Finding Outliers Using IQR

Coral Reef Diversity

Coral reefs only occupy .1% of the ocean's floor, but they are home to 25% of marine fish species. Coral forms a complex ecosystem that supports this biodiversity. The marine fish species that occupy coral reefs have adapted their body shape, size, and color to live in and benefit from the reefs.

​Watch the following TED Talk with Sylvia Earle, a legendary ocean researcher.

Coral Reef Fish Variation

One variation in the extreme diversity of reef fish is their size. Scroll through the following compilation of marine fish species.

✔ Table 1
Record the maximum lenghths of each species of the Anthias family from the list.

​✔ Figure 1
Order the data from Table 1 and construct a boxplot.

​✔ Analysis 1
​Are there any values in the Anthias dataset that look out of place when compared with the rest of the values? Why or why not?

Outliers

✔ Notes 1

An outlier is a data point that is statistically different from the rest of the dataset. A computational method of finding these outlying data points involves the interquartile range (IQR). If a data point is more than IQRx1.5 above the third quartile or below the first quartile, then it is an outlier.

Try an example!

✔ Calculation 1
Consider the dataset for the Anthias family: 
We can mathematically determine whether a data point is an outlier by using the IQR.
  • Record Q1 and Q3.
  • Calculate the IQR of the dataset and record the number.
  • Multiply the IQR by 1.5 and record the number.
  • Subtract the IQRx1.5 from Q1.
  • Add the IQRx1.5 to Q3.

​✔ Analysis 2
​Are there any values outside of the interval you created using IQRx1.5? Identify the species of the Anthias family of fish that are outliers, if any.

Identifying Outliers

Any values outside of the IQRx1.5 interval are outliers. If we compare the interval to the original dataset, the data points of 7 cm and 20 cm are outside the interval.
So, the Diadem Anthias and Squareback Anthias, pictured below, are outliers for their sizes in their family of coral reef fish!
By Izuzuki - http://www.izuzuki.com/, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=32116890
​By Jenny (JennyHuang) from Taipei - Flickr, CC BY 2.0, https://commons.wikimedia.org/w/index.php?curid=1293786

Try It!

✔ Table 2
Pick another family of marine fish (10-30 species) from the Wikipedia list. Record the maximum sizes of each species.

✔ Figure 2
Order the data from Table 2 and construct a boxplot.

✔ Calculation 2
Determine if there are any outliers using interquartile range. Identify the species of the family of fish that are outliers, if any.

✔ Discussion 1
How do outliers affect datasets?

​Coral Reefs and Fish in Danger

Despite the message of the film being largely centered on conservation and the tragedy of taking wild coral fish species from their homes and placing them in glass prisons, Finding Nemo had a sad and ironic effect that spread far beyond the box office. It seemed the clownfish portrayed in the film were too cute for their own good, and became instantly in-demand pets for people who failed to recognize that their demand for a cute pet would cause many more Nemos to be taken from their coral reef ecosystems.