Question

Consider the following sample: 16, 13, 10, 17, 16, 14, 5, 12, 15, 8, 9, 10, 15, 22, 8. Calculate the variance and interquartile range of the sample, respectively. A. 19.38; 7 B. 15.7; 7 C. 4.40; 7 D. 19.38; 7.5 E. 19.38; 6.5

Answer 1

Now we find variance and Interquartile range of the sample
The Sol consider sample: 16, 13, 10, 17, 16, 14, 5, 12, 15, 8 9 10 22,8 is, =) 5, 8, 8, 9, 10, 10, 12, 3, 4, Is IS, 16, 16, 17, 22. where Median = 13 Lower Quarted Q = 9 Upped Quarked Q = 16 Median: f. 7. 8. 9, 8, 8. & ( 13 ) off, ts. so. xo. x, s. p. Median = 13 Lower Quadrea Quarter ai &, 8, 8, 9, 10, X6, 23 th Q = 9 Quartesi Upper Pg 13 A, &, is, 16, p. fr. = 16 3

Interquaatile range = Q3 - Q, Inredquartile range = 16 - 9 Inredquartile range = 7 Now Sample variance s = {(x-x)" n-1 5+8+8+ 9+10+ 10+12+13+ 14 11 Mean tist ist 16+ 16 +17+ 22. 15 =) 190 15 х 12.66 Now {(x-x) = (5-12:46) + (8-12-66) 4 (8-12-66) +(9-12. 66)² + (10-12.66) + (10-12 .6674 (12-1260) +(12-12.66)² + (14-12.66)²+(15-12.66) + (15-12-66) + (16-12.66)² + (16-12-66) + (12-12.66) 4 (22-1266)

{(x-x) = 58.67 +21.71 +21.71+13.39 +7.07 +7.07 +0.43 to 1st 1.795+5.475 t 5.475 +11.15+11.15+18.83 +87.23 {(x-x)² = 271.275.6 o s² {(x-x) 271.2756 15-1 n-1 on 271..2756 Variance = 19.3768 variance = 19.38 Answer! option A That is A. 19-38, 7 variance = 19.38 Interquartile = 7