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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 of the dataset \(5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16\), we need to determine the following values:

  1. Minimum: The smallest value in the dataset.
  2. Maximum: The largest value in the dataset.
  3. Median: The middle value of the dataset.
  4. Quartile 1 (Q1): The median of the lower half of the dataset.
  5. Quartile 3 (Q3): The median of the upper half of the dataset.

Step-by-step Calculation

  1. Minimum:

    • The minimum value is \(5\).

  2. Maximum:

    • The maximum value is \(16\).

  3. Median:

    • The median is the average of the 6th and 7th values in the ordered dataset.
    • \(8\) (6th value), \(8\) (7th value).
    • Median = \(\frac{8 + 8}{2} = 8\).

  4. Quartile 1 (Q1):

    • Q1 is the median of the lower half of the dataset: \(5, 6, 6, 7, 7, 8\) (first 6 values).
    • The median of this subset is the average of the 3rd and 4th values: \(6\) (3rd), \(7\) (4th).
    • Q1 = \(\frac{6 + 7}{2} = 6.5\).

  5. Quartile 3 (Q3):

    • Q3 is the median of the upper half of the dataset: \(8, 9, 9, 14, 16\) (last 6 values).
    • The median of this subset is the average of the 3rd and 4th values: \(9\) (3rd), \(14\) (4th).
    • Q3 = \(\frac{9 + 14}{2} = 11.5\).

Summary of Results

  • Minimum value = 5
  • Maximum value = 16
  • Median = 8
  • Quartile 1 = 6.5
  • Quartile 3 = 11.5

Thus, the 5-number summary is:

  • Minimum: 5
  • Maximum: 16
  • Median: 8
  • Q1: 6.5
  • Q3: 11.5