Statistics is the part of mathematics that deals with collecting, organising, displaying and interpreting data (information, usually numbers or categories). Schools, businesses and governments use it to make decisions: which snacks a school café should sell, which bus route needs more buses, how many vaccines a country needs. In this lesson you will follow the full statistics process – asking a question, collecting discrete data, using a tally chart and frequency table, drawing pictographs and block graphs, drawing conclusions, and finding the mode.
Step 1: Ask a question that data can answer
A good statistical question has an answer that varies and can be counted. “What is your favourite fruit?” is a good survey question because people give different answers that can be sorted into categories. “Do you like fruit?” gives much less useful information. A bigger investigation might ask: “What healthy snacks should our school café sell, and why?” – and then use survey questions to find out.
Step 2: Collect discrete data
Discrete data can only take separate, countable values – usually whole numbers or categories. Examples: the number of brothers and sisters you have (0, 1, 2, …), the number of goals scored, or favourite sport. (Data such as height or time, which can take any value on a scale, is called continuous – you will meet it in later forms.) Ways to collect data include:
- Surveys and questionnaires – asking people questions.
- Observation and counting – for example, counting cars passing the school gate.
- Interviews – talking to people one at a time.
- Experiments – for example, rolling a die 50 times.
- Existing records – newspapers, books, websites and databases.
Step 3: Organise the data – tally chart and frequency table
Here are the favourite sports of 30 students, in the order they answered:
Football, Cricket, Netball, Football, Basketball, Cricket, Football, Athletics, Netball, Football, Cricket, Basketball, Football, Netball, Cricket, Athletics, Football, Basketball, Netball, Cricket, Football, Netball, Basketball, Cricket, Football, Athletics, Netball, Basketball, Cricket, Football.
Go through the list once. For every answer, make a tally mark (|) next to that sport. Every fifth mark is drawn across the previous four, so the marks are in easy-to-count bundles of five. The frequency is how many times each answer occurs.
| Sport | Tally | Frequency |
|---|---|---|
| Football | |||| |||| | 9 |
| Cricket | |||| || | 7 |
| Netball | |||| | | 6 |
| Basketball | |||| | 5 |
| Athletics | ||| | 3 |
| Total | 30 |
Always check that the frequencies add up to the number of answers: 9 + 7 + 6 + 5 + 3 = 30 ✔
Step 4: Display the data
Pictographs
A pictograph (pictogram) uses a small picture or symbol to stand for a number of items. It must have a key. With 30 students, one symbol for every 2 students keeps the graph short; half a symbol stands for 1 student.
| Football | |
| Cricket | |
| Netball | |
| Basketball | |
| Athletics |
Football has 9 students: 9 ÷ 2 = 4 remainder 1, so it gets 4 whole symbols and a half symbol.
Block graphs
A block graph stacks one block (a square) for each item or for a fixed number of items. Blocks are the same size and sit on a common baseline, and the vertical axis is numbered from 0 with an even scale. Give the graph a title and label both axes. A block graph is a stepping stone to the bar graphs you will draw in Term 2. Try building one in the interactive below.
TRY ITTally chart, frequency table and block graph
Collect your own data: press a button for each answer. The tally marks, frequency table, block graph and mode update as you go.
Survey question: “What is your favourite fruit?” Press a button each time someone answers.
| Fruit | Tally | Frequency |
|---|---|---|
| Total | 0 |
Block graph (1 block = 1 person):
Step 5: Interpret and draw conclusions
Reading a graph means answering questions such as: Which category is biggest or smallest? How many more chose one option than another? What fraction of the total chose a category? Drawing a conclusion means saying what the data tells us about the original question – and noticing its limits.
- Football is the most popular sport (9 students) and athletics the least popular (3 students).
- 9 − 3 = 6 more students chose football than athletics.
- Conclusion: in this group, a football club would probably attract the most members. But only 30 students were asked, so the result might be different for the whole school.
