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| source: ncert_exercises |
| topic: statistics |
| class_level: class_9 |
| chapter: ch12 |
| exercise: ex12.4 |
| difficulty: intermediate |
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| Class 9 | Ch12: Statistics | Exercise 12.4 |
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| Key: Grouped data, frequency polygons from histograms. |
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| Q1. The following table gives the distribution of students in two sections according to marks. Represent as frequency polygon. |
| Answer: Find midpoints of class intervals. Plot (midpoint, frequency) for each section. Join points. Both polygons on same graph for comparison. ✅ |
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| Q2. Frequency distribution of daily income of 100 workers of a factory. |
| Daily income (₹): 100-120, 120-140, 140-160, 160-180, 180-200. |
| Workers: 12, 14, 8, 6, 10. |
| Draw frequency polygon. |
| Answer: Midpoints: 110, 130, 150, 170, 190. Plot (midpoint, frequency) and join. Extend to x-axis at both ends (midpoints of imaginary classes before 100-120 and after 180-200). ✅ |
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| Q3. Draw a histogram and then a frequency polygon for marks obtained by students. |
| Marks: 0-10, 10-20, 20-30, 30-40, 40-50. |
| Students: 5, 3, 4, 3, 1. |
| Answer: Step 1: Draw histogram (bars for each class). Step 2: Mark midpoints of tops of bars. Step 3: Join midpoints to get frequency polygon. Extend to x-axis. ✅ |
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| Summary of key formulas for Statistics Chapter: |
| Mean = Σx/n (ungrouped) or Σ(fi×xi)/Σfi (grouped with midpoints). |
| Median: middle value(s) of ordered data. |
| Mode: most frequent value. |
| For grouped data: modal class = class with highest frequency. ✅ |
