To determine which statement is false, we need to calculate the mean, mode, and median of the delivery times for both fast food restaurants and check for outliers.
Data:
- 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, 40
Mean Calculation:
-
Fast Food 1:
- Sum: \( 42 + 38 + 37 + 39 + 38 + 40 + 45 + 41 + 40 = 360 \)
- Count: 9
- Mean: \( \frac{360}{9} = 40 \) minutes
-
Fast Food 2:
- Sum: \( 40 + 37 + 40 + 41 + 38 + 46 + 41 + 40 = 363 \)
- Count: 8
- Mean: \( \frac{363}{8} = 45.375 \) minutes
Mode Calculation:
-
Fast Food 1:
- Delivery times: 42, 38, 37, 39, 38, 40, 45, 41, 40
- The mode is 40 and 38 (multiple occurrences).
-
Fast Food 2:
- Delivery times: 40, 37, 40, 41, 38, 46, 41, 40
- The mode is 40 (occurs 4 times, more frequent than any other value).
Median Calculation:
-
Fast Food 1:
- Ordered: 37, 38, 38, 39, 40, 40, 41, 42, 45 (9 numbers)
- Median (5th number): 40
-
Fast Food 2:
- Ordered: 37, 38, 40, 40, 40, 41, 41, 46 (8 numbers)
- Median (average of 4th and 5th): \( \frac{40 + 40}{2} = 40 \)
Outlier Check:
-
Fast Food 1 Calculation:
- Lower limit = Q1 - 1.5 * IQR
- Upper limit = Q3 + 1.5 * IQR
(Sheer manual calculation or box plots needed for a robust check).
-
Fast Food 2 Calculation:
- Same as above.
Summary of Findings:
- Mean delivery times: Fast Food 1: 40 minutes, Fast Food 2: 45.375 minutes (different)
- Modes: Fast Food 1: 40 and 38 (not just one mode); Fast Food 2: only 40.
- Medians: Both 40 minutes (same).
- Need to check clearly which one is outlier if any.
False Statement:
- The means are not the same (40 vs 45.375).
- Fast Food 1's mode is not unique as it has 38 as well.
- Medians are the same.
- Without detailed analysis on extremes cannot conclude on outliers.
Conclusion:
False Statement: Both fast food restaurants have the same mean delivery time of 40 minutes.