Question
The mean number of cars for sale at dealerships in a small town is 56.
What happens to the mean if a dealership with 14 cars closes down?
Responses
The mean increases.
The mean increases.
The mean remains the same.
The mean remains the same.
The mean decreases.
What happens to the mean if a dealership with 14 cars closes down?
Responses
The mean increases.
The mean increases.
The mean remains the same.
The mean remains the same.
The mean decreases.
Answers
GPT-4o mini
To determine what happens to the mean number of cars for sale when a dealership with 14 cars closes down, we need to consider how the mean is calculated. The mean is calculated by dividing the total number of cars by the number of dealerships.
1. **Initial Mean**: The given mean number of cars is 56.
2. **Calculating Total Cars**: If we let \( n \) be the number of dealerships, the total number of cars for sale initially would be \( 56n \).
3. **After Closing a Dealership**: If one dealership with 14 cars closes down, the new total number of cars would be \( 56n - 14 \), and the number of dealerships would now be \( n - 1 \).
4. **New Mean Calculation**:
\[
\text{New Mean} = \frac{56n - 14}{n - 1}
\]
To see how the mean changes, we can analyze this expression further.
As the number of dealerships decreases by 1 and the total number of cars decreases by 14, the mean can be expected to decrease because the loss of 14 cars (if the dealership had a number higher than the new calculated mean) will typically affect the overall average negatively.
Thus, the conclusion is:
**The mean decreases.**
1. **Initial Mean**: The given mean number of cars is 56.
2. **Calculating Total Cars**: If we let \( n \) be the number of dealerships, the total number of cars for sale initially would be \( 56n \).
3. **After Closing a Dealership**: If one dealership with 14 cars closes down, the new total number of cars would be \( 56n - 14 \), and the number of dealerships would now be \( n - 1 \).
4. **New Mean Calculation**:
\[
\text{New Mean} = \frac{56n - 14}{n - 1}
\]
To see how the mean changes, we can analyze this expression further.
As the number of dealerships decreases by 1 and the total number of cars decreases by 14, the mean can be expected to decrease because the loss of 14 cars (if the dealership had a number higher than the new calculated mean) will typically affect the overall average negatively.
Thus, the conclusion is:
**The mean decreases.**