# Mean, median or mode? How to apply descriptive statistics for the IA.

Travis DixonInternal Assessment (IB)

At first it seems daunting, but you'll actually find the descriptive statistics section is surprisingly easy.

Read carefully so you’ll know how to apply descriptive statistics for the IA PROPERLY! (Or watch the video explanation here). I will freely admit, that I can’t explain it any clearer than what’s included on this excellent post on MyIB. Perhaps the most value I can offer is to make people aware of this resource.

Before we look at what you have to do, it’s important to understand why you’re doing it. You’ve conducted an experiment and now you want to see if there are differences between the conditions. This will suggest if there’s an effect of the IV on the DV or not.

### Quick Checklist

You can get a full IA checklist and more resources in our IA support packs available here.

• Raw data table in appendices and not in the body of the report
• One measure of central tendency (mean, median or mode)
• One measure of dispersion (SD, range, IQR or variation ratio).
• Results clearly summarized in a paragraph (a table is advisable, too)
• You have not accepted/rejected any of your hypotheses based on the descriptive statistics

Descriptive statistics in IB Psychology refers to two calculations you need to apply to your data. You need to apply one each of the following two calculations:

1. Average (aka central tendency). e.g Mean OR median OR mode
2. Dispersion (aka spread), e.g.  standard deviation OR range OR interquartile range OR variation ratio.*

*The IB has published some really useful information on the MyIB Psychology page in the Programme Resource Center. Visit this link or go through the “Additional Guidance” page in the homepage. This is where they say to use variation ratio for nominal data.

### MEAN, MEDIAN OR MODE?

Use the mean if…

• …you have interval or ratio data without outliers.

Use the median if…

• …you have ordinal data,
• Or…you have interval or ratio data with outliers.

Use the mode if…

• …you have nominal data

## Don’t know your type of data?

Your choice of descriptive statistics depends on your level of measurement. There are four possible levels of measurement that your data will be:

• Nominal: your results can’t be ordered from highest to lowest, only put in groups.
• Ordinal: your results can be ordered from highest to lowest, but there is not an equal interval between them.
• Interval: your results can be ordered from highest to lowest, they have equal intervals but there’s no true zero value.
• Ratio: your results can be ordered, have equal intervals and there’s a true zero.

The most common types of results in IB Psychology IAs are:

• Likert scale ratings (asking participants to rate something on a scale, e.g. 1-7)
• Memory tests

According to the IB’s guidance, likert scales are ordinal data and memory tests are ratio data. Speed and time are also examples of ratio data. If you have a different kind of data, you will need to decide for yourself what level of measurement you think it fits.

You can visit the IB’s official page to find out their guidance on which test to use depending on your level of measurement.

Teaching Tip: I have students do all this by themselves first. I only present materials like this post after they’ve tried it for themselves.

### DISPERSION

Your measure of dispersion will depend on the average you calculated above and your type of data.

There’s no need to explain how or why you chose the descriptive stats to use or the level of measurement of your data. It’s enough to write them in a summary. It’s also recommended to put them in a clearly labelled table since this is common practice in psychology.

*The IB’s official website on MyIB says median and range is best for ordinal data. However, IA examiners look for IQR for ordinal data. If you have ordinal data, therefore, use IQR.

Two decimal places is specific enough for descriptive calculations. Do not go to 7 or 8 decimal places like many students do. It doesn’t lose marks but it’s my pet peeve.

### Example Data Table

Here’s an example of a table presenting descriptive data calculations. This is from my example IA included in the IA support pack.

### What to do with outliers?

Sometimes you have extreme values that will skew your mean. For example, someone in your Loftus and Palmer experiment guess 300mph when everyone else was around 60mph. You have two choices:

• Keep it!
• Drop it!

You need to decide what to do with outliers. Once again, the guidance on MyIB is really specific about how to decide whether or not to discard outliers.