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

Fast Food 1 Fast Food 2
This table displays the randomly selected delivery times (in minutes) for two fast food restaurants.
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

Neither data set contains an outlier.
Neither data set contains an outlier.

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.

:)

1 answer

To evaluate which statement is false, we'll analyze the delivery times for both Fast Food 1 and Fast Food 2.

Fast Food 1 Delivery Times:

  • 42, 38, 37, 39, 38, 40, 45, 41, 40
  • Sorted: 37, 38, 38, 39, 40, 40, 41, 42, 45
  • Median: (40 + 40)/2 = 40
  • Mean: (37 + 38 + 38 + 39 + 40 + 40 + 41 + 42 + 45) / 9 = 40 (Total: 360, divided by 9)
  • Mode: 40 (it appears twice)

Fast Food 2 Delivery Times:

  • 40, 37, 41, 38, 46, 41, 37, 40, 40
  • Sorted: 37, 37, 38, 40, 40, 40, 41, 41, 46
  • Median: (40 + 40)/2 = 40
  • Mean: (40 + 37 + 41 + 38 + 46 + 41 + 37 + 40 + 40) / 9 ≈ 40 (Total: 360, divided by 9)
  • Mode: 40 (it appears three times)

Now, let’s assess the statements:

  1. Neither data set contains an outlier. - True

    • Fast Food 1: 37 to 45; Fast Food 2: 37 to 46. No outliers.

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

    • Both have a median of 40 minutes.

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

    • Both have a mean of approximately 40 minutes.

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

    • While both restaurants have 40 as a mode, Fast Food 2 has it appearing three times, thus it is not "exactly one modal delivery time."

Based on this analysis, the false statement is:

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