How Quantities Combine: Understanding Data — Class 9 MCQs with Answers
Class 9 CBSE Mathematics · Chapter 10
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 9 CBSE Mathematics questions from Chapter 10, "How Quantities Combine: Understanding Data". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that top scorers in CBSE Board exams and the JEE & NEET foundation years get right.
To score well in "How Quantities Combine: Understanding Data", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This helps you stay accurate when time is short, just as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on How Quantities Combine: Understanding Data, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 9 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
How Quantities Combine: Understanding Data — important questions & MCQs with answers (Class 9 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation.
- Q1Easy
Class 9A has 20 students with an average score of 60. Class 9B has 30 students with an average score of 70. What is the average score of all 50 students?
A.65B.66✓ CorrectC.64D.68Answer: B. 66
Explanation: Total marks = 20 × 60 + 30 × 70 = 1200 + 2100 = 3300, and 3300 ÷ 50 = 66. Taking (60 + 70)/2 = 65 ignores that 9B has more students.
- Q2Easy
Two glasses hold equal amounts of lemonade. One has 10% jaggery and the other has 30% jaggery. Both are mixed together. What is the concentration of jaggery in the mixture?
A.40%B.20%✓ CorrectC.15%D.30%Answer: B. 20%
Explanation: With y in each glass, jaggery = 0.1y + 0.3y = 0.4y in 2y of lemonade, so 0.4y ÷ 2y = 20%. Equal amounts put the result exactly midway; adding the percentages to get 40% is wrong.
- Q3Easy
Arjun scored 80% in internal tests and 60% in the final exam. The annual score combines internals and final in the ratio 1 : 3. What is his annual score?
A.70%B.75%C.65%✓ CorrectD.52%Answer: C. 65%
Explanation: Annual score = (80 × 1 + 60 × 3) ÷ (1 + 3) = 260 ÷ 4 = 65%. 70% is the plain average, and 75% puts the weight 3 on the wrong mark.
- Q4Easy
In a T20 match, a team scored 6 runs in the first over and 12 runs in the second over. What is the run rate after 2 overs?
A.18B.12C.9✓ CorrectD.6Answer: C. 9
Explanation: Run rate = total runs ÷ overs = (6 + 12) ÷ 2 = 9 runs per over. 18 is the total runs, not the average per over.
- Q5Easy
When is a stacked bar chart a better choice than a cluster-column chart?
A.When we only want to compare one category across groupsB.When the data has just one valueC.When we want to compare the totals and still see the parts that make them up✓ CorrectD.When the values are negativeAnswer: C. When we want to compare the totals and still see the parts that make them up
Explanation: In a stacked bar, the full bar shows the total and the small bars show the parts. A cluster chart is better for comparing one category across groups.
- Q6Easy
What does a 100% stacked bar chart compare?
A.Actual amounts, not sharesB.Proportions or shares, not actual amounts✓ CorrectC.Only the totals of each groupD.Changes over time onlyAnswer: B. Proportions or shares, not actual amounts
Explanation: Every bar has the same length, standing for 100% of that group, so the parts show shares. Like a pie chart, it hides the actual amounts.
- Q7Medium
Section A has 30 students with an average of 68 marks. Section B has 20 students with an average of 78 marks. What is the combined average of both sections?
A.73B.74C.70D.72✓ CorrectAnswer: D. 72
Explanation: (30 × 68 + 20 × 78) ÷ 50 = (2040 + 1560) ÷ 50 = 3600 ÷ 50 = 72. 73 is the simple average of 68 and 78, and 74 swaps the class sizes.
- Q8Medium
300 mL of water with 4% salt is mixed with 100 mL of water with 12% salt. What is the salt concentration of the mixture?
A.8%B.6%✓ CorrectC.10%D.16%Answer: B. 6%
Explanation: Salt = 300 × 0.04 + 100 × 0.12 = 12 + 12 = 24 mL in 400 mL, so 24 ÷ 400 = 6%. 8% is the simple average, and 10% puts the larger amount with the 12% water.
