Data Handling
1. What Is Data?
DATA is a collection of FACTS or INFORMATION.
'Data is everywhere — the number of students in your class, the weather temperature each day, the runs scored in a cricket match. We collect, organise, and study data to find PATTERNS and make decisions.'
Types of Data
| Type | Meaning | Example |
|---|---|---|
| Numerical | Expressed as numbers | Heights of students: 145 cm, 150 cm, 138 cm |
| Categorical | Expressed as categories | Favourite colours: red, blue, green |
| Raw data | Unorganised data collected directly | 45, 67, 45, 78, 67, 45, 90, 67 |
2. Tally Marks
TALLY MARKS are a quick way to count and record data. Each mark stands for ONE item.
How to Use Tally Marks
| Number | Tally Marks |
|---|---|
| 1 | | |
| 2 | || |
| 3 | ||| |
| 4 | |||| |
| 5 | 𝖷 (fifth mark crosses the first four) |
| 6 | 𝖷 | |
| 10 | 𝖷 𝖷 |
'When you reach the FIFTH item, draw a diagonal line across the first four. Grouping by FIVES makes counting EASY — just count the groups of five and add the remainders.'
Tally Table Example
| Favourite Fruit | Tally Marks | Number of Students |
|---|---|---|
| Apple | 𝖷 𝖷 || | 12 |
| Banana | 𝖷 ||| | 8 |
| Mango | 𝖷 || | 7 |
| Orange | 𝖷 | 5 |
| Grape | || | 2 |
| Total | 34 |
Creating a Tally Table
Given the raw data of favourite colours: Red, Blue, Red, Green, Blue, Red, Yellow, Blue, Red, Green Blue, Red, Red, Yellow, Blue, Green, Red, Blue
| Colour | Tally | Count |
|---|---|---|
| Red | 𝖷 ||| | 8 |
| Blue | 𝖷 | | 6 |
| Green | || | 3 |
| Yellow | | | 2 |
| Total | 19 |
'When making a tally table, go through the data ONE item at a time and add ONE tally mark for each. Do not guess or skip.'
3. Pictographs
A PICTOGRAPH uses SYMBOLS or PICTURES to represent data.
Key (Legend)
Each symbol represents a CERTAIN NUMBER of items. The KEY tells you what one symbol means.
Example: Books Read
| Student | Books Read | Symbol |
|---|---|---|
| Ravi | 10 | 📚 📚 📚 📚 📚 |
| Priya | 8 | 📚 📚 📚 📚 |
| Amit | 6 | 📚 📚 📚 |
| Sunita | 12 | 📚 📚 📚 📚 📚 📚 |
Key: Each 📚 = 2 books.
Reading a Pictograph
'The KEY is the MOST important part of a pictograph. Without the key, you cannot interpret what each symbol means.'
| Month | Number of Umbrellas Sold |
|---|---|
| June | ☂️ ☂️ ☂️ ☂️ ☂️ ☂️ |
| July | ☂️ ☂️ ☂️ ☂️ ☂️ ☂️ ☂️ |
| August | ☂️ ☂️ ☂️ ☂️ |
| September | ☂️ ☂️ |
Key: Each ☂️ = 10 umbrellas.
Questions:
- How many umbrellas were sold in July? 7 × 10 = 70.
- Which month had the highest sales? July.
- How many more umbrellas were sold in June than August? 60 − 40 = 20.
- Total umbrellas sold in all four months? 60 + 70 + 40 + 20 = 190.
4. Bar Graphs
A BAR GRAPH uses RECTANGULAR BARS of different heights to show data.
Parts of a Bar Graph
| Part | Description |
|---|---|
| Title | Tells what the graph is about |
| Horizontal axis (X-axis) | Shows the categories |
| Vertical axis (Y-axis) | Shows the numbers or frequency |
| Scale | Tells what each unit on the axis represents |
| Bars | Rectangles of equal width — height shows the value |
Drawing a Bar Graph
Steps to draw a bar graph:
| Step | Action |
|---|---|
| 1 | Choose a SUITABLE SCALE for the vertical axis |
| 2 | Draw the X-axis (categories) and Y-axis (numbers) |
| 3 | Mark equal INTERVALS on the Y-axis |
| 4 | Draw bars of EQUAL WIDTH — height represents the value |
| 5 | Leave EQUAL SPACE between bars |
| 6 | Label EVERYTHING — title, axes, scale |
'Choose a scale that fits your data. If numbers are from 0 to 100, let 1 cm = 10 units. If numbers are from 0 to 10, let 1 cm = 1 unit.'
