To determine which statement is false regarding the delivery times, let's calculate the mean, mode, median, and check for outliers for both Fast Food 1 and Fast Food 2.
Fast Food 1 Delivery Times: 42, 38, 37, 39, 38, 40, 45, 41, 40
Fast Food 2 Delivery Times: 40, 37, 40, 41, 38, 46, 41, 37, 40
Step 1: Calculate the Mean
Fast Food 1 Mean: \[ \text{Mean} = \frac{42 + 38 + 37 + 39 + 38 + 40 + 45 + 41 + 40}{9} = \frac{ 42 + 38 + 37 + 39 + 38 + 40 + 45 + 41 + 40 }{9} = \frac{ 360 }{9} = 40 \]
Fast Food 2 Mean: \[ \text{Mean} = \frac{40 + 37 + 40 + 41 + 38 + 46 + 41 + 37 + 40}{9} = \frac{ 40 + 37 + 40 + 41 + 38 + 46 + 41 + 37 + 40 }{9} = \frac{ 360 }{9} = 40 \]
Step 2: Calculate the Mode
- Fast Food 1: The most frequent delivery times are 38 and 40 (both occur 2 times) → Not exactly one mode.
- Fast Food 2: The most frequent delivery time is 40 (occurs 4 times) → Exactly one mode.
Step 3: Calculate the Median
- Fast Food 1 (arranging in order): 37, 38, 38, 39, 40, 40, 41, 42, 45 → Median (5th value) = 40
- Fast Food 2 (arranging in order): 37, 37, 38, 40, 40, 40, 41, 41, 46 → Median (5th value) = 40
Step 4: Check for Outliers
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Using the IQR method, we calculate for both sets.
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For Fast Food 1:
- Q1 = 38 and Q3 = 40 (IQR = 2)
- Outliers would be anyone below \( Q1 - 1.5 \times IQR \) or above \( Q3 + 1.5 \times IQR\).
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No outliers detected.
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For Fast Food 2:
- Q1 = 38 and Q3 = 40 (IQR = 2)
- Similarly, no outliers detected.
Summary of Results:
- Both fast food restaurants have the same mean delivery time of 40 minutes. (True)
- Both fast food restaurants have exactly one modal delivery time of 40 minutes. (False for Fast Food 1)
- Neither data set contains an outlier. (True)
- Both fast food restaurants have the same median delivery time of 40 minutes. (True)
Conclusion:
The false statement is: Both fast food restaurants have exactly one modal delivery time of 40 minutes.