Question

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?

Answer 1


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

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 right whisker is much longer than the left whisker.

Answer 2

The 5-number summary of the dataset is:

Minimum: 15
Q1 (First Quartile): 16.5
Median (Q2): 18
Q3 (Third Quartile): 19
Maximum: 29

To construct the box plot on a number line, we would plot the five-number summary as follows:

- Draw a number line and mark the minimum (15) and maximum (29) values as endpoints.
- Draw a line segment from Q1 (16.5) to Q3 (19) to represent the box in the box plot.
- Inside the box, mark the median (18) with a vertical line.
- Draw whiskers extending from the ends of the box to the minimum and maximum values.

The dataset is skewed to the right because the right tail of the dataset is much longer than the left tail, causing the median to be closer to the lower quartile (Q1) than the upper quartile (Q3). This is evident in the box plot as the right whisker is longer than the left whisker.