Ch. 2, Practice Problems: 11, 12, 13, 16, and 21
Ch. 3, Practice Problems: 14, 15, 22, and 25
11 - For the following scores, find the (a) mean, (b) median, (c) sum of squared
deviations, (d) variance, and (e) standard deviation: 2, 2, 0, 5, 1, 4, 1, 3, 0, 0, 1, 4, 4, 0, 1,
4, 3, 4, 2, 1, 0
A.
2, 2, 0, 5, 1, 4, 1, 3, 0, 0, 1, 4, 4, 0, 1, 4, 3, 4, 2, 1, 0
Solution:
(a) Mean = sum/21 = 42/21 = 2
(b) Arrange the numbers in ascending order
0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 5
Median = middle number = 2
(c) Sum of squared deviations:
x
x-mean
(x-mean)^2
2
0
0
2
0
0
0
-2
4
5
3
9
1
-1
1
4
2
4
1
-1
1
3
1
1
0
-2
4
0
-2
4
1
-1
1
4
2
4
4
2
4
0
-2
4
1
-1
1
4
2
4
3
1
1
4
2
4
2
0
0
1
-1
1
0
-2
4
sum
56
Sum of squared deviation = 56
(d) Variance = Sum of squared deviation/n – 1 = 56/(21 – 1) = 56/20 = 2.8
(e) Standard deviation = √variance = √2.8 = 1.673
12 - For the following scores, find the (a) mean, (b) median, (c) sum of squared
deviations, (d) variance, and (e) standard deviation: 1,112; 1,245; 1,361; 1,372; 1,472
Solution:
(a) Mean = sum/21 = 6562/5 = 1312.4
(b) Arrange the numbers in ascending order
1112, 1,245, 1361, 1372, 1,472
Median = middle number = 1361
(c) Sum of squared deviations:
x
x-mean
(x-mean)^2
1112
-200.4
40160.16
1245
-67.4
4542.76
1361
48.6
2361.96
1372
59.6
3552.16
1472
159.6
25472.16
Sum
76089.2
Sum of squared deviations = 76089.2
(d) Variance = Sum of squared deviation/n – 1 = 76089.2/(5 – 1) = 76089.2/4 = 19022.3
(e) Standard deviation = √variance = √19022.3 = 137.9
13 - For the following scores, find the (a) mean, (b) median, (c) sum of squared
deviations, (d) variance, and (e) standard deviation: 3.0, 3.4, 2.6, 3.3, 3.5, 3.2
Solution:
(a) Mean = sum/6 = 19/6 = 3.17
(b) Arrange the numbers in ascending order 2.6, 3.0, 3.2, 3.3, 3.4, 3.5
Median = (3.2 + 3.3)/2 = 6.5/2 = 3.25