Let's analyze the delivery times of both fast food restaurants to determine which statement is false.
Delivery Times:
- Fast Food 1: 42, 38, 37, 39, 38, 40, 45, 41, 40
- Fast Food 2: 40, 37, 40, 41, 38, 46, 41, 40, 40
Finding the mode:
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Fast Food 1:
- Frequencies: 37 (1), 38 (2), 39 (1), 40 (2), 41 (1), 42 (1), 45 (1)
- Mode: 38 and 40 (both appear 2 times) - thus, Fast Food 1 does not have exactly one modal delivery time.
-
Fast Food 2:
- Frequencies: 37 (1), 38 (1), 40 (5), 41 (2), 46 (1)
- Mode: 40 (appears 5 times)
Finding the median:
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Fast Food 1: Sorted delivery times: 37, 38, 38, 39, 40, 40, 41, 42, 45
- Median: 40 (5th value)
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Fast Food 2: Sorted delivery times: 37, 38, 40, 40, 40, 40, 41, 41, 46
- Median: 40 (5th value)
So, both restaurants have the same median delivery time of 40 minutes.
Finding outliers: For this analysis, we can use the IQR (Interquartile Range) method:
-
Fast Food 1:
- Q1 = 38, Q3 = 41
- IQR = Q3 - Q1 = 41 - 38 = 3
- Lower Bound = Q1 - 1.5 * IQR = 38 - 4.5 = 33.5
- Upper Bound = Q3 + 1.5 * IQR = 41 + 4.5 = 45.5
- No outliers (all values are within the bounds).
-
Fast Food 2:
- Q1 = 38, Q3 = 40
- IQR = Q3 - Q1 = 40 - 38 = 2
- Lower Bound = 38 - 3 = 35
- Upper Bound = 40 + 3 = 43
- No outliers (all values are within the bounds).
Finding the mean:
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Fast Food 1 Mean: \((42 + 38 + 37 + 39 + 38 + 40 + 45 + 41 + 40) / 9 = 40.33\)
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Fast Food 2 Mean: \((40 + 37 + 40 + 41 + 38 + 46 + 41 + 40 + 40) / 9 = 40.33\)
Now evaluating the statements:
- Both have exactly one modal delivery time - FALSE for Fast Food 1.
- Both have the same median delivery time of 40 minutes - TRUE.
- Neither dataset contains an outlier - TRUE.
- Both have the same mean delivery time - TRUE.
Thus, the false statement is:
"Both fast food restaurants have exactly one modal delivery time of 40 minutes."