Question
A sample was taken of the salaries of 24 employees of a large company. The following...
- A sample was taken of the salaries of 24 employees of a large company. The following are the salaries (in thousands of dollars) for this year. For convenience, the data are ordered.
|
57 |
61 |
62 |
63 |
64 |
65 |
66 |
68 |
68 |
69 |
70 |
73 |
|
73 |
75 |
76 |
79 |
81 |
81 |
82 |
87 |
96 |
104 |
108 |
110 |
-
- Find the following statistics:
- Median
- Find the following statistics:
- Range
- Q1
- Q2
- Q3
- IQR
- Construct a box plot for the given data.
- Based on your results from part b, does the data appear to be skewed? Explain.
Homework Answers
Answer #1
Solution:- Given that samples 57,61,62,63,64,65,66,68,68,69,70,73,73,75,76,79,81,81,82,87,96,104,108,110
a)
i) Median = 73
ii) Range = 53
Explanation
The range is the difference between the highest and lowest values in the data set.
Ordering the data from least to greatest, we get:
57 61 62 63 64 65 66 68 68 69 70 73 73 75 76 79 81 81 82 87 96 104 108 110
The lowest value is 57.
The highest value is 110.
The range = 110 - 57 = 53.
iii) Q1 = 65.5
iv) Q2 = Median = 73
v) Q3 = 81.5
vi) IQR = 16
Explanation
The interquartile range is the difference between the third and first quartiles.
The third quartile is 81.5.
The first quartile is 65.5.
The interquartile range = 81.5 - 65.5 = 16.
b. Box plot :
c. Positive skewed (Right skewed)
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