Data Handling
1. What is Data?
Data is a collection of facts, numbers, or information.
Raw data is unorganized and hard to understand. We organize data using tally marks, pictographs, and bar graphs.
Example: The favourite fruits of 20 students:
Apple, Mango, Banana, Apple, Orange, Mango, Apple, Banana, Mango, Mango, Orange, Apple, Banana, Apple, Mango, Orange, Apple, Mango, Banana, Apple.
This is raw data. Let us organize it.
2. Tally Marks
Tally marks are a way of counting by making marks in groups of five.
| Value | Tally | Frequency |
|---|---|---|
| 1 | 1 | |
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ~~ | |
| 6 | ~~ |
The fifth mark is drawn diagonally across the first four. This makes counting easier.
Worked Example: Organize the favourite fruits data using tally marks.
| Fruit | Tally Marks | Frequency |
|---|---|---|
| Apple | ~~ | |
| Mango | ~~ | |
| Banana | ||
| Orange | ||
| Total | 20 |
Common Mistake: Drawing tally marks without grouping by fives. Always group by 5 for easy counting.
3. Pictographs
A pictograph uses pictures or symbols to represent data. A key tells us what each symbol represents.
Worked Example: Show the fruit data using a pictograph. Let 1 symbol = 2 fruits.
| Fruit | Number of Students | Pictograph |
|---|---|---|
| Apple | 9 | (4 and a half symbols) |
| Mango | 6 | (3 symbols) |
| Banana | 3 | (1 and a half symbols) |
| Orange | 2 | (1 symbol) |
Key: Each fruit symbol = 2 students. Half symbol = 1 student.
Exam Focus (2 marks): 'If one star represents 5 books, how many books do 3 stars represent?'
3 x 5 = 15 books.
Common Mistake: Forgetting half symbols for odd numbers. If a key is 2 units per symbol and you have 5, you need 2 full symbols and 1 half symbol.
4. Bar Graphs
A bar graph displays data using rectangular bars of equal width. The height (or length) of each bar represents the frequency.
Parts of a bar graph:
- Title: Describes what the graph shows.
- Horizontal axis: Shows the categories.
- Vertical axis: Shows the frequency (with a scale).
- Bars: Equal width, uniform gaps between bars.
Worked Example: Draw a bar graph for the favourite fruits data.
Horizontal axis: Fruits (Apple, Mango, Banana, Orange).
Vertical axis: Number of students (scale: 1 unit = 2 students).
Apple bar: up to 9 (need scale to show 9, e.g., 1 cm = 2 units, so 4.5 cm).
Mango bar: up to 6 (3 cm). Banana: up to 3 (1.5 cm). Orange: up to 2 (1 cm).
Worked Example: The number of books read by five students are: Ravi - 8, Sima - 12, Amit - 6, Priya - 15, John - 10. Draw a bar graph.
Scale: 1 unit = 2 books.
Bars: Ravi (4 units), Sima (6 units), Amit (3 units), Priya (7.5 units), John (5 units).
Common Mistake: Drawing bars too thin or too wide. Bars should be equal width with equal gaps between them. Also, the scale should start from 0.
5. Reading and Interpreting Graphs
Worked Example: A bar graph shows the number of rainy days in four months: June (12), July (15), August (10), September (5).
Questions:
- Which month had the most rainy days? (July: 15)
- Which month had the least rainy days? (September: 5)
- How many more rainy days in July than in August? (15 - 10 = 5)
- What is the total number of rainy days? (12 + 15 + 10 + 5 = 42)
Exam Focus (4 marks): 'A bar graph shows sale of umbrellas: Jan (20), Feb (15), Mar (25), Apr (40), May (50), Jun (60). In which month was the sale maximum? What is the difference between the maximum and minimum sales?'
Maximum: June (60). Minimum: February (15). Difference = 60 - 15 = 45.
6. Comparison Table: Data Representations
| Method | Best for | Pros | Cons |
|---|---|---|---|
| Tally marks | Small data sets | Simple, easy to create | Not visual, limited data |
| Pictograph | Categorical data | Visual, engaging | Limited precision, time-consuming |
| Bar graph | Comparing categories | Clear comparison, precise | Requires graph paper/practice |
7. Self-Test
- Prepare a tally chart for: 3, 5, 3, 4, 5, 3, 2, 4, 3, 5, 4, 3, 2, 3.
- If one star = 10 votes, how many stars are needed for 35 votes?
- The number of children in five societies are: A (45), B (60), C (30), D (75), E (50). Draw a bar graph.
- From the bar graph in Q3, which society has the most children? Which has the least?
- A pictograph uses a symbol = 4 students. How many symbols for 20 students? How for 6?
- List three important parts of a bar graph.
8. Answers to Self-Test
- Tally: 2 appears || (2), 3 appears
||||(6), 4 appears ||| (3), 5 appears ||| (3). Total = 14. - 3 full stars (30) + 1 half star (5) = 3.5 stars.
- Draw bar graph: X-axis societies A-E, Y-axis children (scale 1 cm = 10 children). Bars at 4.5, 6, 3, 7.5, 5 cm.
- Society D has the most (75). Society C has the least (30).
- 20 / 4 = 5 symbols. 6: 6 / 4 = 1.5 symbols (1 full + 1 half).
- Title, horizontal axis (categories), vertical axis (frequency with scale), bars of equal width.
