Data Handling
1. What Is Data?
DATA is a collection of FACTS and FIGURES (observations, measurements) used for analysis.
Types of Data
| Type | Description | Example |
|---|---|---|
| Primary data | Collected directly by the investigator | Survey of classmates |
| Secondary data | Obtained from published sources | Census data |
| Raw data | Unprocessed, in original form | 45, 67, 23, 89, 45, 67, 45 |
| Grouped data | Organised into classes/intervals | 20-30: 5 students, 30-40: 8 students |
2. Organisation of Data
Frequency Distribution Table
A table that shows how often each value occurs.
Example: Marks of 20 students: 5, 6, 4, 5, 7, 5, 6, 8, 4, 7, 6, 5, 7, 6, 5, 4, 8, 5, 6, 7
| Marks | Tally Marks | Frequency |
|---|---|---|
| 4 | ||
| 5 | ||
| 6 | ||
| 7 | ||
| 8 | ||
| Total | 20 |
Grouped Frequency Distribution
When data has many distinct values, group into CLASS INTERVALS.
| Class Interval | Tally Marks | Frequency |
|---|---|---|
| 0-10 | ||
| 10-20 | ||
| 20-30 |
3. Measures of Central Tendency
Arithmetic Mean (Average)
Mean = (Sum of all observations) / (Number of observations)
Example: Find mean of 4, 8, 6, 5, 7. Sum = 4 + 8 + 6 + 5 + 7 = 30. Number = 5. Mean = 30/5 = 6.
Median
The MIDDLE value when data is arranged in ascending (or descending) order.
Steps:
- Arrange data in ASCENDING order.
- If number of values (n) is ODD: median = value at (n+1)/2 position.
- If n is EVEN: median = average of values at n/2 and (n/2 + 1) positions.
Example 1 (Odd n): 3, 7, 2, 9, 5. Ascending: 2, 3, 5, 7, 9. n = 5. Median = 3rd value = 5.
Example 2 (Even n): 4, 8, 2, 6, 10, 12. Ascending: 2, 4, 6, 8, 10, 12. n = 6. Median = (6 + 8)/2 = 7.
Mode
The value that occurs MOST FREQUENTLY.
Example: 3, 5, 7, 5, 9, 5, 2. Mode = 5 (occurs 3 times).
When to Use Each
| Measure | Best Used When |
|---|---|
| Mean | Data is evenly distributed, no outliers |
| Median | Data has extreme values (outliers) |
| Mode | Data has frequently occurring values (e.g., shoe sizes) |
4. Bar Graphs
A BAR GRAPH represents data using RECTANGULAR bars of equal width.
Rules for Drawing Bar Graphs
- Choose a SUITABLE scale (e.g., 1 cm = 10 units).
- Draw X-axis (categories) and Y-axis (frequency).
- Bars should have EQUAL width and EQUAL spacing.
- Height of bar = frequency.
- Label axes. Give a TITLE.
Double Bar Graph
Used to compare TWO sets of data side by side.
- Two bars for each category (different colours/shading).
- Include a LEGEND.
5. Pie Charts
A PIE CHART is a circular graph divided into SECTORS proportional to the data.
How to Draw a Pie Chart
- Find TOTAL of all values.
- Find the ANGLE for each category: (Value/Total) × 360°.
- Draw circles and divide into sectors using a protractor.
- Label each sector.
Worked Example (ICSE 2024, 3 marks)
'Draw a pie chart for the data: Science 40, Maths 60, English 50, Hindi 30.'
Solution: Total = 40 + 60 + 50 + 30 = 180. Science: (40/180) × 360 = 80° Maths: (60/180) × 360 = 120° English: (50/180) × 360 = 100° Hindi: (30/180) × 360 = 60°
6. Chance and Probability (Basic)
Probability = (Number of favourable outcomes) / (Total number of possible outcomes)
Value ranges from 0 (impossible) to 1 (certain).
7. ICSE Exam Focus
| Topic | Marks | Frequency |
|---|---|---|
| Mean, median, mode (calculation) | 3 marks | Very High |
| Frequency distribution table | 2-3 marks | High |
| Bar graph (draw and interpret) | 3 marks | Very High |
| Pie chart (draw and interpret) | 3-4 marks | High |
Common Mistakes
- Forgetting to arrange data in ORDER before finding median.
- Mean: dividing by wrong number (COUNT all values carefully).
- Bar graph: bars must have EQUAL width.
- Pie chart: angles must sum to 360°.
Self-Test (5 Questions)
Q1. Find the mean of: 12, 15, 18, 20, 25. (2 marks)
- A) 18
- B) 18.5
- C) 90
- D) 15
Q2. Find the median of: 45, 32, 67, 23, 89, 54, 76. (2 marks)
Q3. Find the mode of: 2, 3, 5, 3, 7, 3, 9, 5, 3. (1 mark)
Q4. 'Draw a bar graph for: A = 25, B = 40, C = 35, D = 20.' (3 marks)
Q5. 'In a pie chart, if one sector is 90°, what percentage of the total does it represent?' (2 marks)
Answers
A1. A) 18. (Sum = 90. n = 5. Mean = 90/5 = 18.) A2. 54. (Ascending: 23, 32, 45, 54, 67, 76, 89. n = 7. Median = 4th value = 54.) A3. 3 (occurs 4 times). A4. Draw bar graph with X-axis (categories A, B, C, D), Y-axis (frequency 0 to 45), scale 1 cm = 5 units. A5. 25%. (90/360 × 100% = 25%.)
