What is data? Types of data
Data are facts we collect: answers, counts or measurements. Information is data that has been organised so it means something.
- Qualitative (categorical) data are words or labels: favourite fruit, eye colour, type of transport.
- Quantitative (numerical) data are numbers.
- Discrete: counted, only certain values, often whole numbers (number of siblings, goals scored).
- Continuous: measured, any value in a range (height 152.4 cm, time 12.37 s, mass 48.6 kg).
Primary data you collect yourself; secondary data someone else collected (census, websites, books).
Collecting data
- Survey / questionnaire: ask people questions. Good questions are clear, short and not leading.
- Observation: watch and count (cars passing the school in 10 minutes).
- Experiment / measurement: measure with instruments (temperature, time).
- Sensors and data logging: devices record data automatically.
- Existing sources: databases, reports, the internet (check that they are reliable).
A sample is a part of the whole group (the population). A bigger, random sample gives fairer results. Bias happens when the sample is not typical, for example asking only your friends.
Organising data: tally marks, frequency tables and structured data
Use tally marks to count: four lines and a fifth line across make a bundle of 5. The count is the frequency.
| Fruit | Tally | Frequency |
|---|---|---|
| Mango | |||| ||| | 8 |
| Banana | |||| | 5 |
| Apple | |||| | 4 |
| Grapes | ||| | 3 |
| Total | 20 |
For many continuous values, group them into class intervals such as 140–150 cm, 150–160 cm.
Structured data fit neatly in rows and columns (a spreadsheet of names, ages and marks). Unstructured data do not (photos, videos, voice notes, free-text reviews). Computers can sort and search structured data easily; unstructured data need extra processing.
Tables and graphs: reading and choosing the right display
| Graph | Use it to | Example |
|---|---|---|
| Pictograph | Show counts with pictures and a key | Books read per month |
| Bar graph | Compare separate groups | Favourite fruit |
| Double bar graph | Compare two sets side by side | Boys and girls per sport |
| Pie chart | Show parts of a whole | How a family spends its money |
| Line graph | Show change over time | Temperature over a week |
| Histogram | Show grouped continuous data | Heights in class intervals |
| Scatter graph | Show a link between two variables | Study hours and marks |
Pie chart angle = (frequency ÷ total) × 360°.
To read a graph: read the title, the axes and their units, the scale, then compare values. Watch for misleading graphs: axes that do not start at 0, uneven scales or 3D pies that hide sizes.
Try it: a fruit survey at home
Ask 10–20 family members or neighbours their favourite fruit. Make a tally and frequency table, then draw a bar graph and a pie chart (use a protractor for the angles). Check that your angles add up to 360°. Then set your mango number in the 3D free play and compare.
Key formulas and definitions
- Frequency = number of times a value appears
- Total = sum of all frequencies
- Pie chart angle = (frequency ÷ total) × 360°
- Percentage = (frequency ÷ total) × 100%
- One tally bundle |||| (crossed) = 5
- Qualitative = words; discrete = counted; continuous = measured
Worked examples
1. Classify: (a) shoe colour (b) number of pets (c) time to run 100 m.
(a) qualitative (b) discrete quantitative (c) continuous quantitative.
2. Write the tally for 13.
Two bundles of 5 and 3 lines: |||| |||| |||, frequency 13.
3. In a survey of 20 students, 8 chose mango. What angle does mango get in a pie chart?
8 ÷ 20 × 360° = 0.4 × 360° = 144°.
4. A pie chart sector for 'walk to school' is 90°. 40 students were asked. How many walk?
90° ÷ 360° = 1/4. 1/4 of 40 = 10 students.
5. A family spends ₹30,000 a month: food ₹12,000, rent ₹9,000, travel ₹3,000, other ₹6,000. Find each pie angle.
Each ₹1,000 = 360° ÷ 30 = 12°. Food 144°, rent 108°, travel 36°, other 72°. Check: 144 + 108 + 36 + 72 = 360°.
6. Which graph would you choose for: (a) monthly rainfall in a year (b) share of electricity sources (c) height vs arm span of 30 students?
(a) line graph or bar graph (change over time), (b) pie chart (parts of a whole), (c) scatter graph (link between two variables).
Common mistakes
- Using a pie chart for data that are not parts of one whole (e.g. temperatures each day).
- Forgetting that pie angles must add up to 360°, or frequencies to the total.
- Calling measured data like height 'discrete'. Measured data are continuous.
- Reading a bar graph without checking the scale; a y-axis that starts at 50 makes small gaps look huge.