A change to an extreme value can increase standard deviation while leaving the interquartile range unchanged. IQR uses the lower and upper quartiles. Standard deviation uses all the values in the data set.
The 2027 SEC G3 Mathematics syllabus (K310) includes both measures of spread. The example below keeps the central values fixed so you can see why the two results differ.
- Order the data and find both quartiles.
- Use all the values when calculating standard deviation.
- Say which part of the spread each measure describes.
Worked example | Change 8 to 16
Set A is 2, 4, 4, 5, 5, 6, 6, 8. Set B is 2, 4, 4, 5, 5, 6, 6, 16. For these eight values, take the median of each half to find the quartiles. The lower quartile is 4 and the upper quartile is 6 in both sets. Both have IQR 6 − 4 = 2.
Set A has mean 5 and a sum of squared deviations from the mean of 22. Its standard deviation is √(22 ÷ 8) ≈ 1.66. Set B has mean 6 and a sum of squared deviations of 126, so its standard deviation is √(126 ÷ 8) ≈ 3.97.
If you use a calculator, select the population standard deviation for the supplied data set, consistent with the K310 formula. You can check by using the mean of the squared deviations as shown here.
Explain both measures in one sentence
A clear comparison is “Both sets have the same IQR, so their middle halves have the same interquartile spread. Set B has the larger standard deviation, which reflects its greater spread around the mean.”
The median remains 5 in both sets. The mean rises from 5 to 6. An extreme change can therefore affect a measure of centre as well as a measure of spread.
Change a middle value instead
In Set A, replace one of the 6s with 7. The ordered upper half becomes 5, 6, 7, 8. Its median becomes 6.5 and the lower quartile stays at 4, so the IQR becomes 2.5.
Ask a study partner to mark the values used in each quartile. Then ask which values go into standard deviation. This makes it easier to explain why the two measures can respond differently.
Frequently asked questions
Is IQR the same as range?
IQR is the upper quartile minus the lower quartile. Range is the maximum minus the minimum.
Can changing an extreme ever change the quartiles?
It depends on the set and how the order changes. Reorder the values and recompute the quartiles when in doubt.
Official information
SEAB’s 2027 SEC G3 Mathematics syllabus (K310), S1 Data Handling and Analysis. Checked 10 November 2026.