# Australian Bureau of Statistics

 ABS Home #search{vertical-align:-3.5px; }
 CensusAtSchool Australia

CaSQ 6B - Box and Whisker Plots with Outliers of Money Earned

You can download this activity as a rich text file (RTF) using the link at the bottom of the page.

 How to: Get a Random Sample from CensusAtSchool Go to the CensusAtSchool Random Sampler to download a sample. Reference year: (select year) Sample size: At least 60 students so that you have two categories with at least twenty students. Select questions: Money received Location: Select location Year level: (select a range of year levels) To protect privacy there is a rule built into the sampler that the requested sample size cannot exceed 10% of the respondents for the parameters entered.
Outliers

All outliers need to be investigated to see whether they are the result of an error or are true outliers. If there are errors we remove them. We can often identify possible outliers by eye as they are different to the rest of the data set. However, it can be useful to have an agreed method to identify outliers.

1. Why might it be useful to have one agreed method to identify outliers rather than just using your eye to identify them?

Using the IQR to Identify Outliers

2. In the CensusAtSchool random sample find the data on the ways students earned or received money in the last week. Remove all the data where students responded ‘No’ and received no money (0 dollars). Select two ways money was earned or received, such as paid work and pocket money. If there are not at least twenty students in each group, choose another sample.

3. For each group calculate and clearly record the 5 figure summary (min, Q1, med, Q3, max) as well as the IQR (inter quartile range).

In a box and whisker plot a value is said to be an outlier if it occurs more than 1.5 the IQR beyond the box.

4. Calculate 1.5 IQR for both of your data sets. Add this number to Q3. This number is called the upper fence. Subtract the same number from Q1. This number becomes the lower fence. Clearly record the IQR and upper and lower fence for both sets of data.

5. Give your work to a classmate to check and sign that you have calculated the fences correctly and that your box and whisker plots show any outliers that you found.
Upper fence correct □ Lower fence correct □

Figure 1. Example of fence shown on box and whisker plot

6. Decide on a scale appropriate for your data and then using the same scale, draw a box and whisker plot for both sets of data. Show the fences with a dotted vertical line. Any values beyond the fences are not joined to the whisker. Instead they are shown with a cross. Each whisker will end at the most extreme values within the fences.

7. Write a paragraph comparing your parallel box and whisker plots in terms of location (median), spread (IQR and range) and outliers. Describe and interpret any differences you observe. Remember to write in the context of your data, which is the amount of money received in a week by Australian students.