Question

The randomly selected delivery times (in minutes) of two fast food restaurants are as follows.

This table displays the randomly selected delivery times (in minutes) for two fast food restaurants.
Fast Food 1 Fast Food 2
42 40
38 37
37 40
39 41
38 38
40 46
45 41
41 37
40 40
Which of the following statements is false?

(1 point)
Responses

Both fast food restaurants have the same median delivery time of 40 minutes.
Both fast food restaurants have the same median delivery time of 40 minutes.

Both fast food restaurants have the same mean delivery time of 40 minutes.
Both fast food restaurants have the same mean delivery time of 40 minutes.

Both fast food restaurants have exactly one modal delivery time of 40 minutes.
Both fast food restaurants have exactly one modal delivery time of 40 minutes.

Neither data set contains an outlier.

Answer 1

To determine which statement is false, we need to calculate the median, mean, mode, and check for outliers for both restaurants.

1. **Fast Food 1 Delivery Times:** 42, 38, 37, 39, 38, 40, 45, 41, 40
- Sorted order: 37, 38, 38, 39, 40, 40, 41, 42, 45
- **Median:** The middle number is 40 (5th number in sorted list).
- **Mean:** (37 + 38 + 38 + 39 + 40 + 40 + 41 + 42 + 45) / 9 = 39.444... (approximately 39.44)
- **Mode:** 38 and 40 (there are two modes).
- **Outlier Check:** No numbers are significantly far from the others; thus, no outliers.

2. **Fast Food 2 Delivery Times:** 40, 37, 40, 41, 38, 46, 41, 37, 40
- Sorted order: 37, 37, 38, 40, 40, 40, 41, 41, 46
- **Median:** The middle number is 40 (5th number in sorted list).
- **Mean:** (40 + 37 + 40 + 41 + 38 + 46 + 41 + 37 + 40) / 9 = 39.444... (approximately 39.44)
- **Mode:** 40 (it appears three times, making it the only mode).
- **Outlier Check:** Similar to Fast Food 1, no significant outliers.

Now, let's evaluate each statement:

1. **Both fast food restaurants have the same median delivery time of 40 minutes.**
- This is **true**.

2. **Both fast food restaurants have the same mean delivery time of 40 minutes.**
- This is **false**. The mean for both is approximately 39.44.

3. **Both fast food restaurants have exactly one modal delivery time of 40 minutes.**
- This is **false** for Fast Food 1, as it has two modes: 38 and 40. Fast Food 2 does have 40 as the only mode.

4. **Neither data set contains an outlier.**
- This is **true**.

The false statements are the second and third. However, since the task specifies selecting which statement is false, the mean statement (2) is clearer based on the provided list of options:

**Both fast food restaurants have the same mean delivery time of 40 minutes.** (This statement is false.)