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Calculate the 5-number summary of the skewed dataset 15, 16, 16, 17, 17, 18, 18, 18, 19, 19, 29. When constructing the box plot on a number line, which explains a reason why the dataset is skewed?(1 point)
Responses

The 5 numbers in the summary are equally spread apart.
The 5 numbers in the summary are equally spread apart.

The median is exactly in the middle of the box.
The median is exactly in the middle of the box.

The whiskers are the same length.
The whiskers are the same length.

The right whisker is much longer than the left whisker.

1 answer

To calculate the 5-number summary of the dataset \(15, 16, 16, 17, 17, 18, 18, 18, 19, 19, 29\), we first identify the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

  1. Minimum: The smallest value in the dataset is 15.
  2. Maximum: The largest value in the dataset is 29.
  3. Median (Q2):
    • Since there are 11 values in the dataset, the median is the 6th value.
    • \( \text{Median} = 18 \).
  4. First Quartile (Q1):
    • The first quartile is the median of the first half of the dataset, which is \(15, 16, 16, 17, 17\).
    • The median of this subset (5 values) is the 3rd value: \(Q1 = 16\).
  5. Third Quartile (Q3):
    • The third quartile is the median of the second half of the dataset, which is \(18, 18, 19, 19, 29\).
    • The median of this subset (5 values) is the 3rd value: \(Q3 = 19\).

Therefore, the 5-number summary is:

  • Minimum: 15
  • Q1: 16
  • Median (Q2): 18
  • Q3: 19
  • Maximum: 29

The 5-number summary is:

  • 15, 16, 18, 19, 29

Regarding the box plot and the skewness of the dataset, the appropriate reason is:

  • The right whisker is much longer than the left whisker.

This indicates that there are extreme values on the right end of the dataset (like 29), which skews the data to the right.