Question

The randomly selected delivery times(in minutes) of two fast food restaurants are as far as
This table displays the randomly selected delivery times for two fast food restaurants
Fast food one: 42, 38, 37, 39, 38, 40, 45, 41, 40
Fast food two: 40, 37, 40, 41, 38, 46, 41, 37, 40
Which of the following statements is false
Both fast food restaurants have the same main delivery time of 40 minutes
Both fast food restaurants have the same median delivery time of 40 minutes
Both fast food restaurants have exactly one modal
delivery time of 40 minutes
Neither data contains an outlier

Answer 1

Let's analyze the delivery times for both fast food restaurants to verify the statements provided.

### Fast Food One Delivery Times:
- **Values**: 42, 38, 37, 39, 38, 40, 45, 41, 40
- **Sorted**: 37, 38, 38, 39, 40, 40, 41, 42, 45

#### Measures of Central Tendency:
- **Mean**:
\[
\text{Mean} = \frac{37 + 38 + 38 + 39 + 40 + 40 + 41 + 42 + 45}{9} = \frac{ 37 + 38 + 38 + 39 + 40 + 40 + 41 + 42 + 45 }{ 9 } = \frac{ 360 }{ 9 } = 40
\]
- **Median**: The median (middle value in sorted data):
- Since there are 9 values (odd number), the median is the 5th value: **40**
- **Mode**: The mode (most frequent value):
- 38 appears twice and 40 appears twice, so both 38 and 40 are modes. **There are two modes, so it's not exactly one modal value.**

### Fast Food Two Delivery Times:
- **Values**: 40, 37, 40, 41, 38, 46, 41, 37, 40
- **Sorted**: 37, 37, 38, 40, 40, 40, 41, 41, 46

#### Measures of Central Tendency:
- **Mean**:
\[
\text{Mean} = \frac{40 + 37 + 40 + 41 + 38 + 46 + 41 + 37 + 40}{9} = \frac{ 40 + 37 + 40 + 41 + 38 + 46 + 41 + 37 + 40 }{ 9 } = \frac{ 360 }{ 9 } = 40
\]
- **Median**:
- The median (middle value in sorted data): Since there are 9 values (odd number), the median is the 5th value: **40**
- **Mode**:
- The most frequent value is 40 (appears three times) which is one mode.

### Assessing the Statements:

1. **Both fast food restaurants have the same main delivery time of 40 minutes.**
- True. (Both have a mean of 40.)

2. **Both fast food restaurants have the same median delivery time of 40 minutes.**
- True. (Both have a median of 40.)

3. **Both fast food restaurants have exactly one modal delivery time of 40 minutes.**
- False for Fast Food One (it has two modes: 38 and 40), but true for Fast Food Two (it has one mode: 40).

4. **Neither data contains an outlier.**
- This statement appears true as there are no values that are significantly different from the others in either set.

### Conclusion:
The false statement is: **"Both fast food restaurants have exactly one modal delivery time of 40 minutes."**