U.S. companies lose $63.2 billon per year from workers with insomnia. Workers lo
ID: 3303128 • Letter: U
Question
U.S. companies lose $63.2 billon per year from workers with insomnia. Workers lose an average of 7.8 days of productivity per year due to lack of sleep (Wal Street Journal, January 23, 2013). The following data show the number of hours of sleep attained during a recent night for a sample of 20 workers, Click on the webfile logo to reference the data WEB 6 5 10 5 6 9 9 59 5 8 7 8 698 96 108 a. What is the mean number of hours of sleep for this sample (to 1 decimal)? 7.4 C b. What is the variance? Standard deviation (to 2 decimals)? 03 43 Variance Standard deviationExplanation / Answer
Solution:
Here, we have to find mean, variance and standard deviation for the given sample data.
Mean = X/n
Variance = (X - mean)^2/(n – 1)
Standard deviation = sqrt[(X - mean)^2/(n – 1)]
Calculation table for above formulas is given as below:
X
(X - Mean)
(X - mean)^2
6
-1.4
1.96
5
-2.4
5.76
10
2.6
6.76
5
-2.4
5.76
6
-1.4
1.96
9
1.6
2.56
9
1.6
2.56
5
-2.4
5.76
9
1.6
2.56
5
-2.4
5.76
8
0.6
0.36
7
-0.4
0.16
8
0.6
0.36
6
-1.4
1.96
9
1.6
2.56
8
0.6
0.36
9
1.6
2.56
6
-1.4
1.96
10
2.6
6.76
8
0.6
0.36
Total
148
58.8
Mean
7.4
Mean = X/n = 148/20 = 7.4
Variance = (X - mean)^2/(n – 1) = 58.8/(20 – 1) = 58.8/19 = 3.094737
Variance = 3.09
Standard deviation = sqrt[(X - mean)^2/(n – 1)] = sqrt(3.094737) = 1.759186
Standard deviation = 1.76
X
(X - Mean)
(X - mean)^2
6
-1.4
1.96
5
-2.4
5.76
10
2.6
6.76
5
-2.4
5.76
6
-1.4
1.96
9
1.6
2.56
9
1.6
2.56
5
-2.4
5.76
9
1.6
2.56
5
-2.4
5.76
8
0.6
0.36
7
-0.4
0.16
8
0.6
0.36
6
-1.4
1.96
9
1.6
2.56
8
0.6
0.36
9
1.6
2.56
6
-1.4
1.96
10
2.6
6.76
8
0.6
0.36
Total
148
58.8
Mean
7.4
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