In the previous problem we noted that the differences in cognitive skills tend t
ID: 3207546 • Letter: I
Question
In the previous problem we noted that the differences in cognitive skills tend to be bigger among older people than among younger people. These differences are often called diversity. Similarly, the differences in performance from trial to trial for the same person are often called consistency. Research in this area suggests that consistency of performance seems to decline as people age. A study by Wegesin and Stern (2004) found lower consistency (more variability) in the memory performance scores for older women than for younger women. The following data represent memory scores obtained for two women, one older and one younger, over a series of memory trials. a. Calculate the variance of the scores for each woman. Are the scores for the younger woman more consistent (less variable)?Explanation / Answer
Younger = x1
Older = x2
( a )
x1
(x1 - x1 bar)
(x1 - x1 bar)^2
8
0.75
0.5625
6
-1.25
1.5625
6
-1.25
1.5625
7
-0.25
0.0625
8
0.75
0.5625
7
-0.25
0.0625
8
0.75
0.5625
8
0.75
0.5625
Total =
58
5.5
x1 bar = Sx1 / n1 = 58 / 8 = 7.25
Variance = S (x1 – x1 bar)^2 / (n1-1) = 5.5 / 7 = 0.7857
The variance for the Younger women is 0.7857
x2
(x2 - x2 bar)
(x2 - x2 bar)^2
7
0.625
0.390625
5
-1.375
1.890625
8
1.625
2.640625
5
-1.375
1.890625
7
0.625
0.390625
6
-0.375
0.140625
8
1.625
2.640625
5
-1.375
1.890625
Total =
51
11.875
x2 bar = Sx2 / n2 = 51 / 8 = 6.375
Variance = S (x2 – x2 bar)^2 / (n2-1) = 11.875 / 7 = 1.6964
The variance for the Younger women is 1.6964
( b )
Here we find the value of coefficient of variation. Whose coefficient of variation is less we can say that is less variable.
CV = (Standard deviation / x bar ) *100
Standard deviation = Ö Variance
Younger = x1
CV = (Ö 0.7857 /7.25) * 100 = 0.1223 = 12.23%
Older = x2
CV = (Ö 0.7857 / 6.375) *100 = 0.2043 = 20.43%
The coefficient value is less for Younger woman. Yes, the score of the younger woman is more consistent.
x1
(x1 - x1 bar)
(x1 - x1 bar)^2
8
0.75
0.5625
6
-1.25
1.5625
6
-1.25
1.5625
7
-0.25
0.0625
8
0.75
0.5625
7
-0.25
0.0625
8
0.75
0.5625
8
0.75
0.5625
Total =
58
5.5
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