NCERT Solutions Class 9 Maths Chapter 10 How Quantities Combine: Understanding Data on Padhaiwise

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 10 How Quantities Combine Exercise Set 10.1

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 10 — Exercise Set 10.1#

Weighted mean: if values $x_1, x_2, \ldots$ come with weights (sizes) $w_1, w_2, \ldots$,
$$\text{Weighted mean} = \dfrac{w_1x_1 + w_2x_2 + \cdots}{w_1 + w_2 + \cdots}$$
To combine averages of groups of different sizes, weight each average by the size of its group.

1. The average score of students on a test in Section A is 72 and that of students in Section B is 76. What is the combined average of both the sections given that Section A has 30 students and Section B has 25 students? #

Solution

Total marks in Section A $= 72 \times 30 = 2160$, and in Section B $= 76 \times 25 = 1900$.

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 10 How Quantities Combine Exercise Set 10.2

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 10 — Exercise Set 10.2#

When parts are combined in a ratio such as $3 : 4 : 5$, the ratio gives the weights. First turn each score into the same scale (a fraction or a percentage), then take the weighted mean.

1. Savitri’s marks in Kashmiri are as follows: 35 out of 50 in internal tests, 44 out of 60 in the project, and 80 out of 100 in the final exam. The annual percentage score is calculated by combining the internals, project, and final exam in the ratio 3 : 4 : 5. Which of the following expression(s) gives her annual score (as a percentage) in Kashmiri? #

$$\text{(i)}\ \dfrac{35 \times 3 + 44 \times 4 + 80 \times 5}{3 + 4 + 5} \qquad \text{(ii)}\ \dfrac{\frac{35}{100} \times 3 + \frac{44}{100} \times 4 + \frac{80}{100} \times 5}{3 + 4 + 5}$$

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 10 How Quantities Combine Exercise Set 10.3

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 10 — Exercise Set 10.3#

$$\text{Weighted mean} = \dfrac{\sum (\text{weight} \times \text{value})}{\sum \text{weights}}$$
A combined average always lies between the smallest and largest of the values being combined, and is closer to the value with the larger weight.

1. A stationery shop owner made ₹8000 selling books, of which 30% is the profit amount, and ₹1000 selling book covers, of which 50% is the profit amount. What is the percentage of profit on the total sales? #

Solution

$$\text{Profit on books} = 30\% \text{ of } ₹8000 = ₹2400$$

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 10 How Quantities Combine Exercise Set 10.4

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 10 — Exercise Set 10.4#

In a stacked bar (or column) chart, the full length of a bar shows a total, and the coloured pieces show the parts that make it up. A piece’s size is read as the difference between its top and bottom ends.

1. The following stacked column chart shows the number of animal species in the IUCN Red List, by class, over time. #

(i) What does the number 14,234 on the top of the column 2019 represent?

It is the total number of animal species on the IUCN Red List in 2019 — the sum of all the classes (mammals, reptiles, birds, insects, amphibians, molluscs, fish and others) stacked in that column.

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 10 How Quantities Combine Exercise Set 10.5

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 10 — Exercise Set 10.5#

In a 100% stacked bar chart, every bar has the same length (100%), and each piece shows a share of the total. It is good for comparing proportions, but it hides the totals.

1. The smart watch data of 5 people was tracked from Monday to Friday. The recorded data tells us how many hours each person spent lying down, sitting, and standing or moving around, etc. #

	Lying down	Sitting	Standing or moving around
Pavani (Patient)	20	3	1
Raghu (Nurse)	7	4	13
Zakir (Teacher)	8	6	10
Sahana (Student)
Julie (______)	8	10	6

(i) How much time does Sahana spend per day in each of these body-states? Make a reasonable guess and fill her row in the table.

Answers will vary. The three numbers must add up to 24 hours. A school student sleeps about 8–9 hours, sits in class and while studying for many hours, and moves about at school, at play and doing chores. A reasonable guess:

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 10 How Quantities Combine End-of-Chapter Exercises

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 10 — End-of-Chapter Exercises#

$$\text{Weighted mean} = \dfrac{\sum (\text{weight} \times \text{value})}{\sum \text{weights}}$$
To combine averages, weight each one by how many items it is the average of.

1. In cricket, the run rate is the average number of runs scored per over. In a T20 match, a team scored 6 runs in the first over making the run rate 6. #

(i) In the second over they scored 12 runs. What is the run rate now?

$$\text{Run rate} = \dfrac{6 + 12}{2}$$