Chapter 2 Extra Practice
2.1 Descriptive Statistics and Frequency Distributions
- What are the two types of descriptive statistical methods?
2.2 Displaying and Describing Categorical Distributions
1. What are the two basic options for graphing categorical data?
2. When describing categorical data we want to note what two aspects?
3. When describing the level of variability in categorical data, we want to think about it as .
2.3 Displaying Quantitative Distributions
1. Create a histogram for the number of books bought by 50 part-time college students at ABC College. The number of books is discrete data since books are counted.
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
2, 2, 2, 2, 2, 2, 2, 2, 2, 2
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
4, 4, 4, 4, 4, 4
5, 5, 5, 5, 5
6, 6
Eleven students buy one book. Ten students buy two books. Sixteen students buy three books. Six students buy four books. Five students buy five books. Two students buy six books.
Because the data are integers, subtract 0.5 from 1, the smallest data value, and add 0.5 to 6, the largest data value. Then the starting point is 0.5, and the ending value is 6.5.
Next calculate the width of each bar or class interval. If the data are discrete, and there are not too many different values, a width that places the data values in the middle of the bar or class interval is the most convenient.
If you are using an offline version of this text, access the activity using the QR code.
Calculate the number of bars as follows:
= 1
1 is the width of a bar. Therefore, bars = 6.
The following histogram displays the number of books on the x-axis and the frequency on the y-axis.
2. We will construct an overlay frequency polygon comparing the scores from the figure below with the students’ final numeric grades.
| Lower bound | Upper bound | Frequency | Cumulative frequency |
|---|---|---|---|
| 49.5 | 59.5 | 5 | 5 |
| 59.5 | 69.5 | 10 | 15 |
| 69.5 | 79.5 | 30 | 45 |
| 79.5 | 89.5 | 40 | 85 |
| 89.5 | 99.5 | 15 | 100 |
Figure 2.60: Frequency distribution for calculus final test scores
| Lower bound | Upper bound | Frequency | Cumulative frequency |
|---|---|---|---|
| 49.5 | 59.5 | 10 | 10 |
| 59.5 | 69.5 | 10 | 20 |
| 69.5 | 79.5 | 30 | 50 |
| 79.5 | 89.5 | 45 | 95 |
| 89.5 | 99.5 | 5 | 100 |
Figure 2.61: Frequency distribution for calculus final test scores
3. Construct a frequency polygon of US Presidents’ ages at inauguration shown in the figure below.[1]
| Age at inauguration | Frequency |
|---|---|
| 41.5–46.5 | 4 |
| 46.5–51.5 | 11 |
| 51.5–56.5 | 14 |
| 56.5–61.5 | 9 |
| 61.5–66.5 | 4 |
| 66.5–71.5 | 3 |
Figure 2.63
4. Construct frequency polygons for the following datasets:
| Pulse rates for women | Frequency |
|---|---|
| 60–69 | 12 |
| 70–79 | 14 |
| 80–89 | 11 |
| 90–99 | 1 |
| 100–109 | 1 |
| 110–119 | 0 |
| 120–129 | 1 |
Figure 2.64
| Actual speed in a 30 MPH zone | Frequency |
|---|---|
| 42–45 | 25 |
| 46–49 | 14 |
| 50–53 | 7 |
| 54–57 | 3 |
| 58–61 | 1 |
Figure 2.65
| Tar (mg) in non-filte