The idea, step by step
Describe the whole pattern
A distribution shows how observations are spread across values. Look for clusters, gaps, a roughly balanced shape and tails. A roughly symmetric distribution has similar sides around its centre. Right-skewed means a longer tail towards larger values; left-skewed means a longer tail towards smaller values.
These are descriptions, not exact rules for a tiny dataset. Explain what you see using the context and actual values. Do not name skew by the side containing most observations: a right-skewed distribution often has most observations towards the lower end.
Unusual is not the same as wrong
An outlier is an observation unusually far from the main group. Check whether it is an error, a different measurement condition or a genuine result. Keep a genuine observation when it belongs to the population and question. Report its influence rather than deleting it to make a graph look smoother.
An extreme value can strongly pull the mean and increase the range. The median depends on middle positions and is often less affected. There is no universal rule that a low or high result should disappear from data.
A common trap
Delete every outlier before calculating an average.
Instead: First establish whether it is an error or a genuine relevant observation. A valid extreme value is still evidence.
See the thinking
Investigate a high reading
Eight daily temperatures are 18, 19, 19, 20, 20, 21, 21, 38°C. Describe the unusual value and compare mean and median.
- Most observations lie from 18°C to 21°C; 38°C is unusually high relative to this group.
- The sum is 176°C; mean = 176÷8=22°C.
- The middle values are 20 and 20, so median=20°C.
- Check the source of 38°C. If it is a genuine day in the period, keep it and explain its effect.
Read the direction of a tail
Waiting times in minutes are 5, 6, 6, 7, 8, 9, 30. Describe the shape.
- Most waits are from 5 to 9 minutes.
- One much larger observation extends the distribution towards larger values.
- The median is 7 minutes, while the long wait increases the mean.
Check your understanding
Most values are near 40, with a tail stretching down to 5. Which direction is the skew?
Show answer
Left-skewed.
The long tail extends towards smaller values on the left.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- Describe the main cluster and an unusual value in 7, 8, 8, 9, 9, 10, 28.2 marks
- Why is “28 is different, so remove it” not enough justification?2 marks
- For 3, 4, 4, 5, 24, find the mean and median.2 marks
- A graph has a long tail towards large values. Is it left-skewed or right-skewed?2 marks
- The minimum is 12 and maximum 31. A genuine new observation of 50 is included. What happens to the range?2 marks
- A recorded plant height is 420 cm while other seedlings are 4–8 cm. Name two things to check before using it.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Describe the main cluster and an unusual value in 7, 8, 8, 9, 9, 10, 28.2 marks
Six observations lie between 7 and 10; one is well above them.
Main cluster 7–10; 28 is unusually high. - Why is “28 is different, so remove it” not enough justification?2 marks
Check recording conditions and the source before deciding whether it is an error.
A genuine relevant observation must not be removed merely because it is unusual. - For 3, 4, 4, 5, 24, find the mean and median.2 marks
The total is 40, so mean=40÷5=8.
The middle ordered observation is 4.
Mean 8; median 4. - A graph has a long tail towards large values. Is it left-skewed or right-skewed?2 marks
Large values lie to the right on the number axis.
Right-skewed. - The minimum is 12 and maximum 31. A genuine new observation of 50 is included. What happens to the range?2 marks
Original range=31−12=19.
New range=50−12=38.
It increases from 19 to 38. - A recorded plant height is 420 cm while other seedlings are 4–8 cm. Name two things to check before using it.2 marks
Review the original measurement and recording rules rather than inventing a correction.
For example, whether 4.20 cm was mistyped as 420 cm, and whether the same units or type of plant were used.
Curriculum reference & lesson scope
Australian Curriculum v9 / South Australian Mathematics Curriculum
Year 7 statistical variables, representations, summary statistics, outliers and an original small investigation; deeper sampling methods develop in Year 8.
Official curriculum source ↗