Box & Whisker Plots Examples

This plot represents the amount of money Mateo earned the past 18 weeks working at this dad's shop.  Create a box and whisker plot of this data.

12|0 represents $120

The median (Q2) is between 136 and 137. It is 136.5.
The lower quartile (Q1) is 130.
The upper quartile (Q3) is 143.

Now, we need to check for any outliers; 165 looks suspiciously high, but we always need to check.

IQR is 143 – 130 = 13
1.5(IQR) = 19.5
143 + 19.5 = 162.5

165 is higher than this, so it is an outlier.

Here is what the plot should look like:

Answer the following questions on the amount of time spent per day on social networking sites using the box plots below.

Approximate the girls' IQR and the boys' IQR. Then, calculate what percentage of girls spend more than 1.25 hours/day on these sites and what percentage of boys spend more than 1.35 hours/day on these sites.

The girls' lower quartile is about 1.25 hours/day and the upper quartile is about 3.5 hours/day.
The boys' lower quartile is about 0.6 hours/day and the upper quartile is about 1.35 hours/day.

Girls' IQR = 3.5 – 1.25 = 2.25 hours/day
Boys' IQR = 1.35 – 0.6 = 0.75 hours/day

1.25 hours/day is the lower quartile, so three sections of the plot are greater than Q1. Each section has 25% of the data, so 75% of the girls spend more than 1.25 hours/day on social networking sites.

1.35 hours/day is the upper quartile, so one section of the plot is greater than Q3. Each section has 25% of the data, so 25% of the boys spend more than 1.35 hours/day on social networking sites.

Using the box and whisker plot in Example 2, answer the following question. If one girl spends 6 hours/day on MyBook and FaceSpace, would she be considered an outlier?

If 6 hours/day is an outlier, it will be more than 1.5(IQR) greater than Q3. The girls' IQR is 2.25 hours/day. The upper quartile is 3.5 hours/day.

1.5(2.25) + 3.5 = 6.875 hours/day

6 hours/day is not greater than 6.875 hours/day, so it isn't an outlier.