Adding the same number to every score moves the entire data set by that amount. The mean, median and quartiles shift by the same amount. The range, interquartile range and standard deviation stay the same.
Picture the scores on a number line. Every point moves the same distance in the same direction, so the gaps between the points stay the same.
- Check whether the adjustment applies to every score.
- Shift the minimum, maximum, mean and quartiles by the stated amount.
- Use differences to check the measures of spread.
Worked example | Add five marks to every score
The original scores are 2, 4, 4 and 6. Adding five gives 7, 9, 9 and 11. The mean rises from 4 to 9. The range stays at 4 because 6 − 2 and 11 − 7 both equal 4.
Using the median-of-halves method, the original quartiles are 3 and 5. The new quartiles are 8 and 10. Both interquartile ranges are 2. You can reach the same conclusion by seeing that both quartiles move up by five.
Why does standard deviation stay the same?
Standard deviation depends on how far the scores sit from their mean. Before the change, the deviations are −2, 0, 0 and 2. After the change, subtract the new mean of 9 from 7, 9, 9 and 11. You get the same deviations.
Because the deviations stay the same, the squared deviations and the standard deviation stay the same too. This argument works regardless of how the original scores were spaced.
Try a shift downwards
A data set has mean 28, range 14, interquartile range 6 and standard deviation 4. Every value is reduced by three. Find the four new measures.
Answer. The new mean is 25. The range is 14, the interquartile range is 6 and the standard deviation is 4.
Frequently asked questions
What if only one score gets five extra marks?
Recalculate the relevant measures. Changing one score can alter its distance from other scores and can also change the mean.
What if every score is doubled?
Doubling all scores doubles every gap. The range, interquartile range and standard deviation all double.
Official information
SEAB, 2027 SEC G3 Mathematics syllabus (K310), Data Analysis, measures of spread. Syllabus checked 11 November 2026. The examples are original.