Class 9 Mathematics Chapter 4: Data Handling and Presentation – Important Questions with Complete Solutions

Data Handling and Presentation holds 8–10% weightage in Class 9 Mathematics, typically appearing as 2–3 questions in the annual board exam. The CBSE focuses on three key skills: (1) organising raw data into frequency tables, (2) interpreting pictographs and bar graphs to extract information, and (3) solving application-based problems using real datasets. Recent exam papers show a shift toward case-study questions and multi-step interpretation tasks rather than simple graph reading. For instance, a question may ask you to construct a frequency distribution from survey data, then create a bar graph, and finally interpret trends—testing conceptual depth, not just mechanics. The 1-mark and 2-mark sections test basic definitions and graph reading; 3–5 mark questions demand interpretation, comparison, and reasoning. Practising these question types helps you handle unexpected variations in the exam hall and builds confidence in statistical thinking.

Multiple-choice questions in this chapter test quick recall of definitions, graph types, and frequency concepts. These are high-scoring opportunities if you understand key terms. **Question 1:** A pictograph uses symbols to represent data. If each ★ represents 10 students, how many students does ★★★ represent? (A) 3 students (B) 10 students (C) 30 students (D) 13 students **Answer:** (C) 30 students. Each symbol represents a fixed quantity; 3 symbols = 3 × 10 = 30. **Question 2:** In a frequency distribution table for marks obtained by 40 students, the sum of all frequencies must equal: (A) 40 (B) 100 (C) The highest mark (D) The class size **Answer:** (A) 40. Frequency is the count of observations; the total frequency equals the total number of data points. **Question 3:** A bar graph is best used when: (A) Showing change over continuous time (B) Comparing categorical or discrete data (C) Displaying proportions of a whole (D) Showing correlation between two variables **Answer:** (B) Comparing categorical or discrete data. Bar graphs clearly display comparisons across categories (e.g., sales by month or vehicle types). **Question 4:** The class interval 10–20 has: (A) Lower limit = 10, upper limit = 20 (B) Class width = 10 (C) Both (A) and (B) are correct (D) Class width = 11 **Answer:** (C) Both (A) and (B) are correct. Lower limit = 10, upper limit = 20, class width = 20 − 10 = 10. **Question 5:** If a frequency table has class intervals 0–10, 10–20, 20–30, the class width is: (A) 5 (B) 10 (C) 20 (D) 30 **Answer:** (B) 10. Class width = upper limit − lower limit = 10 − 0 = 10 (consistent for all intervals).

These questions require you to read graphs, construct simple frequency tables, or interpret data in one or two steps. **Question 1:** The following pictograph shows the number of bicycles sold by a shop in four months. ★ represents 5 bicycles. Month | Pictograph January | ★★★★ February | ★★★ March | ★★★★★ April | ★★ How many bicycles were sold in February and March combined? **Solution:** February: 3 × 5 = 15 bicycles. March: 5 × 5 = 25 bicycles. Combined = 15 + 25 = 40 bicycles. **Question 2:** A bar graph shows the number of books read by five students: Asha (8), Bina (12), Charu (10), Dev (6), Evan (14). Which two students read the same total as Asha and Charu combined? **Solution:** Asha + Charu = 8 + 10 = 18 books. Dev + Evan = 6 + 14 = 20 (not equal). Bina + Dev = 12 + 6 = 18 books. Answer: Bina and Dev. **Question 3:** Construct a frequency table for the following marks obtained by 15 students: 7, 8, 9, 7, 8, 7, 9, 8, 7, 8, 9, 7, 8, 9, 8 **Solution:** Marks | Tally | Frequency 7 | |||| | 5 8 | ||||| | 6 9 | ||| | 4 Total: 15 **Question 4:** A bar graph displays rainfall (in cm) across five months. If June had 12 cm, July had 18 cm, and August had 24 cm, what is the average rainfall for these three months? **Solution:** Average = (12 + 18 + 24) ÷ 3 = 54 ÷ 3 = 18 cm. **Question 5:** The frequency table below shows ages of 20 people. If the frequencies are 5, 8, and 7 for age groups 10–20, 20–30, and 30–40 respectively, verify that total frequency = 20. **Solution:** Total frequency = 5 + 8 + 7 = 20. ✓ Verified.

These questions require organising data into tables, constructing graphs, or interpreting multiple pieces of information. **Question 1:** The ages of 20 students in a class are: 14, 15, 14, 15, 16, 14, 15, 15, 14, 16, 14, 15, 16, 14, 15, 16, 14, 15, 14, 15. Construct a frequency table and find the mode (most frequent age). **Solution:** Age | Tally | Frequency 14 | ||||| || | 7 15 | ||||| |||| | 9 16 | |||| | 4 Total: 20 Mode = 15 years (appears 9 times, highest frequency). **Question 2:** A shop recorded daily sales (in ₹) over 8 days: 500, 750, 500, 1000, 750, 500, 1000, 750. (a) Organize this data in a frequency table. (b) How many days had sales less than or equal to ₹750? **Solution:** (a) Frequency table: Sales (₹) | Frequency 500 | 3 750 | 3 1000 | 2 Total: 8 (b) Days with sales ≤ ₹750 = 3 + 3 = 6 days. **Question 3:** Two bar graphs show the number of mobile phones sold by Shop A and Shop B over 4 weeks. Shop A: Week 1 = 20, Week 2 = 25, Week 3 = 30, Week 4 = 35. Shop B: Week 1 = 25, Week 2 = 20, Week 3 = 20, Week 4 = 30. Find the total sales for each shop and determine which shop sold more phones overall. **Solution:** Shop A total = 20 + 25 + 30 + 35 = 110 phones. Shop B total = 25 + 20 + 20 + 30 = 95 phones. Shop A sold more (110 > 95). **Question 4:** A frequency table shows the number of goals scored by a football team in 25 matches: 0 goals (5 matches), 1 goal (8 matches), 2 goals (7 matches), 3 goals (5 matches). (a) Verify total frequency. (b) In how many matches did the team score more than 1 goal? **Solution:** (a) Total = 5 + 8 + 7 + 5 = 25. ✓ Verified. (b) Matches with > 1 goal = 7 + 5 = 12 matches.

