Section 3.2 Measures of Variation worksheet

Referring back to the student and their relatives data, let us determine the sample mean, variance, and S.D

Students' ages Students' fathers ages Students' younger s. ages x ( ) ( ) 2 x ( ) ( ) 2 x ( ) ( ) 2 18 -1.77 3.12 49 -2.63 6.93 6 -8.17 66.69 19 -0.77 0.59 70 18.37 337.33 9 -5.17 26.69 20 0.23 0.05 42 -9.63 92.80 10 -4.17 17.36 19 -0.77 0.59 43 -8.63 74.53 1 -13.17 173.36 20 0.23 0.05 38 -13.63 185.87 8 -6.17 38.03 18 -1.77 3.12 55 3.37 11.33 8 -6.17 38.03 18 -1.77 3.12 53 1.37 1.87 17 2.83 8.03 19 -0.77 0.59 52 0.37 0.13 6 -8.17 66.69 19 -0.77 0.59 36 -15.63 244.40 9 -5.17 26.69 18 -1.77 3.12 45 -6.63 44.00 10 -4.17 17.36 20 0.23 0.05 68 16.37 267.87 16 1.83 3.36 18 -1.77 3.12 46 -5.63 31.73 11 -3.17 10.03 18 -1.77 3.12 42 -9.63 92.80 15 0.83 0.69 18 -1.77 3.12 45 -6.63 44.00 7 -7.17 51.36 18 -1.77 3.12 42 -9.63 92.80 14 -0.17 0.03 19 -0.77 0.59 43 -8.63 74.53 14 -0.17 0.03 18 -1.77 3.12 52 0.37 0.13 15 0.83 0.69 20 0.23 0.05 70 18.37 337.33 15 0.83 0.69 19 -0.77 0.59 52 0.37 0.13 20 5.83 34.03 21 1.23 1.52 49 -2.63 6.93 6 -8.17 66.69 19 -0.77 0.59 56 4.37 19.07 10 -4.17 17.36 18 -1.77 3.12 51 -0.63 0.40 15 0.83 0.69 18 -1.77 3.12 60 8.37 70.00 21 6.83 46.69 21 1.23 1.52 50 -1.63 2.67 23 8.83 78.03 22 2.23 4.99 50 -1.63 2.67 23 8.83 78.03 20 0.23 0.05 55 3.37 11.33 27 12.83 164.69 20 0.23 0.05 55 3.37 11.33 14 -0.17 0.03 18 -1.77 3.12 58 6.37 40.53 15 0.83 0.69 21 1.23 1.52 54 2.37 5.60 21 6.83 46.69 39 19.23 369.92 68 16.37 267.87 39 24.83 616.69

19.7 ( ) 2 = 421.37 52 ( ) 2 = 2379 14 ( ) 2 = 1696

We know have all means and ingredients to calculate the sample variances and means for each age category.

calculations Students' ages Students' fathers ages Students' younger s. ages Sample variance ( ) 2 1 = 421.37 30 14 ( ) 2 1 = 2379 30 79.3 ( ) 2 1 = 1696 30 56 Sample S.D. (14) 3.7 years (20.3) 9 years (8) 7.5 years

Doe the values acquired in the above table make sense? Justify.

b) How can you justify the values of each category, i.e., student vs parent, vs sibling's ages.

In-class exercise: Pace University's sushi bar sells spinners for students who want to fish at the Pond and then go to the bar to have the freshest sushi . The bar has eight different kinds of spinners and their prices in dollars are: 2.10 1.95 2.60 2.00 1.85 2.25 2.15 2.25.

a) Use a calculator with appropriate statistics keys to verify that for the Trading Post data, and $2.14 and $0.22.

b) Why did I ask you to calculate and instead of and s?

c) Which formula do you think your calculator uses, those of and , or those of and s?Justify

d) Compute the CV of prices for the spinners and explain the meaning of the result