Young Geniuses · Ages 13 to 14
Normal Distribution Graph
Read areas under a normal distribution curve using the 68–95–99.7 rule. A Grade 8–9 statistics worksheet with answer keys.
The learning journey
Every activity is one step. Here is where this one fits.
- PlayLearn the idea in a game
- Practise(you are here)Lock it in on paper
- ReviewCome back and keep it sharp
- MasterTake on a harder challenge
- AchieveEarn a certificate
About Normal Distribution Graph
Normal Distribution Graph introduces ambitious upper-secondary learners to the normal distribution, the famous bell-shaped curve that describes so much real-world data. Each worksheet shows a normal curve with a region shaded around the mean, and the student answers questions using the 68–95–99.7 rule: that about sixty-eight percent of data lies within one standard deviation of the mean, ninety-five percent within two, and almost all within three. The normal distribution and the empirical rule appear in statistics enrichment and early high-school courses across the US, UK, Canada and Australia, and they are the foundation of so much of how heights, test scores, measurements and errors are understood. Reading the curve well means grasping that area under the curve represents proportion of data, and that the curve is perfectly symmetrical about the mean — ideas these questions make concrete. The curve is drawn clearly with the mean and standard deviations marked so students can connect the shaded region to a percentage. The five levels vary the mean and standard deviation so the worksheet stays fresh and reusable. Each page prints cleanly on a standard A4 sheet, and every level downloads with its own answer key. There is no advertising and no sign-up.
Common questions
- What is the 68–95–99.7 rule?
- About 68%, 95% and 99.7% of data lie within one, two and three standard deviations of the mean.
- What grade is this for?
- Grade 8 to Grade 9 learners aged 13 to 14, as an enrichment topic.
- Is an answer key included?
- Yes, every level has its own answer key.
A hand for grown-ups
- Before you start
- Find a calm few minutes with no rush. Let your child know it is fine to find some of it tricky — that is what practice is for.
- While they work
- Sit nearby but let them lead. If they get stuck, ask "what could you try?" rather than giving the answer — the thinking is the point.
- Afterwards
- Ask them to show you one they found easy and one they found hard. Praise the effort on the hard one, not just the right answers.
- Watch out for
- Rushing. If answers come too fast and wrong, slow the pace down together rather than pushing for more.
- Away from the screen
- Look for the same maths in everyday life — counting stairs, sharing snacks, spotting shapes on a walk.
Where to go next
Chosen by the skills this activity practises.