Describe the pattern with numbers, then check the spread, exceptions and possible explanations.
Clean data before calculating. Check units, missing values, duplicate entries and obvious recording errors. An unusual value is not automatically an error; keep it unless there is evidence that it is wrong. Document any exclusion.
The mean adds all values and divides by the number observed. The median is the middle value after ordering, and the mode is the most frequent. For walking times of 5, 5, 10, 15 and 40 minutes, the mean is 15, median 10 and mode 5. The range is 35 minutes. The long journey pulls the mean above the median.
Use proportions when comparing groups of different sizes, while retaining denominators. If 12 of 20 people and 18 of 60 people report a barrier, the proportions are 60% and 30%. The larger count does not imply a higher rate.
A scatter graph pairs two measurements from the same observation. Describe direction, strength and exceptions, then consider mechanisms and other influences. A positive association between distance and difficulty is consistent with a distance effect, but mobility, crossings or heat could also contribute.
Step by step
Summarise fairly
Choose an average suited to the distribution and report spread.
Compare like with like
Retain units, denominators and matching observations.
Explain cautiously
Use the pattern as evidence, not automatic proof of a cause.
Worked example: Describe, then qualify
"Difficulty generally rises from 1 at 100 m to 5 at 500 m. However, the 400 m journey is rated 3, below the 300 m journey's 4. The positive association supports investigating distance, while the exception suggests other route or user factors."
Watch out for this
The highest average identifies the worst experience for every person.
An average summarises a group. Inspect the distribution, subgroup differences and individual exceptions.
Check your understanding
Which group has the higher reported barrier rate: 12 of 20, or 18 of 60?
- 12 of 20: 60%, compared with 30%.
- 18 of 60, because 18 is larger.
- They have equal rates.