Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
What is Data?
Data is information collected for a specific purpose. It can be in the form of numbers, words, or measurements.
Examples of data:
- Number of students absent each day for a week
- Marks scored by students in a test
- Favourite colours of classmates
Raw data: Data collected but not yet organised. Organised data: Data arranged in a systematic way — easier to read and understand.
Recording Data — Tally Marks
Tally marks help record data quickly while counting.
| Count | Tally | ||||
|---|---|---|---|---|---|
| 1 | \ | ||||
| 2 | \ | \ | |||
| 3 | \ | \ | \ | ||
| 4 | \ | \ | \ | \ | |
| 5 | ̷\ | \ | \ | \ | (four with diagonal) |
| 10 | Two groups of 5 |
The diagonal line on every 5th mark makes counting groups of 5 easy.
Frequency
Frequency is the number of times a particular value appears in the data.
Frequency Table: A table showing data values and their frequencies.
Example: Favourite fruits of 20 students:
| Fruit | Tally | Frequency | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Mango | 8 | |||||||||
| Apple | 6 | |||||||||
| Banana | 4 | |||||||||
| Grapes | 2 | |||||||||
| Total | 20 |
Pictograph
A pictograph uses pictures or symbols to represent data.
- Every pictograph has a key/scale — tells you what one symbol represents.
Example: Students who play different sports:
Reading a pictograph:
- Count the number of symbols for each item.
- Multiply by the scale value.
Drawing a pictograph: 1. Choose a suitable symbol. 2. Decide the scale (e.g., 1 symbol = 5 units). 3. Calculate how many symbols needed for each item. 4. Draw the symbols in neat rows.
Bar Graph
A bar graph (bar chart) uses rectangular bars to represent data.
Features of a Bar Graph
- Title: describes what the graph shows
- X-axis (horizontal): categories or items
- Y-axis (vertical): values/frequency
- Scale: equal intervals on the Y-axis
- All bars have equal width; gaps between bars are equal
Example data — Books read by students in a month:
| Student | Books Read |
|---|---|
| Arjun | 4 |
| Priya | 7 |
| Ravi | 3 |
| Meena | 6 |
| Suresh | 5 |
Bar graph: draw bars of heights 4, 7, 3, 6, 5 for each student.
Reading a Bar Graph
- Look at the height of each bar against the Y-axis scale.
- The tallest bar = highest value; the shortest bar = lowest value.
Choosing a Scale
- Scale should be chosen so that all values fit on the graph.
- If maximum value is 35, use scale of 5 (marks: 0, 5, 10, 15, 20, 25, 30, 35).
Choosing the Right Graph
| When to use | Best graph |
|---|---|
| Comparing categories | Bar graph |
| Showing data with symbols | Pictograph |
| Recording raw data quickly | Tally marks table |
Key Vocabulary
| Term | Meaning |
|---|---|
| Data | Collected information |
| Raw data | Unorganised data |
| Tally marks | Marks used to record count (groups of 5) |
| Frequency | How many times a value occurs |
| Frequency table | Table showing values and their frequencies |
| Pictograph | Graph using pictures/symbols |
| Bar graph | Graph using rectangular bars |
| Scale | Unit value in a pictograph or axis label interval |
| Key | Explanation of what each symbol represents in a pictograph |
Exam Tips
- Tally marks: 5th mark is a diagonal, making a group of 5. Always count in groups of 5 for speed.
- Bar graph drawing: use a ruler, equal widths, equal gaps, label both axes, write a title.
- Pictograph: if scale is 1 symbol = 4 items, and you need to show 6 items, draw 1½ symbols.
- Reading bar graphs: the answer is the height of the bar read against the Y-axis — do not approximate.
- Frequency total should equal the total number of data points — check this when verifying your table.
- 3-mark questions often ask to draw a bar graph — practice neat, accurate drawings.