Define the five-number summary, and explain how to depict it visually with a boxplot. Which five numbers are included in the five-number summary for a data set? A. low value, variance, mean, standard deviation, and high value B. Iow value, lower quartile, mean, upper quartile, and high value C. Iow value, variance, median, standard deviation, and high value D. Iow value, lower quartile, median, upper quartile, and high value Explain how to depict the five numbers visually with a boxplot. Choose the correct answer below. Select all that apply. A. Draw a number line that spans all the values in the data set. Enclose the values from the lower to upper quartile in a box. Draw a vertical line through the box at the mean. Add "whiskers" extending to the low and high values. B. Draw a number line that spans all the values in the data set. Enclose the values from the lower to upper quartile in a box. Draw a vertical line through the box at the median. Add "whiskers" extending to the low and high values. C. Draw a number line that spans all the values in the data set. Enclose the values from the lower to upper quartile in a box. Draw a vertical line through the box at the mean. D. Draw a number line that spans all the values in the data set. Enclose the values from the lower to upper quartile in a box.

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UpStudy AI · Accepted Answer

The five-number summary of a data set consists of the following five statistics:
  
- The minimum (low value)
- The first quartile (lower quartile)
- The median
- The third quartile (upper quartile)
- The maximum (high value)

Mathematically, if we denote these as:
  
- $$ 	ext{Min} $$
- $$ Q_1 $$ (first quartile)
- $$ Q_2 $$ (median)
- $$ Q_3 $$ (third quartile)
- $$ 	ext{Max} $$
  
then the five-number summary is $$ \{ 	ext{Min}, Q_1, Q_2, Q_3, 	ext{Max} \} $$.

Thus, the correct answer for the numbers included in the five-number summary is:

D. low value, lower quartile, median, upper quartile, and high value

To depict these numbers visually with a boxplot, follow these steps:
  
1. Draw a number line (horizontal axis) that spans all the values in the data set.
2. Draw a box from $$ Q_1 $$ to $$ Q_3 $$, representing the interquartile range.
3. Within the box, draw a vertical line at $$ Q_2 $$ (the median) which divides the box.
4. Extend lines (called “whiskers”) from the left side of the box to the minimum value and from the right side of the box to the maximum value.

This explanation corresponds to:

B. Draw a number line that spans all the values in the data set. Enclose the values from the lower to upper quartile in a box. Draw a vertical line through the box at the median. Add "whiskers" extending to the low and high values.
The five-number summary includes the minimum (low value), first quartile (lower quartile), median, third quartile (upper quartile), and maximum (high value). To visualize this with a boxplot, draw a number line spanning all data values, create a box from the lower to upper quartile, add a median line within the box, and extend whiskers to the minimum and maximum values.

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