- Q9Medium
Meena scored 40 out of 50 in internals, 45 out of 60 in the project and 72 out of 80 in the final exam. These are combined in the ratio 2 : 3 : 5. What is her annual percentage?
A.57.5%B.83.5%✓ CorrectC.81.67%D.82.63%Answer: B. 83.5%
Explanation: Change each to a percentage first: 80%, 75%, 90%. Then (80 × 2 + 75 × 3 + 90 × 5) ÷ 10 = 835 ÷ 10 = 83.5%. 57.5% uses raw marks out of different totals, and 81.67% ignores the weights.
- Q10Medium
A bird flew an average of 40 km a day over 30 days. On the 31st day it flew 71 km. What is its average daily distance over the 31 days?
A.55.5 kmB.42.37 kmC.40.5 kmD.41 km✓ CorrectAnswer: D. 41 km
Explanation: Total = 30 × 40 + 71 = 1271 km, and 1271 ÷ 31 = 41 km. 55.5 is the simple average of 40 and 71, and 42.37 divides by 30 instead of 31.
- Q11Medium
A family's stacked bar shows, in order, Housing ₹1200, Food ₹1500, Education ₹900 and Transport ₹400. Where does the Education part start and end on the scale?
A.Starts at ₹2700, ends at ₹3600✓ CorrectB.Starts at ₹0, ends at ₹900C.Starts at ₹1500, ends at ₹2400D.Starts at ₹2700, ends at ₹4000Answer: A. Starts at ₹2700, ends at ₹3600
Explanation: Education starts after Housing and Food: 1200 + 1500 = 2700, and ends at 2700 + 900 = 3600. Starting at 0 is true only for the first part.
- Q12Hard
A facility has 40 langurs. Males average 18 kg and females average 12 kg. The average weight of all 40 is 14.4 kg. How many males are there?
A.24B.20C.16✓ CorrectD.18Answer: C. 16
Explanation: Let x be the males: 18x + 12(40 − x) = 14.4 × 40 = 576, so 480 + 6x = 576 and x = 16. 24 is the number of females, which the overall average (nearer 12) shows is the larger group.
- Q13Hard
Brass Batch A weighs 100 kg and is 80% copper. Batch B weighs 200 kg and is 50% copper. Batch C is 40% copper. All three together are 52% copper. What does Batch C weigh?
A.100 kgB.200 kg✓ CorrectC.300 kgD.150 kgAnswer: B. 200 kg
Explanation: Copper: 80 + 100 + 0.4y = 0.52(300 + y), so 180 + 0.4y = 156 + 0.52y, giving 0.12y = 24 and y = 200 kg. Check: 260 ÷ 500 = 52%.
- Q14Hard
Ten customers rated a restaurant. Food: four 5s, four 4s, two 3s. Ambience: one 5, three 4s, four 3s, two 2s. Service: two 5s, two 4s, three 3s, two 2s, one 1. Weights food : ambience : service = 5 : 3 : 2. What is the overall rating?
A.3.57B.3.43C.4.2D.3.73✓ CorrectAnswer: D. 3.73
Explanation: Averages: food 4.2, ambience 3.3, service 3.2. Then (5 × 4.2 + 3 × 3.3 + 2 × 3.2) ÷ 10 = 37.3 ÷ 10 = 3.73. 3.57 ignores the weights, and 3.43 puts weight 5 on service.
Key concepts: How Quantities Combine: Understanding Data (Class 9 Mathematics)
When groups of data are joined, each part must count by how big or how important it is. This chapter builds the weighted mean from averages of averages, mixtures and custom weights for marks and ratings, then shows how stacked and 100% stacked bar charts display totals and shares.
- Average of averages
- To combine groups, add each group's sum (average × count) and divide by the total count. Simply averaging the group averages is wrong when the groups have different sizes.
