Question

Make a box-and-whisker plot for the set of data.

21, 27, 27, 25, 21, 13, 18, 25

Answer 1

To create a box-and-whisker plot, first, you need to find the five key statistical values: minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum.

1. Order the data set from lowest to highest:
13, 18, 21, 21, 25, 25, 27, 27

2. Find the median (Q2): Since there are 8 values, the median will be the average of the two middle values (21 and 21).
Median (Q2) = (21 + 21) / 2 = 21

3. Find the lower quartile (Q1): This is the median of the lower half of the data. In this case, it's the median of 13, 18, 21, and 21.
Lower Quartile (Q1) = (18 + 21) / 2 = 19.5

4. Find the upper quartile (Q3): This is the median of the upper half of the data. In this case, it's the median of 25, 25, 27, and 27.
Upper Quartile (Q3) = (25 + 25) / 2 = 25

5. Identify the minimum (13) and maximum (27) values.

Now you can create the box-and-whisker plot:

1. Draw a number line representing the range of data.

2. Place a vertical line at each of the five key statistical values (13, 19.5, 21, 25, 27).

3. Draw a box connecting the lower quartile (19.5) to the upper quartile (25), and draw a vertical line inside the box at the median (21).

4. Extend whiskers (horizontal lines) from the box to the minimum (13) and maximum (27).

Here's a rough sketch of the box-and-whisker plot:

----|-|-|---|-|---
13 19.5 21 25 27

It should be vertical when it's properly drawn.