Question
The salaries of seven bank employees are $37,000, $38,500, $35,000, $37,000, $45,000, $40,000, and $75,000.
Which statement is true?
Responses
Both the mean and median are appropriate measures of center.
Both the mean and median are appropriate measures of center.
The mean, median, and mode are all appropriate measures of center.
The mean, median, and mode are all appropriate measures of center.
Both the median and mode are appropriate measures of center.
Both the median and mode are appropriate measures of center.
The median is the only appropriate measure of center.
Which statement is true?
Responses
Both the mean and median are appropriate measures of center.
Both the mean and median are appropriate measures of center.
The mean, median, and mode are all appropriate measures of center.
The mean, median, and mode are all appropriate measures of center.
Both the median and mode are appropriate measures of center.
Both the median and mode are appropriate measures of center.
The median is the only appropriate measure of center.
Answers
GPT-4o mini
To determine which statement is true regarding the measures of center (mean, median, and mode) for the salaries of the seven bank employees, we can first calculate the mean and median of the given salaries:
**Salaries:** $37,000, $38,500, $35,000, $37,000, $45,000, $40,000, and $75,000.
1. **Mean:**
- To calculate the mean, we need to sum all the salaries and then divide by the number of employees.
- Sum of salaries = $37,000 + $38,500 + $35,000 + $37,000 + $45,000 + $40,000 + $75,000 = $307,500.
- Number of employees = 7.
- Mean = $307,500 / 7 ≈ $43,214.29.
2. **Median:**
- To calculate the median, we need to arrange the salaries in ascending order:
- $35,000, $37,000, $37,000, $38,500, $40,000, $45,000, $75,000.
- The median is the middle number. Since there are 7 numbers (an odd count), the median is the 4th number:
- Median = $38,500.
3. **Mode:**
- The mode is the number that appears most frequently. In this case, $37,000 appears twice while all other salaries appear once.
- Mode = $37,000.
Now, we analyze the appropriateness of these measures:
- **Mean:** The presence of the outlier ($75,000) significantly skews the mean, making it higher and less representative of the majority of the salaries.
- **Median:** The median is less affected by outliers and represents the central point of the dataset better given the presence of the outlier.
- **Mode:** The mode provides a measure of the most common salary but does not represent the center effectively because it does not take into account the distribution of the rest of the salaries.
Based on this analysis:
- The **mean** is not an appropriate measure of center due to the outlier.
- The **median** is appropriate as it provides a better representation of the central tendency of the data.
- The **mode** could be considered, but it does not reflect the trend of the central tendency in the dataset.
Therefore, the correct statement is:
**The median is the only appropriate measure of center.**
**Salaries:** $37,000, $38,500, $35,000, $37,000, $45,000, $40,000, and $75,000.
1. **Mean:**
- To calculate the mean, we need to sum all the salaries and then divide by the number of employees.
- Sum of salaries = $37,000 + $38,500 + $35,000 + $37,000 + $45,000 + $40,000 + $75,000 = $307,500.
- Number of employees = 7.
- Mean = $307,500 / 7 ≈ $43,214.29.
2. **Median:**
- To calculate the median, we need to arrange the salaries in ascending order:
- $35,000, $37,000, $37,000, $38,500, $40,000, $45,000, $75,000.
- The median is the middle number. Since there are 7 numbers (an odd count), the median is the 4th number:
- Median = $38,500.
3. **Mode:**
- The mode is the number that appears most frequently. In this case, $37,000 appears twice while all other salaries appear once.
- Mode = $37,000.
Now, we analyze the appropriateness of these measures:
- **Mean:** The presence of the outlier ($75,000) significantly skews the mean, making it higher and less representative of the majority of the salaries.
- **Median:** The median is less affected by outliers and represents the central point of the dataset better given the presence of the outlier.
- **Mode:** The mode provides a measure of the most common salary but does not represent the center effectively because it does not take into account the distribution of the rest of the salaries.
Based on this analysis:
- The **mean** is not an appropriate measure of center due to the outlier.
- The **median** is appropriate as it provides a better representation of the central tendency of the data.
- The **mode** could be considered, but it does not reflect the trend of the central tendency in the dataset.
Therefore, the correct statement is:
**The median is the only appropriate measure of center.**