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Class 9 Ganita Manjari • Chapter 10
📖 Textbook Reference: 10.2 Visualising and Interpreting Data
Stacked bar charts are used when we want to compare the totals but also want to keep track of the components that make up those totals.[cite: 2]
The total length of a full stacked bar represents the total value. The length of a smaller colored bar within the stack represents the value of that specific component.
Important Note: Except for the bottom-most bar, the rest of the stacked bars do not begin from 0. This makes it slightly harder to estimate the exact quantity of middle components, as you must subtract the top and bottom values of that specific block.[cite: 2]
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?
(ii) Approximately how many reptile species were in the list in 2016?
(iii) Which class(es) of species have seen a relatively small increase in count between 2007 and 2019?[cite: 2]
(i) What does the number 14,234 on the top of the column 2019 represent?
(ii) Approximately how many reptile species were in the list in 2016?
(iii) Which class(es) of species have seen a relatively small increase in count between 2007 and 2019?[cite: 2]
1
A stacked column chart allows us to quickly see the grand total for a specific year, while also tracking the individual components that make up that total.[cite: 2]
2
The exact value of any single component (except the bottom one) is determined by finding the Y-axis value at its top edge and subtracting the Y-axis value at its bottom edge.
1
Hint for (i): Look at the placement of the number $14,234$. It sits at the very top of the entire stacked bar for the year $2019$.
2
Hint for (ii): Go to the $2016$ column. Look at the legend to find the color for "Reptiles" (Dark Red). Follow the dotted red reference lines I have drawn for you to the left Y-axis. Calculate the difference.
3
Hint for (iii): Scan visually from left ($2007$) to right ($2019$). Which color bands maintain roughly the same thickness across all the years?
!
The Baseline Trap: When estimating the number of reptiles in 2016, do NOT just look at the top edge of the red bar! The top edge might align with ~2200 on the Y-axis, but the bottom edge starts at ~1200. The true value is the *difference* between them ($\sim 1000$).[cite: 2]
Answers and Analysis
(i) What does 14,234 represent?
It represents the total number of endangered animal species across all listed classes in the year 2019.
(ii) Approx. how many reptile species were in 2016?
Locate the 2016 column and find the dark red segment (Reptiles).
Using the red reference lines, you can see the top edge sits slightly below 3000, and the bottom edge sits slightly above 1000.
Ans: Approximately 1,000 species.
(iii) Which classes saw a relatively small increase?
Look at the thickness of each color band from 2007 to 2019.
The green band (Insects), yellow band (Amphibians), and light blue band (Fish) clearly become much thicker.
However, the dark blue band at the bottom and the medium blue band stay almost the exact same thickness.
Ans: Mammals and Birds.
Based on the IUCN stacked chart, did the number of endangered Fish (light blue) more than double between 2007 and 2019? Use visual estimation.
1
You can estimate component growth by visually comparing the vertical thickness of the color band in the starting year versus the ending year.
1
Locate the light blue band (Fish) in the 2007 column. Estimate its vertical thickness.
2
Locate the light blue band (Fish) in the 2019 column.
3
Does the 2019 band look more than twice as thick as the 2007 band?
!
Do not compare the *top edge* of the Fish band in 2007 to the *top edge* in 2019. The top edge is pushed higher by all the growth in Mammals, Reptiles, Birds, Insects, Amphibians, and Molluscs underneath it! You must isolate the thickness of the light blue band itself.[cite: 2]
Visual Analysis
In $2007$, the light blue "Fish" band is relatively thin.
By $2019$, the light blue band has expanded significantly. Visually, its thickness appears to be slightly more than double its original size in 2007.
*(Exact mathematical verification: Fish in 2007 were ~1200, and in 2019 were ~2600. So yes, it more than doubled!)*
Ans: Yes, the number of endangered Fish more than doubled.
Why is it slightly more difficult to estimate the exact number of endangered Insects in 2013 compared to the number of endangered Mammals in 2013?
A Because there are more insects than mammals.
B Because the Mammal bar starts at the zero baseline, while the Insect bar "floats" in the middle, requiring subtraction.
C Because the color green is harder to see than dark blue.
D Because the total number 11,212 is not evenly divisible by the number of categories.
1
In a stacked column chart, only the bottom-most category is aligned with the X-axis (zero).[cite: 2]
Logical Explanation
The Mammals category is at the very bottom of the stack. Because its bottom edge sits at zero, you only have to read the value of its top edge against the Y-axis to know its exact value.[cite: 2]
The Insects category sits in the middle of the stack. Its bottom edge does not align with zero.
To find its value, you must estimate the Y-value of its top edge, estimate the Y-value of its bottom edge, and subtract the two. This makes it inherently more difficult and prone to estimation errors.[cite: 2]
Ans: Option (B)
If a researcher only cared about analyzing how the proportion or percentage of Amphibians compared to the total list has changed over time, what chart would be better suited than this standard stacked column chart?
A A simple line graph
B A clustered column chart
C A 100% stacked bar chart
D A scatter plot
1
A standard stacked chart focuses on tracking absolute totals and components. A 100% stacked chart focuses exclusively on tracking relative fractions and percentages.[cite: 2]
Logical Breakdown
In the current chart, the total number of species increases every year (the bars get taller). This makes it hard to see if Amphibians are taking up a larger or smaller slice of the overall pie.
In a 100% stacked bar chart, every column is stretched to be exactly the same total height (representing 100%).[cite: 2]
This makes it incredibly easy to compare the relative percentage of Amphibians across the years, independent of the total growth.[cite: 2]
Ans: Option (C)
