(a)
To find:
The class width for the given frequency distribution.
(a)
Answer to Problem 2E
Solution:
The class width of the given frequency distribution is
Explanation of Solution
Formula used:
The formula to calculate the class width is,
Given:
The table is given as,
| Braking Times for Vehicles at 60 mph (in minutes) |
|
| Class | Frequency |
| 12 | |
| 15 | |
| 14 | |
| 15 | |
| 14 | |
The upper limit of the distribution is given as
Calculation:
The smallest number that can belong to a particular class is termed as lower class limit and the largest number that can belong to a particular class is termed as upper class limit.
Substitute
(b)
To find:
The class boundary for each class of the given frequency distribution.
(b)
Answer to Problem 2E
Solution:
The class boundary for each class of the given frequency distribution is shown in Table
| Class | Frequency | Class boundaries |
| 12 | ||
| 15 | ||
| 14 | ||
| 15 | ||
| 14 |
Explanation of Solution
Formula used:
The formula to calculate the class boundary is,
Given:
The table is given as,
| Braking Times for Vehicles at 60 mph (in minutes) |
|
| Class | Frequency |
| 12 | |
| 15 | |
| 14 | |
| 15 | |
| 14 | |
Calculation:
It is known that the smallest number that can belong to a particular class is termed as lower class limit and the largest number that can belong to a particular class is termed as upper class limit.
For the first class, since, the largest number is 0.07 and 0.08 is the smallest number in the next class, then, substitute
Continuing the same way, the class boundaries of all the five classes are shown in the table given below,
Table 1
| Class | Frequency | Class boundaries |
| 12 | ||
| 15 | ||
| 14 | ||
| 15 | ||
| 14 |
(c)
To find:
The midpoint of each class for the given frequency distribution.
(c)
Answer to Problem 2E
Solution:
The midpoint of each class for the given frequency distribution is shown in Table
| Class | Frequency | Class boundaries | Midpoint |
| 12 | |||
| 15 | |||
| 14 | |||
| 15 | |||
| 14 |
Explanation of Solution
Formula used:
The formula to calculate the midpoint of any class is,
Given:
The table is given as,
| Braking Times for Vehicles at 60 mph (in minutes) |
|
| Class | Frequency |
| 12 | |
| 15 | |
| 14 | |
| 15 | |
| 14 | |
Calculation:
The smallest number that can belong to a particular class is termed as lower class limit and the largest number that can belong to a particular class is termed as upper class limit.
For the first class,
Substitute
Continuing the same way, the midpoint of all the five classes are shown in the table given below,
Table 2
| Class | Frequency | Class boundaries | Midpoint |
| 12 | |||
| 15 | |||
| 14 | |||
| 15 | |||
| 14 |
(d)
To find:
The relative frequency of each class for the given frequency distribution.
(d)
Answer to Problem 2E
Solution:
The relative frequency of each class for the given frequency distribution is shown in Table
| Class | Frequency | Class boundaries | Midpoint | Relative frequency |
| 12 | ||||
| 15 | ||||
| 14 | ||||
| 15 | ||||
| 14 |
Explanation of Solution
Formula used:
The formula to calculate the relative frequency of any class is,
Here
Given:
The table is given as,
| Braking Times for Vehicles at 60 mph (in minutes) |
|
| Class | Frequency |
| 12 | |
| 15 | |
| 14 | |
| 15 | |
| 14 | |
Calculation:
The sum of the frequencies is,
For the first class,
Substitute 12 for
Continuing the same way, the relative frequency of all the five classes are shown in the table given below,
Table 3
| Class | Frequency | Class boundaries | Midpoint | Relative frequency |
| 12 | ||||
| 15 | ||||
| 14 | ||||
| 15 | ||||
| 14 |
(e)
To find:
The cumulative frequency of each class for the given frequency distribution.
(e)
Answer to Problem 2E
Solution:
The cumulative frequency of each class for the given frequency distribution is shown in Table
| Class | Frequency | Class boundaries | Midpoint | Relative frequency | Cumulative frequency |
| 12 | 12 | ||||
| 15 | |||||
| 14 | |||||
| 15 | |||||
| 14 |
Explanation of Solution
Formula used:
The cumulative frequency of any class is calculated by adding the frequency of that class and all the previous classes.
Given:
The table is given as,
| Braking Times for Vehicles at 60 mph (in minutes) |
|
| Class | Frequency |
| 12 | |
| 15 | |
| 14 | |
| 15 | |
| 14 | |
Calculation:
The cumulative frequency of all the five classes are shown in the table given below,
Table 4
| Class | Frequency | Class boundaries | Midpoint | Relative frequency | Cumulative frequency |
| 12 | 12 | ||||
| 15 | |||||
| 14 | |||||
| 15 | |||||
| 14 |
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Chapter 2 Solutions
Beginning Statistics, 2nd Edition
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