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

a) 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