Interquartile range

🔗What you need to know first

How to

The interquartile range (IQR) measures the spread of the middle 50% of a dataset. It is less affected by extreme values (outliers) than the range.

$$\text{IQR} = Q3 - Q1$$

where $Q1$ is the lower quartile (25th percentile) and $Q3$ is the upper quartile (75th percentile).

Finding quartiles for small datasets:

Example: Data: 3, 5, 7, 8, 10, 12, 15 $Q1 = 5$, $Q2 = 8$, $Q3 = 12$, so $\text{IQR} = 12 - 5 = 7$

A smaller IQR means the data is more consistent. Compare IQRs when comparing two distributions.

Common error: including the median in both halves when calculating Q1 and Q3 for an odd-numbered dataset — exclude the median from each half.

Common topics that go alongside

❓Questions to practise

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📝Past paper questions

💬What the examiners say

"Show a clear method on the graph—without marked lines showing where you've read values, answers just outside the required range won't be awarded marks."
"Stronger responses showed an understanding that there was an even number of people in the sample, and this meant that the median didn't have to be an explicit value in the data set, but that it was the mean of the middle two values."

⬆️How you can quickly improve

After calculating both IQR values, write a direct comparison: 'Group A's IQR is lower, so Group A is more consistent.'
Work out 25% and 75% of the total frequency and write both values down before reading anything from the graph.
Learn the structure of a box plot: each of the four sections holds 25% of the data, and the box itself (Q1 to Q3) contains the middle 50%.

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🔓What this unlocks

ℹ️Calculator tricks