A sample of 389 people is selected. The people are classified according to place of residence ("urban", "suburban", or "rural"). They are also classified according to highest educational degree earned ("no college degree", "two-year degree", "four-year degree", or "advanced degree"). The results are given in the contingency table below. No college degree Two-year degree Four-year degree Advanced degree Urban 25 23 38 48 Suburban 40 26 41 45 Rural 35 28 23 17 What is the relative frequency of people in the sample whose place of residence is urban and who do not have a college degree?
A sample of 389 people is selected. The people are classified according to place of residence ("urban", "suburban", or "rural"). They are also classified according to highest educational degree earned ("no college degree", "two-year degree", "four-year degree", or "advanced degree"). The results are given in the contingency table below. No college degree Two-year degree Four-year degree Advanced degree Urban 25 23 38 48 Suburban 40 26 41 45 Rural 35 28 23 17 What is the relative frequency of people in the sample whose place of residence is urban and who do not have a college degree?
A First Course in Probability (10th Edition)
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![**Educational Resource on Contingency Tables and Relative Frequency**
**Contingency Table Analysis**
A sample of 389 people is selected. The people are classified according to place of residence ("urban", "suburban", or "rural"). They are also classified according to the highest educational degree earned ("no college degree", "two-year degree", "four-year degree", or "advanced degree"). The results are given in the contingency table below.
| | No college degree | Two-year degree | Four-year degree | Advanced degree |
|----------------------|----------------------|------------------|-------------------|-------------------|
| **Urban** | 25 | 23 | 38 | 48 |
| **Suburban** | 40 | 26 | 41 | 45 |
| **Rural** | 35 | 28 | 23 | 17 |
**Question**:
What is the relative frequency of people in the sample whose place of residence is urban and who do not have a college degree?
**Solution**:
To find the relative frequency, use the following steps:
1. **Find the number of people who are urban and do not have a college degree**:
From the table, this number is 25.
2. **Find the total sample size**:
The total number of people in the sample is 389.
3. **Calculate the relative frequency**:
\[\text{Relative frequency} = \frac{\text{Number of urban, no college degree individuals}}{\text{Total sample size}}\]
\[\text{Relative frequency} = \frac{25}{389} \approx 0.0643\]
4. **Round to two decimal places**:
The relative frequency rounded to two decimal places is 0.06.
So, the relative frequency of people in the sample whose place of residence is urban and who do not have a college degree is **0.06**.
**NOTE**:
For the purpose of deeper understanding, a **contingency table** is a type of table in a matrix format that displays the multivariate frequency distribution of the variables. It is particularly useful for understanding the relationships between different categorical variables.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F424746dd-29d3-476a-868c-5a06ada19580%2Fd705c905-891e-4c84-be98-2bf43bbf6c92%2Fa3sa5vm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Resource on Contingency Tables and Relative Frequency**
**Contingency Table Analysis**
A sample of 389 people is selected. The people are classified according to place of residence ("urban", "suburban", or "rural"). They are also classified according to the highest educational degree earned ("no college degree", "two-year degree", "four-year degree", or "advanced degree"). The results are given in the contingency table below.
| | No college degree | Two-year degree | Four-year degree | Advanced degree |
|----------------------|----------------------|------------------|-------------------|-------------------|
| **Urban** | 25 | 23 | 38 | 48 |
| **Suburban** | 40 | 26 | 41 | 45 |
| **Rural** | 35 | 28 | 23 | 17 |
**Question**:
What is the relative frequency of people in the sample whose place of residence is urban and who do not have a college degree?
**Solution**:
To find the relative frequency, use the following steps:
1. **Find the number of people who are urban and do not have a college degree**:
From the table, this number is 25.
2. **Find the total sample size**:
The total number of people in the sample is 389.
3. **Calculate the relative frequency**:
\[\text{Relative frequency} = \frac{\text{Number of urban, no college degree individuals}}{\text{Total sample size}}\]
\[\text{Relative frequency} = \frac{25}{389} \approx 0.0643\]
4. **Round to two decimal places**:
The relative frequency rounded to two decimal places is 0.06.
So, the relative frequency of people in the sample whose place of residence is urban and who do not have a college degree is **0.06**.
**NOTE**:
For the purpose of deeper understanding, a **contingency table** is a type of table in a matrix format that displays the multivariate frequency distribution of the variables. It is particularly useful for understanding the relationships between different categorical variables.
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