How Quantities Combine: Understanding Data

In a badminton academy, 8 seniors have an average height of 165.5 cm and 3 juniors have an average height of 149.33 cm. Why is \((165.5 + 149.33) \div 2\) NOT the average height of the whole group?

1. aHeights must be added in metres, not in centimetres
2. bIt treats both averages equally, though there are many more seniors than juniors
3. cThe average of a group can never be found from the averages of its parts
4. dThe juniors’ heights should be left out because they are smaller

A table gives the weekly expenditure of three families A, B and C on six categories such as housing, food and healthcare. You want a cluster-column chart that makes it easiest to answer ‘Which family spent the least on housing?’. How should the chart be made?

1. aEach family is one bar showing only its total expenditure
2. bEach cluster is a family, with one bar for each category
3. cEach cluster is a category, with one bar for each family
4. dEach category is one bar showing the total of all families

300 mL of lemonade with 10% jaggery is mixed with 200 mL of lemonade with 20% jaggery. What is the concentration of jaggery in the mixture?

1. a14%
2. b16%
3. c15%
4. d12%

Batch A of brass weighs 100 kg and is 60% copper. Batch B is 40% copper. When the two batches are combined, the alloy is 48% copper. What is the weight of Batch B?

1. a100 kg
2. b120 kg
3. c200 kg
4. d150 kg

Arjun scored 70% in internal tests, 80% in the project and 90% in the final exam. His annual score combines these in the ratio 1 : 2 : 2. What is his annual score?

1. a80%
2. b82%
3. c84%
4. d78%

A white stork’s average daily distance over 20 days is 44.5 km. On the 21st day it flies 55 km. What is its average daily distance over the 21 days?

1. a45 km
2. b49.75 km
3. c44.5 km
4. d46 km

According to the chapter, stacked bar charts are used when we want to:

1. acompare only percentages, without the actual values
2. bshow every small bar starting from 0
3. csplit a full angle of \(360^\circ\) into parts
4. dcompare totals while keeping track of the parts that make up the totals

In an animal facility, the average weight of the male langurs is 16.5 kg, that of the female langurs is 13.8 kg, and that of all the langurs together is 14.925 kg. If there are 20 male langurs, how many female langurs are there?

1. a20
2. b28
3. c35
4. d14

Suvarna owns 1 g of gold that she bought at ₹15k per gram. Which next purchase makes the average price of all her gold exactly ₹20k per gram?

1. a1 g at ₹30k per gram
2. b2 g at ₹30k per gram
3. c0.5 g at ₹30k per gram
4. d0.5 g at ₹15k per gram

A 100% stacked bar chart is drawn for three athletes, showing the time each spent swimming, cycling and running in a triathlon. Which question can be answered by looking at just that chart?

1. aWho finished the race first?
2. bAbout what fraction of their race time did Athlete 1 spend cycling?
3. cWhich athlete took the longest time for running?
4. dHow many minutes did Athlete 2 take to swim?

Assertion (A): If every weight in a weighted mean is doubled, the weighted mean does not change.

Reason (R): Doubling every weight doubles both the numerator \(w_{1}x_{1} + w_{2}x_{2} + \ldots + w_{n}x_{n}\) and the denominator \(w_{1} + w_{2} + \ldots + w_{n}\).

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

Assertion (A): From a stacked bar chart, the corresponding 100% stacked bar chart can always be made.

Reason (R): From a 100% stacked bar chart, the corresponding stacked bar chart can always be made.

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

Assertion (A): Mixing 500 mL of lemonade with 10% jaggery and 200 mL of lemonade with 20% jaggery gives a mixture with 15% jaggery.

Reason (R): Each concentration influences the final concentration according to the quantity of mixture it contributes.

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

1. I. I. In winter, Naveen’s garden had more blooms than Fatima’s garden.
2. II. II. Over the whole year, both gardens had the same number of blooms.
3. III. III. In Naveen’s garden, more flowers bloomed in monsoon than in winter.

A 100% stacked bar chart shows: in Fatima’s garden 50% of the flowers bloomed in summer, 30% in monsoon and 20% in winter; in Naveen’s garden 40% bloomed in summer, 35% in monsoon and 25% in winter. Which of the statements can be inferred from this chart alone?

1. aOnly I
2. bOnly I and III
3. cOnly II and III
4. dOnly III

1. I. I. In pie charts, comparing angles in different orientations may be difficult.
2. II. II. A single stacked bar showing how the 24 hours of a day are spent can also be read as a 100% stacked bar.
3. III. III. In a stacked bar chart, every small bar in a stack begins from 0.

Which of the statements above is/are correct?

1. aOnly I and II
2. bOnly II and III
3. cOnly I
4. dI, II and III

1. I. I. In a weighted mean, the word ‘weighted’ always refers to actual weights measured in kilograms.
2. II. II. When collections are all of the same size, their combined average can be found by adding their averages and dividing by the number of collections.

Which of these statements about averages is/are correct?

1. aOnly I
2. bBoth I and II
3. cOnly II
4. dNeither I nor II

Match each name or term in List I with what the chapter says about it in List II:

1. a(i)-R, (ii)-S, (iii)-Q, (iv)-P
2. b(i)-S, (ii)-R, (iii)-Q, (iv)-P
3. c(i)-Q, (ii)-R, (iii)-S, (iv)-P
4. d(i)-S, (ii)-Q, (iii)-R, (iv)-P

Match each situation in List I with its answer in List II:

1. a(i)-R, (ii)-S, (iii)-P, (iv)-Q
2. b(i)-Q, (ii)-P, (iii)-S, (iv)-R
3. c(i)-S, (ii)-P, (iii)-R, (iv)-Q
4. d(i)-R, (ii)-P, (iii)-S, (iv)-Q

At a panipuri stall, 12 litres of pani (spiced water) has 8% spice. Customers say it is too spicy, so the owner wants the spice concentration to be 6%. How much plain water should be mixed in?

1. a4 litres
2. b3 litres
3. c2 litres
4. d6 litres

A café asks customers to rate its food, service and ambience from 1 to 5, and combines the ratings with weights 5 : 3 : 2. Neha rates food 4, service 3 and ambience 5. What is her combined rating?

1. a4.0
2. b4.2
3. c3.9
4. d3.6