Worksheets › Class 9 › How Quantities Combine: Understanding Data
Class 9 How Quantities Combine: Understanding Data worksheet
CBSE Mathematics. Weighted averages, mixtures, mark schemes, stacked and 100% stacked bar charts. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
The combined average of two groups of different sizes is:
- closer to the average of the smaller group
- the larger of the two averages
- always the simple average of the two
- closer to the average of the larger group
Answer
(d) closer to the average of the larger group
each value counts once, so the bigger group pulls harder
- 2.
Class A has 12 students with average 24 marks; class B has 25 with average 98. The combined average is:
- 74
- 61
- 75
- 73
Answer
(a) 74
(12 × 24 + 25 × 98) ÷ 37 = 2738 ÷ 37
- 3.
2 kg of rice at Rs 134 per kg is mixed with 1 kg at Rs 137 per kg. The mixture costs per kg:
- Rs 133
- Rs 135.5
- Rs 137
- Rs 135
Answer
(d) Rs 135
(2 × 134 + 1 × 137) ÷ 3 = 405 ÷ 3
Section B · short answer
- 4.
Science counts theory as 60% and practical as 40%. A student scores 70 in theory and 72 in practical (both out of 100). Find the final percentage.
Answer
70.8%
60% of 70 + 40% of 72 = 42 + 28.8
- 5.
In what ratio must rice at Rs 35 per kg be mixed with rice at Rs 80 per kg so the mixture costs Rs 73 per kg?
Answer
7 : 38
cheap : dear = (80 − 73) : (73 − 35) = 7 : 38
Section C · long answer
- 6.
A school counts term 1 as 25%, term 2 as 25% and the final exam as 50%. Rahul scores 96, 82 and 46 (out of 100). Find the overall mark, and say how much higher or lower it is than the simple average.
Answer
67.5; 7.17 lower than the simple average
25% of 96 + 25% of 82 + 50% of 46 = 67.5; simple average = 224 ÷ 3 = 74.67
Fresh sheets for your child
In the app, every How Quantities Combine: Understanding Data sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
Coming soon for Android and iPhone.