23. For the data in the following sample: 1, 1,9, Find the S , variance, and sta

Question

23. For the data in the following sample: 1, 1,9, Find the S , variance, and standard deviation. Now change the score of X - 9 to X -3, and find the new values for SS, variance, and standard deviation Describe how one extremc score influcnces the mean and standard deviation. a. b. c. 24. Arden and Plomin (2006) published a study report ing that 1Q scores for boys are more variable than IQ scores for girls. A researcher would like to know if this same phenomenon applies to other measures of cognitive ability. A standard cognitive skills test is given to a sample of n=15adolescent boys and a sample of n = 15 adolescent girls, and resulted in the following scores. Boys 95397 5248 74973 Girls 6 5467 6 4768 5786 a. Compute the mean, the variance, and the standard deviation for each group. Is one group of scores noticeably more variable than the other? b. 25. Apopulation has a mean of = 50 and a standard deviation of 2(),

Explanation / Answer

a. For boys

Sum of all these numbers = x = 90

Mean x =  x/ n = 90/15 = 6

where x is the skill parameter and n = total number of boys

Variance =  (x- x)2 /(n-1) as the given set is a sample not population

Calculating Variance from given table

(x- x)2 = 82

Variance s2= 82/14 = 5.86

Standard deviation s = sqrt (5.86) = 2.42

For girls :

Sum of all these numbers = x = 90

Mean x =  x/ n = 90/15 = 6

where x is the skill parameter and n = total number of boys

Variance =  (x- x)2 /(n-1) as the given set is a sample not population

Calculating Variance from given table

(x- x)2 = 22

Variance s2= 22/14 = 1.57

Standard deviation s = sqrt (1.57) =1.2536

b. We will find which group is more variable by calculating Coefficient of Variation.

CV(for boys) = standard deviation/ Mean = 2.42/6 = 0.4033

CV(for girls) =  standard deviation/ Mean = 1.2536/6 = 0.2089

so CV(for boys) > CV(for girls)

so the group of boys is more variable than the girl group.

Boys (x-6)^2 9 9 5 1 3 9 9 9 7 1 5 1 2 16 4 4 8 4 8 4 7 1 4 4 9 9 7 1 3 9 sum 90 82

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