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Calculate the values for the 5-number summary of the skewed dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16.(2 points)

The minimum value=(_)
. The maximum value=(__)
. The median=(___)
. Quartile 1=(____)
. Quartile 3=(_____)
.

1 answer

To calculate the 5-number summary for the dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16, we first need to identify the minimum, maximum, median, and the first and third quartiles.

  1. Minimum value: The smallest number in the dataset.

    • Minimum = 5

  2. Maximum value: The largest number in the dataset.

    • Maximum = 16

  3. Median: This is the middle value when the numbers are sorted. Since there are 12 data points (even number), the median will be the average of the two middle values (6th and 7th values).

    • The sorted dataset is: 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16.
    • The two middle values are 8 and 8.
    • Median = (8 + 8) / 2 = 8

  4. Quartile 1 (Q1): This is the median of the lower half of the dataset (the first half of the data). The lower half is 5, 6, 6, 7, 7, 8 (6 values).

    • The middle value is the average of the 3rd and 4th values (6 and 7).
    • Q1 = (6 + 7) / 2 = 6.5

  5. Quartile 3 (Q3): This is the median of the upper half of the dataset (the second half of the data). The upper half is 8, 8, 9, 9, 14, 16 (6 values).

    • The middle value is the average of the 3rd and 4th values (9 and 9).
    • Q3 = (9 + 9) / 2 = 9

Now summarizing the results:

  • Minimum = 5
  • Maximum = 16
  • Median = 8
  • Quartile 1 (Q1) = 6.5
  • Quartile 3 (Q3) = 9

Thus, the 5-number summary is:

  • Minimum value = (5)
  • Maximum value = (16)
  • Median = (8)
  • Quartile 1 = (6.5)
  • Quartile 3 = (9)