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

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

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

Mean: 5:00, Median: 6:00
Mean: 5:00, Median: 6:00
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1 answer

To calculate the mean and median of the alarm clock settings from the dot plot data:

  1. Data Representation from the Dot Plot:

    • 5 AM: 2 dots
    • 5:30 AM: 3 dots
    • 6:00 AM: 5 dots
    • 6:30 AM: 4 dots
    • 7:00 AM: 1 dot

  2. Translating this into values:

    • 5 AM: 2 times (5, 5)
    • 5:30 AM: 3 times (5.5, 5.5, 5.5)
    • 6 AM: 5 times (6, 6, 6, 6, 6)
    • 6:30 AM: 4 times (6.5, 6.5, 6.5, 6.5)
    • 7 AM: 1 time (7)

  3. List of all times: The complete list of times (in hours): \[ 5, 5, 5.5, 5.5, 5.5, 6, 6, 6, 6, 6, 6.5, 6.5, 6.5, 6.5, 7 \]

  4. Calculating the Mean: To compute the mean:

    • Sum = \(5 + 5 + 5.5 + 5.5 + 5.5 + 6 + 6 + 6 + 6 + 6 + 6.5 + 6.5 + 6.5 + 6.5 + 7\)
    • Sum = 5 + 5 + 5.5 + 5.5 + 5.5 + 6 + 6 + 6 + 6 + 6 + 6.5 + 6.5 + 6.5 + 6.5 + 7 = 88.5
    • Count of values = 15
    • Mean = Total / Count = \(88.5 / 15 = 5.9\)

    Rounding to the nearest half-hour gives: 6:00 AM.

  5. Calculating the Median:

    • To find the median, we need to identify the middle value of the ordered data.
    • The ordered list is already provided, and since there are 15 values, the median is the 8th value.
    • The 8th value in the ordered list is 6.

Now putting both together:

  • Mean: 6:00
  • Median: 6:00

Therefore, the correct response is:

Mean: 6:00, Median: 6:00