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NCERT Solutions · Class 9 Mathematics How Quantities Combine: Understanding Data

33 questions · 33 still being checked

Exercise Set 10.4 1–2 (part 4 of 7)

  1. Exercise 1

    NCERT_Question_Class9_Maths_Ch10_Ex10-4_Q1
    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\displaystyle 14,234 on the top of the column 2019\displaystyle 2019 represent?
    (ii)
    Approximately how many reptile species were in the list in 2016\displaystyle 2016?
    (iii)
    Which class(es) of species have seen a relatively small increase in count between 2007\displaystyle 2007 and 2019\displaystyle 2019?

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    This solution has not been cross-checked against the answer printed in NCERT.

    (i) The column height is the total for $\displaystyle 2019$: all eight class bands together. \[\text{Mammals}+\text{Reptiles}+\text{Birds}+\text{Insects}+\text{Amphibians}+\text{Molluscs}+\text{Fish}+\text{Others}=14{,}234 \](ii) In the $\displaystyle 2016$ column the reptile band starts where the mammal band ends and stops at the top of the reptile band. \[\text{bottom} \approx 1200, \qquad \text{top} \approx 2300 \] \[2300 - 1200 \approx 1100 \](iii) Band thickness in $\displaystyle 2007$ and $\displaystyle 2019$ (read from the chart, to the nearest $\displaystyle 50$):\[\begin{array}{l|rrr} \text{Class} & 2007 & 2019 & \text{Increase} \\ \hline \text{Mammals} & 1150 & 1300 & 150 \\ \text{Birds} & 1250 & 1450 & 200 \\ \text{Amphibians} & 1900 & 2200 & 300 \\ \text{Reptiles} & 400 & 1450 & 1050 \\ \text{Insects} & 500 & 1600 & 1100 \\ \text{Molluscs} & 900 & 2250 & 1350 \\ \text{Fish} & 1150 & 2700 & 1550 \\ \text{Others} & 600 & 1250 & 650 \end{array} \]Mammals, birds and amphibians grew by only $\displaystyle 150$ to $\displaystyle 300$; every other class grew by $\displaystyle 650$ or more.Answer: (i) the total number of animal species, all classes together, in the $\displaystyle 2019$ list; (ii) about $\displaystyle 1100$; (iii) mammals, birds and amphibians.

  2. Exercise 2

    TestODIT20
    Home62\displaystyle 62100\displaystyle 10032\displaystyle 32
    Overseas172\displaystyle 17249\displaystyle 4971\displaystyle 71
    The wickets taken by a bowler in International Cricket matches till 2025\displaystyle 2025 are shown in the table. Complete the given stacked bar charts (the bar lengths can be approximate),
    (i)
    comparing the total wickets taken at home vs. overseas: NCERT_Question_Class9_Maths_Ch10_Ex10-4_Q2_i
    (ii)
    The total wickets taken in each format: NCERT_Question_Class9_Maths_Ch10_Ex10-4_Q2_ii

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    This solution has not been cross-checked against the answer printed in NCERT.

    Each bar is stacked in the legend order, so the segments start where the previous one ends.(i) Home and Overseas, split by format (Test, ODI, T20): \[\text{Home: } 0 \to 62 \to 162 \to 194, \qquad 62+100+32=194 \] \[\text{Overseas: } 0 \to 172 \to 221 \to 292, \qquad 172+49+71=292 \](ii) Each format, split into Home and Overseas: \[\text{Test: } 0 \to 62 \to 234, \qquad 62+172=234 \] \[\text{ODI: } 0 \to 100 \to 149, \qquad 100+49=149 \] \[\text{T20: } 0 \to 32 \to 103, \qquad 32+71=103 \] The two charts must show the same grand total: \[194+292 = 234+149+103 = 486 \]Answer: (i) Home bar $\displaystyle 194$ ($\displaystyle 62$ | $\displaystyle 100$ | $\displaystyle 32$) and Overseas bar $\displaystyle 292$ ($\displaystyle 172$ | $\displaystyle 49$ | $\displaystyle 71$); (ii) Test $\displaystyle 234$ ($\displaystyle 62$ | $\displaystyle 172$), ODI $\displaystyle 149$ ($\displaystyle 100$ | $\displaystyle 49$), T20 $\displaystyle 103$ ($\displaystyle 32$ | $\displaystyle 71$).