Class 9 Mathematics Chapter 14: Data Handling and Probability MCQ with Answers

The rationalized CBSE Class 9 syllabus emphasizes conceptual understanding over rote learning, and MCQs are the ideal vehicle for this shift. Unlike long-answer questions, MCQs force you to make quick, decisive judgments—a critical skill in board exams and competitive entrance tests. In Chapter 14 specifically, MCQs test whether you can distinguish between mean, median, and mode; interpret pie chart sectors correctly; and apply probability rules to real scenarios. The new pattern also includes assertion–reason MCQs, where you must evaluate the truth of both a statement and its justification. This format rewards deep understanding: you can't guess your way through when asked 'Both A and R are correct, but R is not the reason for A.' CBSE data shows that students who practice 25–30 quality MCQs before exams score 15–20% higher on multiple-choice sections. By solving these questions systematically, you'll internalize shortcuts (e.g., median is the middle value when data is ordered), recognize common trap options, and manage exam time efficiently.

These questions test core definitions and straightforward calculations—the baseline for any student aiming for 60+ marks. **Q1.** The mean of the data set {4, 8, 6, 10, 2} is: (A) 6 (B) 8 (C) 5 (D) 7 **Correct Answer:** (A) 6 **Reason:** Mean = (4 + 8 + 6 + 10 + 2) ÷ 5 = 30 ÷ 5 = 6. **Q2.** The median of {3, 1, 9, 5, 7} when arranged in order is: (A) 5 (B) 7 (C) 3 (D) 9 **Correct Answer:** (A) 5 **Reason:** Ordered data: {1, 3, 5, 7, 9}; median is the middle (3rd) value. **Q3.** The mode of {2, 3, 3, 5, 3, 7} is: (A) 2 (B) 3 (C) 5 (D) 7 **Correct Answer:** (B) 3 **Reason:** Mode is the most frequently occurring value; 3 appears three times. **Q4.** A pie chart represents a full circle as 360°. If 25% of data is shown, the sector angle is: (A) 60° (B) 90° (C) 120° (D) 45° **Correct Answer:** (B) 90° **Reason:** 25% of 360° = 0.25 × 360° = 90°. **Q5.** The probability of an impossible event is: (A) 1 (B) 0 (C) 0.5 (D) undefined **Correct Answer:** (B) 0 **Reason:** Impossible events have zero likelihood of occurrence. **Q6.** When a fair die is thrown, the sample space contains: (A) 3 outcomes (B) 6 outcomes (C) 12 outcomes (D) 8 outcomes **Correct Answer:** (B) 6 outcomes **Reason:** A die has 6 faces: {1, 2, 3, 4, 5, 6}. **Q7.** If a coin is flipped twice, how many outcomes are in the sample space? (A) 2 (B) 3 (C) 4 (D) 8 **Correct Answer:** (C) 4 **Reason:** Outcomes: {HH, HT, TH, TT}; total = 2 × 2 = 4. **Q8.** The range of a data set {5, 12, 3, 18, 7} is: (A) 12 (B) 15 (C) 18 (D) 5 **Correct Answer:** (B) 15 **Reason:** Range = Max – Min = 18 – 3 = 15. **Q9.** A bar graph is best used to compare: (A) Continuous data (B) Discrete categories (C) Angles (D) Percentages only **Correct Answer:** (B) Discrete categories **Reason:** Bar graphs display frequency of distinct categories clearly. **Q10.** The probability of a certain event is: (A) 0 (B) less than 0.5 (C) 1 (D) greater than 1 **Correct Answer:** (C) 1 **Reason:** Certain events occur with 100% probability (P = 1).

