sample grade point averages for ten male students and ten female students are listed. find the coefficient…

sample grade point averages for ten male students and ten female students are listed. find the coefficient of variation for each of the two data sets. then compare the results.\nmales 2.3 3.9 3.9 3.9 2.6 2.6 3.4 3.5 3.9 1.9\nfemales 2.8 3.5 2.3 3.8 3.8 4.1 2.1 3.9 3.9 2.2\nthe coefficient of variation for males is (%). (round to one decimal place as needed.)

sample grade point averages for ten male students and ten female students are listed. find the coefficient of variation for each of the two data sets. then compare the results.\nmales 2.3 3.9 3.9 3.9 2.6 2.6 3.4 3.5 3.9 1.9\nfemales 2.8 3.5 2.3 3.8 3.8 4.1 2.1 3.9 3.9 2.2\nthe coefficient of variation for males is (%). (round to one decimal place as needed.)

Answer

Explanation:

Step1: Calculate the mean for male students

Let (x_{1},x_{2},\cdots,x_{10}) be the male - students' GPAs. The mean (\bar{x}m) is given by (\bar{x}m=\frac{\sum{i = 1}^{10}x{i}}{10}). (\sum_{i=1}^{10}x_{i}=2.3 + 3.9+3.9+3.9+2.6+2.6+3.4+3.5+3.9+1.9 = 32.9) (\bar{x}_m=\frac{32.9}{10}=3.29)

Step2: Calculate the standard - deviation for male students

The formula for the sample standard - deviation (s_m) is (s_m=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x}m)^2}{n - 1}}). ((2.3−3.29)^2=( - 0.99)^2 = 0.9801), ((3.9−3.29)^2=(0.61)^2 = 0.3721) (repeated 4 times), ((2.6−3.29)^2=( - 0.69)^2 = 0.4761) (repeated 2 times), ((3.4−3.29)^2=(0.11)^2 = 0.0121), ((3.5−3.29)^2=(0.21)^2 = 0.0441), ((1.9−3.29)^2=( - 1.39)^2 = 1.9321) (\sum{i = 1}^{10}(x_{i}-\bar{x}m)^2=0.9801+4\times0.3721 + 2\times0.4761+0.0121+0.0441+1.9321) (\sum{i = 1}^{10}(x_{i}-\bar{x}_m)^2=0.9801 + 1.4884+0.9522+0.0121+0.0441+1.9321=5.409) (s_m=\sqrt{\frac{5.409}{9}}\approx0.77)

Step3: Calculate the coefficient of variation for male students

The coefficient of variation (CV_m) is given by (CV_m=\frac{s_m}{\bar{x}_m}\times100%). (CV_m=\frac{0.77}{3.29}\times100%\approx23.4%)

Answer:

23.4