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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. (6 points) Minimum value: Maximum value: Median: Quartile 1: Quartile 3: IQR:

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To calculate the 5-number summary of the given dataset \(5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16\), we need to determine the following values:

  1. Minimum value: The smallest number in the dataset.
  2. Maximum value: The largest number in the dataset.
  3. Median: The middle value of the dataset.
  4. Quartile 1 (Q1): The median of the first half of the dataset.
  5. Quartile 3 (Q3): The median of the second half of the dataset.
  6. Interquartile Range (IQR): The difference between Q3 and Q1.

Step 1: Identify the minimum and maximum values

  • Minimum value: 5
  • Maximum value: 16

Step 2: Find the median Since there are 12 numbers (even count), the median will be the average of the 6th and 7th numbers in the sorted dataset.

  • The 6th number is 8 and the 7th number is also 8.
  • Median = \((8 + 8) / 2 = 8\)

Step 3: Find Q1 and Q3 To find Q1, we look at the first half of the data (the first 6 numbers): \(5, 6, 6, 7, 7, 8\)

  • For Q1, we take the average of the 3rd (6) and 4th (7) numbers.
  • Q1 = \((6 + 7) / 2 = 6.5\)

To find Q3, we look at the second half of the data (the last 6 numbers): \(8, 8, 9, 9, 14, 16\)

  • For Q3, we take the average of the 3rd (9) and 4th (9) numbers.
  • Q3 = \((9 + 9) / 2 = 9\)

Step 4: Calculate the IQR

  • IQR = Q3 - Q1 = \(9 - 6.5 = 2.5\)

Summary of 5-number summary:

  • Minimum value: 5
  • Maximum value: 16
  • Median: 8
  • Quartile 1 (Q1): 6.5
  • Quartile 3 (Q3): 9
  • IQR: 2.5

Final Values:

  • Minimum value: 5
  • Maximum value: 16
  • Median: 8
  • Quartile 1: 6.5
  • Quartile 3: 9
  • IQR: 2.5