source: ncert_exercises
topic: statistics
class_level: class_9
chapter: ch12
exercise: ex12.4
difficulty: intermediate
Class 9 | Ch12: Statistics | Exercise 12.4
Key: Grouped data, frequency polygons from histograms.
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. ✅
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). ✅
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. ✅
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. ✅