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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 Fast Food 2
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

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.

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

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

To determine which statement is false, we need to find the median, mean, and mode for both sets of delivery times.

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

Step 1: Calculate the Median

  • Fast Food 1: Sort the data

    • Sorted: 37, 38, 38, 39, 40, 41, 42, 45
    • Median (middle value): (40+41)/2 = 40.5

  • Fast Food 2: Sort the data

    • Sorted: 37, 38, 40, 40, 40, 41, 41, 46
    • Median (middle value): (40+40)/2 = 40

Step 2: Calculate the Mean

  • Fast Food 1: (42 + 38 + 37 + 39 + 38 + 40 + 45 + 41 + 40) / 9 = 40.33
  • Fast Food 2: (40 + 37 + 40 + 41 + 38 + 46 + 41 + 40) / 8 = 40.125

Step 3: Determine the Mode

  • Fast Food 1: Mode is 40 (occurs twice)
  • Fast Food 2: Mode is 40 (occurs four times)

Step 4: Identify Outliers Using the IQR (Interquartile Range) method to check for outliers:

  • Fast Food 1: Q1 = 38, Q3 = 41, IQR = 3. Outliers: No
  • Fast Food 2: Q1 = 38, Q3 = 41.5, IQR = 3. Outliers: No

Conclusion: Checking the Statements

  • "Both fast food restaurants have the same median delivery time of 40 minutes." (False, Fast Food 1 median is 40.5)
  • "Neither data set contains an outlier." (True)
  • "Both fast food restaurants have the same mean delivery time of 40 minutes." (False, Fast Food 1 mean is 40.33, Fast Food 2 mean is 40.125)
  • "Both fast food restaurants have exactly one modal delivery time of 40 minutes." (True)

The false statements are:

  • "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."

However, since only one statement is required as false, the first one related to the median is conclusively false, and it can be selected.