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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: 42, 38, 37, 39, 38, 40, 45, 41, 40
Fast Food 2: 40, 37, 40, 41, 38, 46, 41, 37, 40
Which of the following statements is FALSE?
1. Both fast food restaurants have the same mean delivery time of 40 minutes.
2. Both fast food restaurants have exactly one modal delivery time of 40 minutes.
3. Both fast food restaurants have the same median delivery time of 40 minutes.
4. Neither data set contains an outlier.

1 answer

To determine which statement is FALSE, we will calculate the mean, mode, median, and check for outliers for both fast food restaurants.

Fast Food 1 Data:

  • Delivery times: 42, 38, 37, 39, 38, 40, 45, 41, 40

  1. Mean: \[ \text{Mean} = \frac{42 + 38 + 37 + 39 + 38 + 40 + 45 + 41 + 40}{9} = \frac{ 42 + 38 + 37 + 39 + 38 + 40 + 45 + 41 + 40}{9} = \frac{ 380}{9} \approx 42.22 \]

  2. Mode:

    • The frequencies are:
      • 37: 1 time
      • 38: 2 times
      • 39: 1 time
      • 40: 2 times
      • 41: 1 time
      • 42: 1 time
      • 45: 1 time
    • Both 38 and 40 repeat the most (2 times).
    • Modes are 38 and 40 (no unique mode).

  3. Median:

    • Sorted: 37, 38, 38, 39, 40, 40, 41, 42, 45 \[ \text{Median} = 40 \quad (\text{5th number in sorted list}) \]

Fast Food 2 Data:

  • Delivery times: 40, 37, 40, 41, 38, 46, 41, 37, 40

  1. Mean: \[ \text{Mean} = \frac{40 + 37 + 40 + 41 + 38 + 46 + 41 + 37 + 40}{9} = \frac{398}{9} \approx 44.22 \]

  2. Mode:

    • The frequencies are:
      • 37: 2 times
      • 38: 1 time
      • 40: 3 times
      • 41: 2 times
      • 46: 1 time
    • The only mode is 40 (it appears 3 times).

  3. Median:

    • Sorted: 37, 37, 38, 40, 40, 40, 41, 41, 46 \[ \text{Median} = 40 \quad (\text{5th number in sorted list}) \]

Summary of Findings:

  • Fast Food 1:

    • Mean: 42.22
    • Mode: 38 and 40 (no unique mode)
    • Median: 40

  • Fast Food 2:

    • Mean: 44.22
    • Mode: 40 (unique mode)
    • Median: 40

Evaluating Statements:

  1. False: Both fast food restaurants do not share the same mean delivery time.
  2. False: Fast Food 1 does not have a unique mode.
  3. True: Both have the same median delivery time of 40 minutes.
  4. True: To check for outliers, we can look at the IQR, but based on the values provided, those are not extreme values and do not show significant outliers.

Answer:

The FALSE statement is 1. Both fast food restaurants do not have the same mean delivery time of 40 minutes.