Question Help * decides to investigate the amount of sick leave taken by its emp
ID: 3322471 • Letter: Q
Question
Question Help * decides to investigate the amount of sick leave taken by its employees. A sample of seven employees yields the following numbers of days of sick leave taken in the past year. 1140062 Use this information to answer parts a through c a. Find and interpret the range. The range is 1-1 days Choose the correct interpretation of the range below. O A. The range gives the most useful value for measuring the spread of the data. B. The largest difference between the m ean and any other value is equal to the range. C. The range represents the average distance of an observation from the mean O D. The number of days separating the fewest and most sick days taken is equal to the range b. Find and interpret the standard deviation s. s= (Round to two decimal places as needed.) Choose the correct interpretation of the standard deviation below d A. The standard deviation represents the sum of the deviations from the mean. O B. The standard deviation represents finding the deviation for each observation, squaring each deviation, and then adding them up ° C. Since the standard deviation uses the square of the units of measurement for the original data, it is not easy to interpret ( D. The standard deviation represents a typical distance of an observation from the mean. Click to select your answer(s)Explanation / Answer
Part a
Range = Maximum – minimum
Maximum = 6
Minimum = 0
Range = 6 – 0 = 6
Interpretation:
D. The number of days separating the fewest and most sick days taken is equal to the range.
Part b
Here, we have to find sample standard deviation S.
Formula for sample standard deviation is given as below:
S = sqrt[(X - mean)^2/(n – 1)]
Calculation table is given as below:
No.
X
(X - mean)^2
1
1
1
2
1
1
3
4
4
4
0
4
5
0
4
6
6
16
7
2
0
Total
14
30
Mean
2
SD = 2.236068
We have
(X - mean)^2 = 30
Var = (X - mean)^2/(n – 1) = 30/(7 – 1) = 30/6 = 5
S = sqrt[(X - mean)^2/(n – 1)] = sqrt(5) = 2.236068
Interpretation:
D. The standard deviation represents a typical distance of an observation from the mean.
Part c
We have to replace 6 by 60, and do part a and b again.
Range = Maximum – minimum
Maximum = 60
Minimum = 0
Range = 60 – 0 = 60
S = sqrt[(X - mean)^2/(n – 1)]
Calculation table is given as below:
No.
X
(X - mean)^2
1
1
75.93878049
2
1
75.93878049
3
4
32.65306449
4
0
94.36735249
5
0
94.36735249
6
60
2528.653032
7
2
59.51020849
Total
68
2961.428571
Mean
9.714286
493.5714286
Var = 493.5714286
S = sqrt(493.5714286) = 22.21646751
What is effect of the outlier?
Answer: C
Both the range and standard deviation increase when an outlier is added.
(For part c, we get more range and standard deviation as compared to part a and b.)
No.
X
(X - mean)^2
1
1
1
2
1
1
3
4
4
4
0
4
5
0
4
6
6
16
7
2
0
Total
14
30
Mean
2
SD = 2.236068
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