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How Quantities Combine: Understanding Data: CBSE Class 9 Mathematics practice questions

Practise 50 questions on How Quantities Combine: Understanding Data, free, with an explanation for each answer.

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Sample questions

A badminton academy has 6 seniors and 2 juniors. The mean height of the seniors is 168 cm168\ \text{cm} and of the juniors is 152 cm152\ \text{cm}. What is the mean height of all 8 players together?

Two groups of badminton players of different sizes with their mean heights
  1. 160 cm160\ \text{cm}
  2. 164 cm164\ \text{cm}
  3. 156 cm156\ \text{cm}
  4. 656 cm656\ \text{cm}
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B. 164 cm164\ \text{cm}

Each group total is mean ×\times size: 168×6=1008168\times 6=1008 and 152×2=304152\times 2=304. Combined mean =1008+3046+2=13128=164=\dfrac{1008+304}{6+2}=\dfrac{1312}{8}=164. The trap is the average of averages, 168+1522=160\dfrac{168+152}{2}=160, which treats the 2 juniors as if they were as many as the 6 seniors. Swapping the weights gives 156156, and dividing 13121312 by 2 groups instead of 8 players gives 656656.

This is Brahmagupta’s idea of mean depth. A pit 20 hastas long is dug in four sections. The sections are 3, 4, 5 and 8 hastas long. They are dug to depths of 8, 6, 4 and 2 hastas respectively. What is the mean depth of the pit?

Side view of a pit with four sections of different lengths and depths
  1. 5 hastas
  2. 21 hastas
  3. 4.2 hastas
  4. 84 hastas
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C. 4.2 hastas

Mean depth =8×3+6×4+4×5+2×83+4+5+8=24+24+20+1620=8420=4.2=\dfrac{8\times 3+6\times 4+4\times 5+2\times 8}{3+4+5+8}=\dfrac{24+24+20+16}{20}=\dfrac{84}{20}=4.2. The plain mean of depths 8+6+4+24=5\dfrac{8+6+4+2}{4}=5 gives the long shallow section too little say. Dividing 8484 by 4 sections gives 2121, and forgetting to divide at all gives 8484.

Brass batch A weighs 100 kg and is 60% copper. Batch B weighs 150 kg and is 40% copper. Batch C is 30% copper. When all three are melted together the alloy is 40% copper. What is the weight of Batch C?

Three batches of brass drawn as bars with an unknown weight for the third
  1. 200 kg
  2. 20 kg
  3. 100 kg
  4. 250 kg
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A. 200 kg

0.4=100×0.6+150×0.4+y×0.3100+150+y=120+0.3y250+y0.4=\dfrac{100\times 0.6+150\times 0.4+y\times 0.3}{100+150+y}=\dfrac{120+0.3y}{250+y}. So 0.4(250+y)=120+0.3y0.4(250+y)=120+0.3y, i.e. 100+0.4y=120+0.3y100+0.4y=120+0.3y, giving 0.1y=200.1y=20 and y=200y=200. Stopping at 0.1y=200.1y=20 (not dividing by 0.1) gives the trap 2020, and 250250 is just the weight of A and B together. Check: copper =60+60+60=180=60+60+60=180 in 450 kg450\ \text{kg} is 40%40\%.

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