These questions require multi-step thinking, data interpretation, and application of formulas in varied contexts. **Q11.** The mean age of 5 students is 12 years. If a new student aged 10 years joins, the new mean is: (A) 11.67 years (B) 11.5 years (C) 12 years (D) 10.5 years **Correct Answer:** (A) 11.67 years **Reason:** New mean = (5 × 12 + 10) ÷ 6 = 70 ÷ 6 ≈ 11.67 years. **Q12.** A data set has 7 observations: {4, 8, x, 12, 6, 10, 5}. If the median is 8, then x must be: (A) 8 (B) 7 (C) 9 (D) Any value ≥ 8 **Correct Answer:** (A) 8 **Reason:** Ordered set with x = 8 gives {4, 5, 6, 8, 8, 10, 12}; 4th value (middle) = 8. **Q13.** In a pie chart, one sector has a central angle of 72°. This sector represents: (A) 15% (B) 20% (C) 25% (D) 30% **Correct Answer:** (B) 20% **Reason:** 72° ÷ 360° = 0.2 = 20%. **Q14.** A class of 40 students is surveyed: 12 prefer Science, 16 prefer Math, 12 prefer English. The probability a randomly selected student prefers Math is: (A) 0.3 (B) 0.4 (C) 0.5 (D) 0.6 **Correct Answer:** (B) 0.4 **Reason:** P(Math) = 16 ÷ 40 = 0.4. **Q15.** Two dice are thrown simultaneously. The number of outcomes where the sum is 7 is: (A) 4 (B) 5 (C) 6 (D) 7 **Correct Answer:** (C) 6 **Reason:** Pairs: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes. **Q16.** The mean of four numbers is 20. If three numbers are 18, 22, and 20, the fourth number is: (A) 20 (B) 18 (C) 19 (D) 21 **Correct Answer:** (A) 20 **Reason:** Sum = 4 × 20 = 80; fourth = 80 – (18 + 22 + 20) = 20. **Q17.** In a bar graph showing monthly rainfall, the bar for June reaches 150 mm. If the scale is 1 cm = 50 mm, the bar height should be: (A) 1.5 cm (B) 2 cm (C) 3 cm (D) 4 cm **Correct Answer:** (C) 3 cm **Reason:** 150 ÷ 50 = 3 cm on the graph. **Q18.** A bag contains 5 red balls and 3 blue balls. The probability of drawing a red ball is: (A) 5/8 (B) 3/8 (C) 5/3 (D) 3/5 **Correct Answer:** (A) 5/8 **Reason:** P(red) = 5 ÷ (5 + 3) = 5/8. **Q19.** The data set {10, 20, 30, 40, 50} has no mode because: (A) All numbers are equal (B) All numbers appear once (C) It has five values (D) It is in order **Correct Answer:** (B) All numbers appear once **Reason:** Mode requires a value to repeat; each value here has frequency 1. **Q20.** If P(A) = 0.25, then P(not A) equals: (A) 0.25 (B) 0.5 (C) 0.75 (D) 0.25 × 2 **Correct Answer:** (C) 0.75 **Reason:** P(not A) = 1 – P(A) = 1 – 0.25 = 0.75.

These challenge your conceptual depth and require evaluation of logical relationships—typical of CBSE's harder tiers and competitive exams. **Q21.** **Assertion (A):** The median is always a value present in the original data set. **Reason (R):** The median is the middle value when data is arranged in order. (A) Both A and R are correct; R explains A (B) Both A and R are correct; R does not explain A (C) A is correct, R is incorrect (D) A is incorrect, R is correct **Correct Answer:** (D) A is incorrect, R is correct **Reason:** With even-length data (e.g., {1, 2, 3, 4}), median is 2.5, not in the set; R is the definition but doesn't guarantee A. **Q22.** A pie chart shows 5 categories. If one category occupies 144°, another 108°, and a third 72°, the remaining two categories together occupy: (A) 36° (B) 54° (C) 72° (D) 90° **Correct Answer:** (A) 36° **Reason:** 360° – (144° + 108° + 72°) = 360° – 324° = 36°. **Q23.** **Assertion (A):** Mean is always affected by extreme values (outliers). **Reason (R):** Median and mode are robust measures less affected by outliers. (A) Both A and R are correct; R explains A (B) Both A and R are correct; R does not explain A (C) A is correct, R is incorrect (D) A is incorrect, R is correct **Correct Answer:** (A) Both A and R are correct; R explains A **Reason:** Outliers shift the sum, thus the mean; median/mode depend on position/frequency, not magnitude. **Q24.** A spinner divided into 8 equal sectors is spun. If 3 sectors are red, 2 are blue, and 3 are green, the probability of landing on a non-green sector is: (A) 3/8 (B) 5/8 (C) 2/8 (D) 1/8 **Correct Answer:** (B) 5/8 **Reason:** Non-green = red + blue = 3 + 2 = 5; P = 5/8. **Q25.** The mean of 10 numbers is 50. If each number is increased by 5, the new mean becomes: (A) 50 (B) 55 (C) 45 (D) 500 **Correct Answer:** (B) 55 **Reason:** Adding a constant to all values increases the mean by that constant: 50 + 5 = 55. **Q26.** **Assertion (A):** In a bar graph, the height of each bar is proportional to the frequency it represents. **Reason (R):** Bar graphs use scale to convert absolute frequencies into visual heights. (A) Both A and R are correct; R explains A (B) Both A and R are correct; R does not explain A (C) A is correct, R is incorrect (D) R is correct, A is incorrect **Correct Answer:** (A) Both A and R are correct; R explains A **Reason:** The definition of a bar graph relies on scale to make frequency visually comparable. **Q27.** Two events A and B are mutually exclusive. If P(A) = 0.3 and P(B) = 0.4, then P(A or B) is: (A) 0.7 (B) 0.12 (C) 0.1 (D) 0.6 **Correct Answer:** (A) 0.7 **Reason:** P(A or B) = P(A) + P(B) for mutually exclusive events = 0.3 + 0.4 = 0.7. **Q28.** A data set has an odd number of observations. Which measure can never be calculated? (A) Mean (B) Median (C) Mode (D) None; all can always be calculated **Correct Answer:** (D) None; all can always be calculated **Reason:** Mean sums all values; median is the middle value (always exists for odd count); mode may not exist but can be stated as 'no mode.' **Q29.** **Assertion (A):** The probability of at least one head in two coin flips is 3/4. **Reason (R):** Sample space = {HH, HT, TH, TT}; favorable outcomes = 3. (A) Both A and R are correct; R explains A (B) Both A and R are correct; R does not explain A (C) A is correct, R is incorrect (D) A is incorrect, R is correct **Correct Answer:** (A) Both A and R are correct; R explains A **Reason:** Only TT has no heads; 3 outcomes have at least one head, so P = 3/4. **Q30.** A school recorded students' heights (in cm). The data is most appropriately displayed using: (A) Pie chart (B) Histogram (C) Line graph (D) Pictograph **Correct Answer:** (B) Histogram **Reason:** Histograms show frequency distribution of continuous data (height); pie charts suit categorical proportions; line graphs track trends over time.

