More freshmen: For the data in Exercise 6:
- Construct a frequency
polygon . - Construct a relative frequency polygon.
- Construct a frequency ogive.
- Construct a relative frequency ogive.
a.
To construct:A frequency polygon.
Explanation of Solution
Given information: The following frequency distribution presents the number of freshmen elected in each of the past 53 elections from 1912 to 2016.
Number of Freshmen | Frequency |
20-39 | 2 |
40-59 | 15 |
60-79 | 10 |
80-99 | 14 |
100-119 | 7 |
120-139 | 3 |
140-159 | 1 |
160-179 | 1 |
Formula used:
Calculation:
Number of Freshmen | Class Midpoints | Frequency |
20-39 | 2 | |
40-59 | 15 | |
60-79 | 10 | |
80-99 | 14 | |
100-119 | 7 | |
120-139 | 3 | |
140-159 | 1 | |
160-179 | 1 |
Now plotting the points whose x-coordinates are the class midpoints and whose y-coordinates are the frequencies. Then the frequency polygon is connecting the points with straight line
b.
To construct: A relative frequency polygon.
Explanation of Solution
Given information: The following frequency distribution presents the number of freshmen elected in each of the past 53 elections from 1912 to 2016.
Number of Freshmen | Frequency |
20-39 | 2 |
40-59 | 15 |
60-79 | 10 |
80-99 | 14 |
100-119 | 7 |
120-139 | 3 |
140-159 | 1 |
160-179 | 1 |
Formula used:
Calculation:
Number of Freshmen | Class Midpoints | Frequency | Relative Frequency |
20-39 | 2 | ||
40-59 | 15 | ||
60-79 | 10 | ||
80-99 | 14 | ||
100-119 | 7 | ||
120-139 | 3 | ||
140-159 | 1 | ||
160-179 | 1 |
Now plotting the points whose x-coordinates are the class midpoints and whose y-coordinates are therelative frequencies. Then the relative frequency polygon is connecting the points with straight line.
s
c.
To construct: A frequency ogive.
Explanation of Solution
Given information: The following frequency distribution presents the number of freshmen elected in each of the past 53 elections from 1912 to 2016.
Number of Freshmen | Frequency |
20-39 | 2 |
40-59 | 15 |
60-79 | 10 |
80-99 | 14 |
100-119 | 7 |
120-139 | 3 |
140-159 | 1 |
160-179 | 1 |
Definition used: The cumulative frequency of a class is the sum of the frequencies of that class and all previous classes.
Anogive plots the cumulative frequencies.
Calculation:
The cumulative classes are given by in the following table.
Number of Freshmen | Frequency | Cumulative Frequency |
20-39 | 2 | 2 |
40-59 | 15 | |
60-79 | 10 | |
80-99 | 14 | |
100-119 | 7 | |
120-139 | 3 | |
140-159 | 1 | |
160-179 | 1 |
The frequency ogive is is given by
d.
To construct: A relative frequency ogive.
Explanation of Solution
Given information: The following frequency distribution presents the number of freshmen elected in each of the past 53 elections from 1912 to 2016.
Number of Freshmen | Frequency |
20-39 | 2 |
40-59 | 15 |
60-79 | 10 |
80-99 | 14 |
100-119 | 7 |
120-139 | 3 |
140-159 | 1 |
160-179 | 1 |
Definition used: The cumulative relative frequency of a class is given by
A relative frequency ogive plots the cumulative relative frequencies.
Calculation:
The cumulative classes are given by in the following table.
Number of Freshmen | Frequency | Cumulative Frequency | Cumulative relative Frequency |
20-39 | 2 | 2 | |
40-59 | 15 | ||
60-79 | 10 | ||
80-99 | 14 | ||
100-119 | 7 | ||
120-139 | 3 | ||
140-159 | 1 | ||
160-179 | 1 |
The relative frequency ogive is is given by
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