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A dot plot is labeled 'Alarm Clock Set.' The horizontal axis ranges from 5 AM to 7 in increments of 30 minutes. The plot show 2 dots above 5 AM, 3 dots above 5:30, 5 dots above 6:00, 4 dots above 6:30, and 1 dot above 7.

Calculate the mean and median of the given data. Round your answers to the nearest half-hour increment as needed.

(1 point)
Responses

Mean: 6:00, Median: 5:00
Mean: 6:00, Median: 5:00

Mean: 5:00, Median: 5:00
Mean: 5:00, Median: 5:00

Mean: 5:00, Median: 6:00
Mean: 5:00, Median: 6:00

Mean: 6:00, Median: 6:00
Mean: 6:00, Median: 6:00
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1 answer

To calculate the mean and median of the given data from the dot plot, we first need to list out all of the times represented by the dots.

  1. Listing the Data Points:
    • 2 dots at 5 AM: 5:00, 5:00
    • 3 dots at 5:30 AM: 5:30, 5:30, 5:30
    • 5 dots at 6:00 AM: 6:00, 6:00, 6:00, 6:00, 6:00
    • 4 dots at 6:30 AM: 6:30, 6:30, 6:30, 6:30
    • 1 dot at 7:00 AM: 7:00

So, the full list is:

  • 5:00, 5:00
  • 5:30, 5:30, 5:30
  • 6:00, 6:00, 6:00, 6:00, 6:00
  • 6:30, 6:30, 6:30, 6:30
  • 7:00

This gives us the following data points:

  • 5:00, 5:00
  • 5:30, 5:30, 5:30
  • 6:00, 6:00, 6:00, 6:00, 6:00
  • 6:30, 6:30, 6:30, 6:30
  • 7:00

  1. Calculating the Mean:

    • Total number of observations = 2 + 3 + 5 + 4 + 1 = 15
    • Sum of all times:
      • 5:00 * 2 = 10:00
      • 5:30 * 3 = 16:30
      • 6:00 * 5 = 30:00
      • 6:30 * 4 = 26:00
      • 7:00 * 1 = 7:00

    Total time:

    • 10:00 + 16:30 + 30:00 + 26:00 + 7:00 = 89:30 (equivalent to 89 hours and 30 minutes)

    To find the mean:

    • Convert total time to minutes: 89 hours = 5340 minutes, and 30 minutes = 30 minutes, so total minutes = 5340 + 30 = 5370 minutes.
    • Mean = Total minutes / Number of observations = 5370 / 15 = 358 minutes.

    Convert 358 minutes back to hours:

    • 358 minutes = 5 hours and 58 minutes, which rounds to approximately 6:00 AM.

  2. Calculating the Median: To find the median, we need to list the times in order:

    • 5:00, 5:00, 5:30, 5:30, 5:30, 6:00, 6:00, 6:00, 6:00, 6:00, 6:30, 6:30, 6:30, 6:30, 7:00.

    The middle observation (the 8th value, since there are 15) is:

    • The 8th value is 6:00.

Therefore, the computed results are:

  • Mean: 6:00
  • Median: 6:00

So the correct response is: Mean: 6:00, Median: 6:00.