Question

The daily number of patients visiting a dentist's office during one week are 8, 41, 35, 39, 36, and 42.

Which statement is true?



Responses

The median is the only appropriate measure of center.
The median is the only appropriate measure 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 mean and median are appropriate measures of center.
Both the mean and median are appropriate measures of center.

Both the median and mode are appropriate measures of center.

Answer 1

To determine which statement is true regarding the measures of center for the daily number of patients visiting a dentist's office, we need to calculate the mean, median, and mode.

### Given data:
- Daily number of patients: 8, 41, 35, 39, 36, 42

### Calculations:

1. **Mean**:
\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{8 + 41 + 35 + 39 + 36 + 42}{6} = \frac{201}{6} \approx 33.5
\]

2. **Median**:
First, we need to sort the data:
- Sorted data: 8, 35, 36, 39, 41, 42
- Since there are 6 numbers (even), the median is the average of the 3rd and 4th numbers:
\[
\text{Median} = \frac{36 + 39}{2} = \frac{75}{2} = 37.5
\]

3. **Mode**:
The mode is the number that appears most frequently. In this dataset, all numbers are unique, so there is no mode.

### Summary of Measures:
- Mean: \( \approx 33.5 \)
- Median: \( 37.5 \)
- Mode: None

### Appropriate Measures of Center:
- Both the mean and median can be used as measures of center since mean and median are valid for this dataset.
- The mode is not applicable since there is no repeated value.

### Conclusion:
Based on the calculations:
- The mean and median are both appropriate measures of center, while the mode is not.

Thus, the correct statement is:
**Both the mean and median are appropriate measures of center.**