Concept explainers
a.
The
a.
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Answer to Problem 23CQ
The mean of the given data is
Explanation of Solution
Given Info:
Total numbers in the data set are 10.
The data represent the number of highway miles per gallon of the 10 worst vehicles.
Calculation:
Formula to calculate the sample mean is,
Substitute the value of
Thus, mean of the data is 15.3.
b.
The
b.
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Answer to Problem 23CQ
The median of given data is
Explanation of Solution
Calculation:
Arrange the data in ascending order.
12 | 13 | 14 | 15 | 15 | 16 | 16 | 17 | 17 | 18 |
There is an even number of data values. That is 10.
The middle two data values are
Determine the average of two middle values.
Thus the median of the data is 15.5.
c.
The
c.
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Answer to Problem 23CQ
The mode of given data are 15, 16 and 17.
Explanation of Solution
Calculation:
Since the values 15, 16 and 17 occurs two times in given data, the mode is
d.
The midrange of given data.
d.
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Answer to Problem 23CQ
The midrange of given data is
Explanation of Solution
Calculation:
Formula to calculate the mid
Substitute 12 for lowest value and 18 for maximum value in the above formula,
Thus the mid range of the data is 15.
e.
The range of given data.
e.
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Answer to Problem 23CQ
The range of given data 6.
Explanation of Solution
Calculation:
Formula to calculate the range of the data is,
Substitute 12 for lowest value and 18 for highest value in the above formula to get range,
Thus, the range of the data is 6.
f.
The variance of given data.
f.
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Answer to Problem 23CQ
The variance of given data is 3.57.
Explanation of Solution
Calculation:
Formula to calculate the variance of the data is,
Determine the deviation for each data value and square each of the deviation,
X |
|
|
|
12 |
|
|
10.89 |
15 |
|
|
0.09 |
13 |
|
|
5.29 |
14 |
|
|
1.69 |
15 |
|
|
0.09 |
16 |
|
|
0.49 |
17 |
|
|
2.89 |
16 |
|
|
0.49 |
17 |
|
|
2.89 |
18 |
|
|
7.29 |
Determine the sum of the squares,
Substitute 32.1 for
Thus, the population variance is 3.57.
g.
The standard deviation of the given data.
g.
![Check Mark](/static/check-mark.png)
Answer to Problem 23CQ
The standard deviation of the given data is 1.9.
Explanation of Solution
Calculation:
Formula to calculate the sample standard deviation is,
Take the square root of 3.57 to get population standard deviation.
Thus the population standard deviation is 1.9
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Chapter 3 Solutions
ELEMENTARY STATISTICS: STEP BY STEP- ALE
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