of both columns of numbers using your computer or calculator. Replot the data. Have things improved in any way? Calculate the correlation. Is the correlation more appropriate now?

d) What is one obvious reason (for example, a lurking variable) for such a high correlation between the two log counts here? Suggest another useful way of defining the two variables that would produce a smaller correlation. (In real-life studies, there are always issues about how to best define and measure the relevant variables.)

Urban Centre Cantonese Mandarin Abbotsford (BC) 310 400 Barrie (ON) 215 295 Brantford (ON) 125 90 Calgary (AB) 20 175 11 380 Edmonton (AB) 13 595 7295 Guelph (ON) 770 650 Halifax (NS) 460 805 Hamilton (ON) 1975 2215 Kelowna (BC) 235 210 Kingston (ON) 335 395 Kitchener-Cambridge- 1390 3 060 Waterloo (ON) London (ON) 1165 1415 Moncton (NB) 70 75 Montral (QC) 10 515 10 180 Oshawa (ON) 730 645 Ottawa-Gatineau (ON-QC) 6570 7 275 Peterborough (ON) 90 110 Qubec (QC) Regina (SK) 5650 130 270 505 Saguenay (QC) 0 15 Saint John (NB) 45 125 Saskatoon (SK) 865 790 Sherbrooke (QC) 201 65 St. Catharines-Niagara (ON)) 640 555 St. John's (NL) 105 165

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