Example: Favourite Sport
| Sport | Number of Students |
|---|---|
| Cricket | 30 |
| Football | 25 |
| Kabaddi | 15 |
| Hockey | 20 |
| Tennis | 10 |
Scale: 1 unit (1 cm) = 5 students.
Y-axis: 0, 5, 10, 15, 20, 25, 30, 35. X-axis: Cricket, Football, Kabaddi, Hockey, Tennis.
Reading a Bar Graph
'When reading a bar graph, first READ the title to know what the graph is about. Then look at both axes labels. Then look at the scale.'
Interpreting Data from a Bar Graph
Questions based on the bar graph above:
| Question | Answer |
|---|---|
| Which is the most popular sport? | Cricket (30 students) |
| Which is the least popular sport? | Tennis (10 students) |
| How many students like Football? | 25 |
| How many more like Cricket than Kabaddi? | 30 − 15 = 15 |
| Total students surveyed? | 30 + 25 + 15 + 20 + 10 = 100 |
5. Reading and Interpreting Data
Questions to Ask About Data
| Type of Question | Example |
|---|---|
| Find the HIGHEST / LOWEST | Which month had the most rainfall? |
| Find the DIFFERENCE | How much more rain fell in July than in May? |
| Find the TOTAL | What is the total rainfall for all months? |
| Find the AVERAGE | What is the average rainfall per month? |
| Make a COMPARISON | Which two months had the same rainfall? |
Example: Rainfall in a City
| Month | Rainfall (mm) |
|---|---|
| January | 20 |
| February | 15 |
| March | 10 |
| April | 5 |
| May | 25 |
| June | 200 |
Total rainfall = 20 + 15 + 10 + 5 + 25 + 200 = 275 mm.
'Data often tells a STORY. In this rainfall data, you can SEE that June has the monsoon and April is the driest month. ALWAYS think about what the data is telling you.'
Key Facts to Remember
- Tally marks group by 5 — four vertical lines crossed by a diagonal.
- Every pictograph MUST have a KEY.
- Every bar graph MUST have a TITLE, labelled axes, and a SCALE.
- Bars in a bar graph have EQUAL WIDTH and EQUAL SPACING.
- 'Data handling is not just about DRAWING graphs — it is about READING and INTERPRETING what the data says.'
Common Mistakes
| Mistake | Why It Is Wrong | Correct Approach |
|---|---|---|
| Bars of different widths | All bars must be the same width — only height changes | Keep width constant, vary height |
| No scale on Y-axis | Without a scale, the graph has NO meaning | Always label the scale on the Y-axis |
| Forgetting gaps between bars | Bars should NOT touch in a simple bar graph | Leave small gaps between bars |
| Wrong tally count | Counting errors happen when tally marks are messy | Group by 5 neatly |
Exam Focus (ICSE Class 5)
| Topic | Marks (Typical) | Question Type |
|---|---|---|
| Tally marks and frequency tables | 3-4 marks | Complete the tally table |
| Reading a pictograph | 3 marks | Answer questions based on pictograph |
| Drawing a bar graph | 4-5 marks | Given data, draw and label a bar graph |
| Interpreting a bar graph | 3-4 marks | Read and answer questions from a bar graph |
| Data interpretation | 3 marks | Highest, lowest, difference, total |
Self-Test: 5 Questions
Q1. The following are favourite subjects of 25 students: Math, Science, English, Science, Math, Math, English, Science, Math, English, Science, Math, English, Math, English, Math, Science, Math, English, Math, English, Math, Math, Science, Math. Make a tally table.
Q2. In a pictograph, if one 🍎 = 5 apples, how many apples do 6 🍎 represent?
Q3. Draw a bar graph for the data: Number of trees planted — Class A: 25, Class B: 30, Class C: 20, Class D: 35.
Q4. The bar graph shows: Monday = 40 visitors, Tuesday = 55, Wednesday = 30, Thursday = 45, Friday = 60. Find the total visitors and the difference between the highest and lowest.
Q5. Explain why choosing the right SCALE is important when drawing a bar graph.
Answers
A1. Math: 𝖷 𝖷 |||| = 14. Science: 𝖷 | = 6. English: 𝖷 = 5. Total = 25.
A2. 6 × 5 = 30 apples.
A3. Draw X-axis with Class A, B, C, D. Y-axis from 0 to 40. Scale: 1 unit = 5 trees. Bars of heights 5, 6, 4, 7 units.
A4. Total = 40 + 55 + 30 + 45 + 60 = 230. Highest = 60 (Friday). Lowest = 30 (Wednesday). Difference = 30.
A5. The scale determines how the data is VISUALLY represented. A poor scale can make small differences look huge or hide important patterns. The scale must be UNIFORM and FIT all the data.