The mode
The mode is the value (or category) that occurs most often – the one with the highest frequency. In Table 1 the mode is football. A set of data can have more than one mode if two values tie, or no useful mode if every value occurs equally often.
Worked example: The mode from a frequency table
Question: 25 students were asked how many brothers and sisters they have. Find the mode and answer the questions.
- Table: 0 siblings – 4 students; 1 sibling – 9 students; 2 siblings – 7 students; 3 siblings – 3 students; 4 siblings – 2 students.
- The highest frequency is 9, and it belongs to the value 1 sibling.
- Check the total: 4 + 9 + 7 + 3 + 2 = 25 ✔
- Students with 2 or more siblings: 7 + 3 + 2 = 12.
Answer: The mode is 1 sibling (not 9 – the 9 is the frequency, not the value).
Common mistakes
- Giving the frequency as the mode. The mode is the value with the highest frequency (“1 sibling”, “football”), not the frequency itself.
- Ignoring the pictograph key. If one symbol stands for 4 people, 3 symbols mean 12 people, not 3.
- Drawing the fifth tally mark as a fifth upright stroke. The fifth mark crosses the other four, making a bundle you can count by fives.
- Uneven blocks or scales. Every block must be the same size, and the numbers on the axis must go up in equal steps from 0.
- Not checking the total. If the frequencies do not add up to the number of answers, a tally was missed or doubled.
Practice questions
Try these yourself first, then open each answer to check your working.
1. How do you show a frequency of 13 with tally marks?
Show answer
Two bundles of five (four strokes with a fifth across them), then three single strokes: 5 + 5 + 3 = 13.
2. These are the colours of 15 cars that passed a school gate (R = red, B = blue, W = white, S = silver): R, B, W, W, S, R, W, B, W, S, W, R, B, W, S. Make a frequency table and find the mode.
Show answer
Red 3, Blue 3, White 6, Silver 3 (total 15). The mode is white.
3. In a pictograph, one book symbol stands for 4 books. A row shows 3½ symbols. How many books is that?
Show answer
3½ × 4 = 14 books.
4. Using the siblings table in the worked example, how many students were asked, and how many have no brothers or sisters?
Show answer
25 students were asked; 4 have no siblings.
5. Why is “Which bus route do you use to get to school?” a better survey question than “Do you take the bus?” for planning bus routes?
Show answer
It gives the actual routes (categories that can be counted), so planners can see which routes are used most. “Do you take the bus?” only gives yes or no.
6. In a block graph each block stands for 5 people. The “Mango” column has 9 blocks. How many people chose mango?
Show answer
9 × 5 = 45 people.
Quick check
1. What is discrete data?
Show answer
Data that can only take separate, countable values, such as whole numbers or categories.
2. What does the frequency column in a table tell you?
Show answer
How many times each value or category occurs.
3. What must every pictograph have so that it can be read?
Show answer
A key showing how many items each symbol stands for.
4. What is the mode?
Show answer
The value or category that occurs most often (highest frequency).
Next: Introduction to Algebra: Variables, Constants, Expressions and Substitution
Curriculum link: This post is relevant to the Trinidad and Tobago National Lower Secondary (NCSE) Mathematics Curriculum – Form 1, Term 1, Strand 1.3 Statistics and Probability, Topic 1.3.1 Statistics – Learning Outcomes 1.3.1.1 (formulating a problem or questions that data can answer), 1.3.1.2 (collecting discrete data), 1.3.1.3 (tallying ungrouped discrete data into a frequency table), 1.3.1.4 (constructing pictographs and block graphs with suitable scales), 1.3.1.5 (interpreting them), 1.3.1.6 (drawing conclusions from them) and 1.3.1.7 (finding the mode from a frequency table).
Attributions to media used in this post:
Tally Marks.png – 293u8h1 – CC0 (via Wikimedia Commons)
© 2026 Vedesh Kungebeharry. All rights reserved.