CBSE MCQs are carefully designed; wrong answers often test misconceptions. Here are 5 deadly traps seen repeatedly in Chapter 14 questions: **Trap 1: Confusing Mean with Median** Example: Data = {1, 2, 3, 100}. Mean = 26.5, Median = 2.5. Students often pick 'Median = 26.5' if they miscalculate. *Guard:* Always arrange data and count to find the middle value(s). **Trap 2: Forgetting to Simplify Probability Fractions** Example: P(event) = 8/12. Correct answer is 2/3, but 8/12 appears as an option. *Guard:* Always reduce fractions to lowest terms; compare your simplified answer to all four options. **Trap 3: Sector Angle = Percentage Directly** Example: A sector is 90°. Students say 90% (wrong) instead of 25%. *Guard:* Always divide sector angle by 360° first, then multiply by 100 to get percentage. **Trap 4: Mode = Most Values Instead of Most Frequent** Example: Data = {5, 5, 5, 10, 15}. Mode is 5, not 15 (largest). *Guard:* Count frequency; the value appearing most often is the mode. **Trap 5: Misreading 'At Least' vs. 'Exactly' in Probability** Example: 'Probability of at least one head in two flips' = 3/4 (HH, HT, TH), not 1/2 (just HT). *Guard:* Write out the sample space explicitly; 'at least one' includes multiple favorable cases.

Chapter 14 MCQs typically appear in a 30–40 minute window during CBSE exams. Strategic time allocation is crucial: **Phase 1: Quick Wins (8–10 minutes)** Start with **Easy MCQs (Q1–Q10)**. These carry marks with minimal risk. Allocate 45–60 seconds per question. If you're stuck, skip and return; easy questions rarely have ambiguity. **Phase 2: Moderate Depth (12–15 minutes)** Move to **Medium MCQs (Q11–Q20)**. These need one or two calculation steps. Spend 60–90 seconds each. For 'find x' questions, substitute your answer back to verify. For probability/graph questions, write quick notes (e.g., 'P(X) = favorable ÷ total'). **Phase 3: Conceptual Rigor (10–12 minutes)** Attempt **Hard & Assertion–Reason MCQs (Q21–Q30)**. These are worth the same points but take longer. On assertion–reason: first verify A, then R, then the logical link. If unsure about the link, re-read the reason carefully—it must logically support A, not just be true. **Phase 4: Review & Verification (3–5 minutes)** Use remaining time to verify answers to Medium/Hard questions, especially where you guessed. Check calculation errors (e.g., in mean = sum ÷ count, confirm your division). Flip back to Medium if you spotted an error. **Pro Tips:** - **Flag, Don't Stall:** If a question takes >2 minutes, flag it mentally and move on. You'll often see clues in later questions. - **Use Margins:** For pie chart and probability questions, sketch the scenario in your exam margin—it prevents careless errors. - **Sanity Check:** If your probability answer > 1 or < 0, or if a percentage > 100%, you've made an error; recalculate immediately. - **Assertion–Reason Shortcut:** If both A and R are obviously false, pick (C) or (D) and move on; don't waste time on false premises. Practice these 30 MCQs in timed sessions (30 minutes for all 30). Track which topics (mean, median, mode, probability, graphs) slow you down, then revisit those concepts on cbsetutor.ai, where video lessons break down Chapter 14 step-by-step. Start a 3-day free trial at cbsetutor.ai to access interactive problem-solving and live doubt sessions with expert tutors.