Probability: Formula, Sample Space and Examples
Math Education7 min read
Math Education
8 min read
Statistics: Full School Guide, Formulas and Examples
Published: 12.08.2026·Updated: 12.08.2026
Dewi Lestari
Mathematics Specialist
Statistics is the branch of mathematics concerned with collecting, presenting, processing and interpreting data. At school it arrives in stages: simple data presentation in primary years, measures of central tendency in Year 6 and Year 8, then grouped data and standard deviation in senior secondary. This page summarises the whole topic and links to each formula in detail.
The Vocabulary You Actually Need
| Term | Meaning | Example |
|---|---|---|
| Data | A collection of observed values | Test scores for one class |
| Population | Every object under study | All secondary students in a school |
| Sample | A subset taken from the population | 30 randomly chosen students |
| Datum | A single data value | One student's score of 85 |
| Frequency | How often a value occurs | The score 8 appears 5 times |
Telling a population from a sample is the question that appears most often in tests and is answered wrongly most often.
Measures of Central Tendency
These three answer the question "which single value represents the whole data set".
Mean — the sum of all values divided by how many there are.
Median — the middle value once the data is sorted. With an even count, it is the average of the two middle values.
Mode — the value that occurs most often.
Take the data 6, 7, 7, 8, 9, 9, 9, 10.
- Mean = 65 ÷ 8 = 8.125
- Median = (8 + 9) ÷ 2 = 8.5
- Mode = 9
Each formula is covered in full in how to calculate the mean, the median formula and the mode formula.
When to Use Which
This is rarely taught and the most useful part. When one extreme value exists, the mean is dragged towards it and misleads. Salaries of 3, 3, 4, 4, 50 (million) have a mean of 12.8 — yet four of the five people earn under 5. Here the median is more honest. For non-numeric data such as favourite colour or best-selling shoe size, the mode is the only measure that works at all.
Measures of Spread
These answer "how widely scattered is the data".
- Range = largest value − smallest value
- Quartiles — the three values splitting sorted data into four equal parts (Q1, Q2, Q3). Q2 is the median.
- Interquartile range = Q3 − Q1
- Standard deviation — the average distance of each value from the mean, studied in senior secondary
Presenting Data
| Format | Best suited to |
|---|---|
| Frequency table | Large raw data sets with repeats |
| Bar chart | Comparing categories |
| Line graph | Change over time |
| Pie chart | Showing proportions of a whole |
For a pie chart, each slice is angle = (frequency ÷ total) × 360°, or percentage = (frequency ÷ total) × 100%. See also how to calculate percentages.
The Mistakes That Actually Cost Marks
1. Finding the median without sorting first. This is the single biggest source of error across the whole topic, and it is entirely avoidable.
2. Confusing mean, median and mode. A memory hook that sticks: mode = most frequent; median = middle.
3. Dividing by the wrong number when frequencies are involved. For "5 students scored 8", the divisor is the number of students, not the number of table rows.
4. Reading a chart without checking its scale. A bar chart whose axis does not start at zero makes a small gap look dramatic. A child trained to check the scale will not misread a graph, at school or in the news.
5. Assuming a pie chart need not total 100%. If the percentages do not add to 100, something has been miscalculated.
