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

a Both the mean and median are appropriate measures of center.
a Both the mean and median are appropriate measures of center.

b The mean, median, and mode are all appropriate measures of center.
b The mean, median, and mode are all appropriate measures of center.

c The median is the only appropriate measure of center.
c The median is the only appropriate measure of center.

d Both the median and mode are appropriate measures of center.

Answer 1

To analyze which statement is true, we first need to calculate the mean, median, and mode of the given daily patient counts: 8, 41, 35, 39, 36, and 42.

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

2. **Median**:
To find the median, we first arrange the numbers in ascending order:
\[
8, 35, 36, 39, 41, 42.
\]
The median is the average of the two middle values (36 and 39):
\[
\text{Median} = \frac{36 + 39}{2} = \frac{75}{2} = 37.5.
\]

3. **Mode**:
The mode is the value that occurs most frequently. In this case, all the numbers are unique, so there is no mode.

Now, let's evaluate the statements:
- **Mean**: 33.5
- **Median**: 37.5
- **Mode**: None (since all numbers are unique)

Now, let's evaluate each of the responses:

a. Both the mean and median are appropriate measures of center.
- True, as both the mean and median exist.

b. The mean, median, and mode are all appropriate measures of center.
- False, because there is no mode.

c. The median is the only appropriate measure of center.
- False, because the mean is also appropriate.

d. Both the median and mode are appropriate measures of center.
- False, because there is no mode.

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