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class 9 ganita manjari chapter 10
📖 Textbook Reference: 10.2.2 An Alternative to Pie Chart
To convert raw, absolute data into a 100% stacked bar chart, you must first calculate the percentage share of each component relative to its total.
By doing this, you eliminate the absolute size differences (like 1000 units vs 2000 units) and force both bars to represent exactly 100%, making it extremely easy to compare their relative distributions.
Example 7: The average category-wise daily electricity consumption of a house, in kWh, in 2005 and 2025 is shown in the table below.
Calculate the percentage shares for each year, and observe the difference between the standard stacked bar chart and the 100% stacked bar chart. Make the corresponding 100% stacked bar chart.
Calculate the percentage shares for each year, and observe the difference between the standard stacked bar chart and the 100% stacked bar chart. Make the corresponding 100% stacked bar chart.
| Year | Lighting | Cooling | Kitchen appliances |
Other appliances |
|---|---|---|---|---|
| 2005 | 360 | 300 | 120 | 220 |
| 2025 | 220 | 800 | 460 | 520 |
1
To make a 100% stacked bar chart, you must convert every absolute value into a percentage of the grand total for that specific group.
2
$\text{Percentage Share} = \frac{\text{Value}}{\text{Total Sum}} \times 100$. Do this independently for the year 2005 and the year 2025.
1
Step 1: Find the Total sum for 2005 ($360 + 300 + 120 + 220$).
2
Step 2: Divide each 2005 value by that total and multiply by 100. (e.g., $\frac{360}{1000} \times 100 = 36\%$).
3
Step 3: Find the Total sum for 2025 ($220 + 800 + 460 + 520$).
4
Step 4: Divide each 2025 value by the new total and multiply by 100.
!
Ignoring the shifting baseline: A common mistake is looking at absolute numbers and wondering why the percentages look so wildly different. For example, "Lighting" went down from $360$ to $220$, which is a moderate drop in absolute numbers. But its percentage dropped massively from $36\%$ to $11\%$! Why? Because while the lighting usage went down slightly, the total house usage doubled. So its "slice of the pie" became tiny!
Step-by-Step Calculation
Year 2005 Calculation:
Total $= 360 + 300 + 120 + 220 = 1000\text{ units}$.
Lighting: $\frac{360}{1000} \times 100 = 36\%$
Cooling: $\frac{300}{1000} \times 100 = 30\%$
Kitchen: $\frac{120}{1000} \times 100 = 12\%$
Other: $\frac{220}{1000} \times 100 = 22\%$
Year 2025 Calculation:
Total $= 220 + 800 + 460 + 520 = 2000\text{ units}$.
Lighting: $\frac{220}{2000} \times 100 = 11\%$
Cooling: $\frac{800}{2000} \times 100 = 40\%$
Kitchen: $\frac{460}{2000} \times 100 = 23\%$
Other: $\frac{520}{2000} \times 100 = 26\%$
Ans: See the dynamic SVG chart above to visually verify these percentages!
A farm uses 200 Litres of water for crops and 50 Litres for livestock in the Winter. In the Summer, it uses 600 Litres for crops and 150 Litres for livestock. What is the percentage share of crop water usage in Winter versus Summer?
1
Calculate the total water usage for each season independently, then find the percentage share for crops in both seasons.
1
Winter Total = $200 + 50 = 250\text{L}$.
2
Winter Crop Share = $\frac{200}{250} \times 100$.
3
Summer Total = $600 + 150 = 750\text{L}$.
4
Summer Crop Share = $\frac{600}{750} \times 100$.
!
Even though the absolute amount of water tripled ($200$ to $600$), the percentage share might stay exactly the same if the total also tripled! Absolute growth does not necessarily mean relative growth.
Step-by-Step Calculation
Winter Calculation:
Total = $250$. Crops = $\frac{200}{250} = \frac{4}{5} = 80\%$.
Summer Calculation:
Total = $750$. Crops = $\frac{600}{750} = \frac{4}{5} = 80\%$.
Ans: The percentage share is exactly 80% in both seasons!
Looking at the two charts for the house's electricity consumption, which category saw the most dramatic increase in its relative proportion (slice of the pie) between 2005 and 2025?
A. Lighting
B. Cooling
C. Kitchen appliances
D. Other appliances
1
Use the bottom chart (100% Stacked Chart) to answer questions about relative proportions. Compare the width of the colored blocks and the percentage numbers directly.
Visual Explanation
In the 100% stacked chart, look at the Red block (Cooling).
In 2005, Cooling took up $30\%$ of the total power usage.
In 2025, Cooling took up a massive $40\%$ of the total power usage.
While Kitchen and Other appliances also grew in percentage, Cooling became the single largest slice of the pie by a very wide margin.
Ans: Option (B)
Why did the "Lighting" percentage shrink so drastically (from 36% down to 11%) even though the absolute amount of electricity used for lighting only decreased slightly (from 360 to 220)?
A. Because modern LED lights are much more efficient.
B. Because the total energy consumption of the house doubled, making the lighting portion mathematically look much smaller relative to the massive new total.
C. Because 360 divided by 2 is 180, not 220.
D. Because 100% stacked bar charts are inaccurate for comparing absolute decreases.
1
A percentage is a fraction: $\frac{\text{Part}}{\text{Whole}}$. If the Whole (denominator) gets massive, the fraction gets tiny, even if the Part (numerator) doesn't change much!
Logical Breakdown
In 2005, the house used $1000$ units total. $360$ units out of $1000$ is a big chunk ($36\%$).
In 2025, the total usage skyrocketed to $2000$ units (driven mostly by cooling and appliances).
Now, the lighting is $220$ units out of $2000$. Because the denominator doubled, the resulting percentage fraction gets severely crushed down to $11\%$.
Ans: Option (B)
