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Chapter 10: How Quantities Combine: Understanding DataAll 2 Questions on This Page

Class 9 Maths Chapter 10 Exercise Set 10.4 Solutions

Step-by-step solutions for Class 9 Mathematics Ganita Manjari Part 1I Chapter 10 Exercise Set 10.4 (Questions 1–2). Covers interpreting stacked column charts of animal species on the IUCN Red List and constructing stacked bar charts for international cricket bowler wickets.

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Key Concepts for Exercise Set 10.4

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1

Interpreting Stacked Column and Bar Charts

In a stacked column or bar chart, the total height or length of a bar represents the combined sum of all its constituent segments. Each individual colored segment shows the share or count of a specific component or category.

Total Bar Height/Length = Segment₁ + Segment₂ + … + Segmentₖ
2

Constructing Stacked Bar Charts

Component segments are plotted end-to-end starting from 0. Each subsequent category begins at the cumulative sum of all previous categories, allowing visual comparison of both overall totals and their component compositions.

Cumulative Endpoint = w₁ + w₂ + … + wᵢ
Question 1
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Figure 10.7 shows the number of animal species in different classes that are on the IUCN Red List of Threatened Species for different years.

Endangered Animal Species on the IUCN Red ListFigure 10.7
Stacked column chart showing the number of animal species in different classes on the IUCN Red List of Threatened Species from 2007 to 2019

Figure 10.7: Endangered animal species on the IUCN Red List from 2007 to 2019

  • (i)What does the number 14,234 on top of the column for 2019 represent?
  • (ii)Approximately how many reptile species were in the list in 2016?
  • (iii)Which classes of species have seen a relatively small increase in count between 2007 and 2019?
Solution
(i) What does the number 14,234 on top of the column for 2019 represent?

In a stacked column chart, the total height of a column represents the sum of all its segments.

Therefore, 14,234 represents the total number of animal species across all the classes shown on the IUCN Red List in 2019.

14,234 animal species

(ii) Approximately how many reptile species were in the list in 2016?

Reptiles form the second segment from the bottom of the 2016 column. The number of reptile species is estimated by reading the height of this segment using the vertical scale.

From the chart, there were approximately 1,100 reptile species in 2016.

Approximately 1,100 reptile species

(iii) Which classes of species have seen a relatively small increase in count between 2007 and 2019?

By comparing the thickness of each coloured segment in the 2007 and 2019 columns, mammals, reptiles and birds appear to have experienced relatively small increases compared with several other classes.

Answer:(i) 14,234 animal species | (ii) Approximately 1,100 reptile species | (iii) Mammals, reptiles and birds
Question 2
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The table shows the wickets taken by a bowler in international cricket matches at home and overseas till 2025.

Match format Test ODI T20
Home 62 100 32
Overseas 172 49 71

Complete the two stacked bar charts below:

  • • The first one is useful for comparing the total wickets taken at home vs overseas.
Template for stacked bar chart comparing home vs overseas wickets
  • • The second one is useful for seeing the total wickets taken in each format.
Template for stacked bar chart comparing wickets in each match format
  • (i)Comparing the total wickets taken at home vs. overseas.
  • (ii)The total wickets taken in each format.
Solution
(i) Comparing the total wickets taken at home vs. overseas

Total wickets taken at home:

= 62 + 100 + 32
= 194

Total wickets taken overseas:

= 172 + 49 + 71
= 292
Therefore,
Home = 194 wickets
Overseas = 292 wickets

To complete the first stacked bar chart, draw the segments in the order Test, ODI, T20. Use the given scale from 0 to 300.

•Home: Test = 62, ODI = 100, T20 = 32. The cumulative endpoints are 62, 162, 194.
•Overseas: Test = 172, ODI = 49, T20 = 71. The cumulative endpoints are 172, 221, 292.
Completed stacked bar chart comparing home and overseas wickets
(ii) The total wickets taken in each format

Test matches:

62 + 172 = 234

ODI matches:

100 + 49 = 149

T20 matches:

32 + 71 = 103
Therefore,
Test = 234 wickets
ODI = 149 wickets
T20 = 103 wickets

To complete the second stacked bar chart, draw the segments in the order Home, Overseas, using the same scale.

•Test: Home = 62, Overseas = 172. Cumulative endpoints: 62, 234.
•ODI: Home = 100, Overseas = 49. Cumulative endpoints: 100, 149.
•T20: Home = 32, Overseas = 71. Cumulative endpoints: 32, 103.
Completed stacked bar chart comparing format-wise wickets

The Test format has the highest total, with 234 wickets.

Answer:Home = 194 wickets, Overseas = 292 wickets | Test = 234 wickets, ODI = 149 wickets, T20 = 103 wickets (Test is highest)

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