- Sum from an average
- If n values have average a, their sum is an. This one step turns any group average back into a total that can be combined with others.
- Equal-sized collections
- When every collection has the same size p, (ap + bp + cp)/3p = (a + b + c)/3, so adding the averages and dividing by the number of collections works.
- Concentration of a mixture
- Concentration = quantity of the substance ÷ quantity of the mixture. Equal amounts mixed give a result midway; unequal amounts pull it towards the larger part.
- Weighted mean (weighted average)
- Each value is multiplied by its weight, the products are added and the total is divided by the sum of the weights. The weights can be counts, volumes, real weights or importance.
- Brahmagupta and Śrīdharācārya
- Brahmagupta wrote the weighted mean formula in the Brāhmasphuṭasiddhānta (c. 628 CE) for the mean depth of a pit. Śrīdharācārya (c. 750 CE) used it for the purity of gold in varṇa, where k varṇa means k/16 gold.
- Where a weighted mean lies
- A weighted mean always lies between the smallest and largest values, nearer the value with more weight. So mixing can never give a concentration outside the range of the parts.
- Custom weights
- Marks or ratings are combined in a given ratio such as 3 : 2 : 5 to show relative importance. Weights 3, 2, 5 act as if the values were repeated 3, 2 and 5 times.
- Changing the weights
- Multiplying all weights by the same number (for example doubling) leaves the weighted mean unchanged. Adding the same number to all weights changes the ratio, pulling the mean towards the simple average.
- Updating an average
- To add or remove values, rebuild the total (average × count), add or subtract the values, and divide by the new count. Run rate, share prices and daily distances all work this way.
- Cluster-column chart
- Bars stand side by side from 0, so single categories are easy to compare. The choice of cluster (by category or by group) depends on which comparison matters.
- Stacked bar chart
- Small bars are joined end to end, so the full bar shows the total and its parts. Only the first part starts at 0, so comparing other parts across bars is harder.
- 100% stacked bar chart
- Every bar has the same length (100%) split in proportion to the parts, like a pie chart splitting 360°. It compares shares within each bar, not actual amounts.
- What a 100% chart cannot tell
- Comparing a share across bars says nothing about actual numbers, because the totals are unknown. A stacked chart can be turned into a 100% chart, but not the other way round.
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Start this chapter free →How Quantities Combine: Understanding Data — FAQs
What are the key concepts in Class 9 Mathematics How Quantities Combine: Understanding Data?+
When groups of data are joined, each part must count by how big or how important it is. This chapter builds the weighted mean from averages of averages, mixtures and custom weights for marks and ratings, then shows how stacked and 100% stacked bar charts display totals and shares. Key ideas include Average of averages, Sum from an average, Equal-sized collections, Concentration of a mixture, Weighted mean (weighted average), Brahmagupta and Śrīdharācārya.
What does Class 9 Mathematics Chapter 10 (How Quantities Combine: Understanding Data) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "How Quantities Combine: Understanding Data": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.
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Yes. Sign in with Google to practise "How Quantities Combine: Understanding Data" free. Full unlimited access is ₹999/year. One year from the day you pay. You stay in Class 9 till 31 March; on 1 April your account moves up to Class 10 and the rest of your year carries over. No chapter is charged separately.
How should I revise "How Quantities Combine: Understanding Data" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "How Quantities Combine: Understanding Data" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "How Quantities Combine: Understanding Data" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from How Quantities Combine: Understanding Data (Class 9 Mathematics)?+
The questions that matter most test Average of averages, Sum from an average, Equal-sized collections, Concentration of a mixture, Weighted mean (weighted average), Brahmagupta and Śrīdharācārya. This page shows 14 solved important MCQs with answers and explanations. Sign in to practise all 90 questions on the chapter as timed quizzes.
Is there an online quiz for How Quantities Combine: Understanding Data?+
Yes — Class 9 Mathematics How Quantities Combine: Understanding Data has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.