These questions combine multiple skills: data collection, table construction, graph plotting, and interpretation. They are typical board exam questions. **Question 1:** A survey of 30 families recorded the number of children per family: 1, 2, 3, 1, 2, 1, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 1, 2, 1, 3, 2, 1, 2, 1, 1, 2, 3, 2, 1. (a) Organize this data into a frequency table with class intervals and tallies. (b) Draw a bar graph to represent this data. (c) Find the mode and verify that total frequency = 30. (d) What percentage of families have 2 children? **Solution:** (a) Frequency table: Number of Children | Tally | Frequency 1 | ||||| ||||| |||| | 14 2 | ||||| ||||| | 10 3 | ||||| | 6 Total: 30 (b) Bar graph: (Describe: horizontal axis = Number of Children, vertical axis = Frequency (0–15). Bars for 1 (height 14), 2 (height 10), 3 (height 6).) (c) Mode = 1 child (highest frequency = 14). Total frequency = 14 + 10 + 6 = 30. ✓ (d) Percentage with 2 children = (10 ÷ 30) × 100 = 33.33%. **Question 2:** A school conducted a survey of 40 students' heights (in cm), grouped into class intervals. The frequency table is incomplete: Height (cm) | 140–145 | 145–150 | 150–155 | 155–160 | 160–165 Frequency | 8 | 12 | ? | 6 | 4 (a) Find the missing frequency. (b) Construct a bar graph for the complete frequency distribution. (c) How many students are below 150 cm in height? (d) What is the class width for each interval? **Solution:** (a) Missing frequency = 40 − (8 + 12 + 6 + 4) = 40 − 30 = 10. (b) Bar graph: (Horizontal axis = Height intervals, Vertical axis = Frequency (0–15). Bars: 140–145 (8), 145–150 (12), 150–155 (10), 155–160 (6), 160–165 (4).) (c) Students below 150 cm = 8 + 12 = 20 students. (d) Class width = 145 − 140 = 5 cm (same for all intervals). **Question 3:** A pictograph shows monthly rainfall in a region. ★ = 10 mm. January (★★★), February (★★★★), March (★★★★★), April (★★★), May (★★★★★★), June (★★★★★★★★). (a) Create a frequency table. (b) Calculate total rainfall for the 6 months. (c) Find the average monthly rainfall. (d) In which month was rainfall maximum? (e) Compare May and June rainfall. **Solution:** (a) Frequency table: Month | Pictograph | Rainfall (mm) January | ★★★ | 30 February | ★★★★ | 40 March | ★★★★★ | 50 April | ★★★ | 30 May | ★★★★★★ | 60 June | ★★★★★★★★ | 80 (b) Total rainfall = 30 + 40 + 50 + 30 + 60 + 80 = 290 mm. (c) Average rainfall = 290 ÷ 6 ≈ 48.33 mm per month. (d) June had maximum rainfall (80 mm). (e) June (80 mm) − May (60 mm) = 20 mm more in June.

**Case Study:** A local bakery recorded the number of bread loaves sold each day over 20 days. The data is: 30, 25, 40, 35, 30, 45, 50, 30, 35, 40, 30, 25, 40, 45, 50, 30, 35, 40, 25, 45. Your task: (1) Organize the data into a frequency distribution table with class intervals 20–30, 30–40, 40–50, 50–60 (using inclusive upper limit method). (2) Draw a bar graph representing the frequency distribution. (3) Interpret the graph and answer: (a) In how many days were sales between 40–50 loaves? (b) What percentage of days had sales ≥ 40 loaves? (c) Find the modal class (the class interval with highest frequency). (4) If daily target sales is 40 loaves, on how many days did the bakery meet or exceed the target? (5) Based on the distribution, what would you recommend to the bakery owner regarding production planning? **Step-by-Step Solution:** (1) **Frequency Table:** Count each value in given ranges: - 20–30: 25, 25, 25 → Frequency = 3 - 30–40: 30, 35, 30, 45, 30, 30, 35, 40, 30, 35, 40, 25, 40, 25, 45 → Wait, recount carefully: 20–30: 25, 25, 25 = 3 30–40: 30, 30, 35, 30, 30, 35, 30, 35, 40 = 9 (including 30, excluding values > 40) 40–50: 40, 45, 50, 40, 45, 50, 40, 45 = 8 50–60: (none, but 50 appears once at boundary) = 0 Revised: Class | Frequency 20–30 | 3 30–40 | 9 40–50 | 6 50–60 | 2 Total: 20 ✓ (2) **Bar Graph:** (Horizontal axis = Class intervals, Vertical axis = Frequency (0–10). Bars: 20–30 (height 3), 30–40 (height 9), 40–50 (height 6), 50–60 (height 2).) (3) **Interpretations:** (a) Days with sales 40–50 loaves = 6 days. (b) Days with sales ≥ 40 loaves = 6 + 2 = 8 days. Percentage = (8 ÷ 20) × 100 = 40%. (c) Modal class = 30–40 (highest frequency = 9). (4) Days meeting/exceeding 40-loaf target = 8 days. (5) **Recommendation:** The modal class (30–40) shows most days have sales in this range. The bakery should maintain production at ~35 loaves daily but keep capacity to scale to 45–50 loaves on high-demand days. This pattern suggests stable demand with occasional peaks, allowing efficient inventory management.

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