The data below reflect the number of vacation days that a sample of employees at
ID: 3304396 • Letter: T
Question
The data below reflect the number of vacation days that a sample of employees at a certain company have left to take before the end of the year. Complete parts a through c.
10 2 8 11 3 2 6
a. Compute the range for these sample data.
The range is ________
b. Compute the variance for these sample data.
The variance is ______ (Round to two decimal places as needed.)
c. Compute the standard deviation for these sample data.
The standard deviation is_____ (Round to two decimal places as needed.)
Explanation / Answer
10 2 8 11 3 2 6
a. Maximum value = 11
Minimum value = 2
The range is 11 - 2 = 9.
b. Mean = (10 + 2 + 8 + 11 + 3 + 2 + 6) / 7
= 6
Sum of squares of differences = (10-6)2 + (2-6)2 + (8-6)2 + (11-6)2 + (3-6)2 + (2-6)2 + (6-6)2
= 16 + 16 + 4 + 25 + 9 + 16 + 0
= 86
Sample variance = 86 / (7-1) = 86 / 6 = 14.33
c. Standard deviation = 14.33 = 3.79
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