I need help with #23 compute the range, the variance, and the standardagainintheluesginaldeviation. New scores: 0, 0, 12, 12c. According to the range, how do the two distribu-tions compare in variability? How do they compareaccording to the variance and standard deviation?23. For the data in the following sample: 1, 1, 9, 1a. Find the SS, variance, and standard deviation.b. Now change the score of X = 9 to X 3, andfind the new values for SS, variance, and standarddeviation.c. Describe how one extreme score influences the3, thelevia-eanmean and standard deviation.24. Arden and Plomin (2006) published a study report-ing that IQ scores for boys are more variable than 1Qscores for girls. A researcher would like to know ifthis same phenomenon applies to other measures ofcognitive ability. A standard cognitive skills test is2iven to a sample of nandactr theng15 adolescent boys and a1adolescent girls, and resulted in the

(a) The sample scores are 1, 1, 9, and 1. The formula of sample mean is, M=∑xin The formula of Sum…

Answered: 23. For the data in the following…

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I need help with #23

compute the range, the variance, and the standard
again
in
the
lues
ginal
deviation. New scores: 0, 0, 12, 12
c. According to the range, how do the two distribu-
tions compare in variability? How do they compare
according to the variance and standard deviation?
23. For the data in the following sample: 1, 1, 9, 1
a. Find the SS, variance, and standard deviation.
b. Now change the score of X = 9 to X 3, and
find the new values for SS, variance, and standard
deviation.
c. Describe how one extreme score influences the
3, the
levia-
ean
mean and standard deviation.
24. Arden and Plomin (2006) published a study report-
ing that IQ scores for boys are more variable than 1Q
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
2iven to a sample of n
and
act
r the
ng
15 adolescent boys and a
1adolescent girls, and resulted in the

Expert Solution

Step 1

(a)

The sample scores are 1, 1, 9, and 1.

The formula of sample mean is,

$M = \frac{\sum x_{i}}{n}$

The formula of Sum of squared deviations is,

$S S = \sum {(x i - M)}^{2}$

The formula of sample variance is,

$s 2 = \frac{S S}{n - 1}$

The formula of sample standard deviation is,

$s = \sqrt{s^{2}}$

The mean of scores is,

$\begin{array}{rcl} M & = & \frac{\sum x_{i}}{n} \\ = & \frac{1 + 1 + 9 + 1}{4} \\ = & 3 \end{array}$

The sum of squared deviations (SS) of scores is,

$S S = \sum {(x i - M)}^{2} = {(1 - 3)}^{2} + {(1 - 3)}^{2} + {(9 - 3)}^{2} + {(1 - 3)}^{2} = 4 + 4 + 36 + 4 = 48$

The variance of sample scores is,

$\begin{array}{rcl} s^{2} & = & \frac{S S}{n - 1} \\ = & \frac{48}{4 - 1} \\ = & \frac{48}{3} \\ = & 16 \end{array}$

The sample standard deviation is,

$\begin{array}{rcl} s & = & \sqrt{s^{2}} \\ = & \sqrt{16} \\ = & 4 \end{array}$

Thus, the required SS, variance and standard deviation for the sample scores are 48, 16 and 4.

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23. For the data in the following sample: 1, 1, 9, 1 a. Find the SS, variance, and standard deviation. b. Now change the score of X 9 to X 3, and find the new values for SS, variance, and standard deviation. %3D c. Describe how one extreme score influences the mean and standard deviation.