| --- |
| source: ncert |
| topic: statistics |
| class_level: class_8 |
| chapter: ch5 |
| difficulty: beginner |
| --- |
| |
| Class 8 | Ch5: Data Handling |
| GROUPED DATA AND FREQUENCY: |
| Class interval: range of values grouped together. e.g., 0-10, 10-20, 20-30. |
| Class width = upper limit - lower limit. |
| Frequency: number of observations in each class. |
| Cumulative frequency: sum of all frequencies up to that class. |
| HISTOGRAM: bar graph for continuous data (no gaps between bars). |
| CIRCLE GRAPH (PIE CHART): |
| Central angle for each component = (component value/total) × 360°. |
| Example: Wheat 40% → angle = 0.40×360 = 144°. |
| PROBABILITY: |
| Experiment: activity with outcomes (throwing die, tossing coin). |
| Event: collection of one or more outcomes. |
| P(event) = number of favourable outcomes / total number of outcomes. |
| P(sure event)=1. P(impossible event)=0. 0≤P(E)≤1. |
| P(E)+P(not E)=1. So P(not E)=1-P(E). |
| SOLVED EXAMPLES: |
| Example 1: Die thrown. Find P(number>4). |
| Favourable: 5,6 → 2 outcomes. Total=6. P=2/6=1/3. |
| Example 2: Pie chart for budget. Food=40%, Rent=25%, Education=20%, Others=15%. |
| Angles: Food=144°, Rent=90°, Education=72°, Others=54°. Total=360°. |
| Example 3: P(drawing red card from deck)=26/52=1/2. |
| P(face card)=12/52=3/13. P(ace)=4/52=1/13. |
| COMMON MISTAKES: |
| In histogram, class intervals must be continuous (no gaps). |
| P(E)+P(not E)=1 always. P(E) cannot be greater than 1 or negative. |
