Question

Question
The mean number of patients Dr. Keller sees daily is 23.

What happens to the mean if Dr. Keller only sees 5 patients on Monday?

Responses

The mean remains the same.
The mean remains the same.

The mean decreases.
The mean decreases.

The mean increases.

Answer 1

To determine how the mean changes if Dr. Keller sees only 5 patients on Monday, we need to calculate the new mean based on the total number of patients seen over a given period.

Assuming Dr. Keller typically sees an average of 23 patients per day over 7 days (a week), the total number of patients seen over that week would be:

\[
23 \, \text{patients/day} \times 7 \, \text{days} = 161 \, \text{patients}
\]

Now, if on Monday he only sees 5 patients instead of the average of 23, his total for that week would decrease:

1. Total patients for the week with Monday's average:
- Total = 161 patients
2. Replace Monday's average with the actual number seen:
- New total = 161 - 23 + 5 = 143 patients

Now, let's calculate the new mean for the 7 days:

\[
\text{New mean} = \frac{143 \, \text{patients}}{7 \, \text{days}} \approx 20.43 \, \text{patients/day}
\]

The new mean of approximately 20.43 patients per day is less than the original mean of 23 patients per day.

Thus, the answer is:

**The mean decreases.**