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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=BLANK. The maximum value=BLANK. The median=BLANK. Quartile 1=BLANK. Quartile BLANK.

1 answer

To find the 5-number summary of the dataset, we need to determine the minimum, maximum, median (Q2), and the first (Q1) and third quartiles (Q3).

The dataset provided is:
5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16.

  1. Minimum value: This is the smallest number in the dataset.

    • Minimum = 5

  2. Maximum value: This is the largest number in the dataset.

    • Maximum = 16

  3. Median (Q2): The median is the middle value. Since there are 12 numbers in the dataset (an even number), the median is the average of the 6th and 7th values. The 6th and 7th values are both 8.

    • Median = (8 + 8) / 2 = 8

  4. Quartile 1 (Q1): This is the median of the first half of the dataset. The first half consists of the first 6 numbers (5, 6, 6, 7, 7, 8). The median of these six numbers (an even count) is the average of the 3rd and 4th values:

    • Q1 = (6 + 7) / 2 = 6.5

  5. Quartile 3 (Q3): This is the median of the second half of the dataset. The second half consists of the last 6 numbers (8, 8, 9, 9, 14, 16). The median of these six numbers (an even count) is the average of the 3rd and 4th values:

    • Q3 = (9 + 9) / 2 = 9

Putting it all together, we have:

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

Here’s the final answer:

  • The minimum value = 5
  • The maximum value = 16
  • The median = 8
  • Quartile 1 = 6.5
  • Quartile 3 = 9