Question

# You want to compare the number of words per sentence in a sports magazine to the number of words per sentence in a political magazineThe data represent random samples of the number of words in 10 sentences from each magazine. Compare the samples using measures of center and variation. Can you use the data to make a valid comparison about the magazines? Explain.Sports magazine: 9, 21, 15, 14, 25, 26, 9, 19, 22, 30Political magazine: 31, 22, 17, 5, 23, 15, 10, 20, 20, 17

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Solution

## Step 1: $\mathrm{Data}\mathrm{of}\mathrm{sports}\mathrm{magzine}=9,21,15,14,25,26,9,19,22,30\phantom{\rule{0ex}{0ex}}\mathrm{Order}:91415192122252630\phantom{\rule{0ex}{0ex}}\mathrm{Median}\mathrm{of}\mathrm{Sports}\mathrm{magzine}=21\phantom{\rule{0ex}{0ex}}\mathrm{Mean}\mathrm{of}\mathrm{Sports}\mathrm{magzine}=9+21+15+14+25+26+9+19+22+30÷10=190÷10=19\phantom{\rule{0ex}{0ex}}\mathrm{Variation}\mathrm{of}\mathrm{Sports}\mathrm{magzine}={\left(9-19\right)}^{2}+{\left(21-19\right)}^{2}+{\left(15-19\right)}^{2}+{\left(14-19\right)}^{2}+{\left(25-19\right)}^{2}+{\left(26-19\right)}^{2}+{\left(9-19\right)}^{2}+{\left(19-19\right)}^{2}+{\left(22-19\right)}^{2}+{\left(30-19\right)}^{2}÷10={\left(-10\right)}^{2}+{\left(2\right)}^{2}+{\left(-4\right)}^{2}+{\left(-5\right)}^{2}+{\left(6\right)}^{2}+{\left(7\right)}^{2}+{\left(-10\right)}^{2}+{\left(0\right)}^{2}+{\left(3\right)}^{2}+{\left(11\right)}^{2}÷10\phantom{\rule{0ex}{0ex}}=100+4+16+25+36+49+100+0+9+121÷10\phantom{\rule{0ex}{0ex}}=460÷10\phantom{\rule{0ex}{0ex}}=46\phantom{\rule{0ex}{0ex}}$Step 2:$\mathrm{Data}\mathrm{of}\mathrm{Political}\mathrm{magzine}=31,22,17,5,23,15,10,20,20,17\phantom{\rule{0ex}{0ex}}\mathrm{Order}:510151720222331\phantom{\rule{0ex}{0ex}}\mathrm{Median}\mathrm{of}\mathrm{Political}\mathrm{magzine}=17+20÷2=37÷2=13.5\phantom{\rule{0ex}{0ex}}\mathrm{Mean}\mathrm{of}\mathrm{Political}\mathrm{magzine}=31+22+17+15+23+15+10+20+20+17÷10\phantom{\rule{0ex}{0ex}}=180÷10\phantom{\rule{0ex}{0ex}}=18$Step 3: $\mathrm{Variation}\mathrm{of}\mathrm{Sports}\mathrm{magzine}={\left(31-18\right)}^{2}+{\left(22-18\right)}^{2}+{\left(17-18\right)}^{2}+{\left(5-18\right)}^{2}+{\left(23-18\right)}^{2}+{\left(15-18\right)}^{2}+{\left(10-18\right)}^{2}+{\left(20-18\right)}^{2}+{\left(20-18\right)}^{2}+{\left(17-18\right)}^{2}÷10\phantom{\rule{0ex}{0ex}}={\left(13\right)}^{2}+{\left(4\right)}^{2}+{\left(-1\right)}^{2}+{\left(-13\right)}^{2}+{\left(5\right)}^{2}+{\left(-3\right)}^{2}+{\left(-8\right)}^{2}+{\left(2\right)}^{2}+{\left(2\right)}^{2}+{\left(-1\right)}^{2}÷10\phantom{\rule{0ex}{0ex}}=169+16+1+169+25+9+4+4+1÷10\phantom{\rule{0ex}{0ex}}=462÷10\phantom{\rule{0ex}{0ex}}=46.2\phantom{\rule{0ex}{0ex}}$Final Answer: Variation of Sports magazine is having greater measure in variation and Median of Sports magazine is having greater value of center.

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