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How Quantities Combine: Understanding Data - Stacking Columns

Grade 9CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A stacked column chart (or subdivided bar diagram) is used to represent data where each bar represents a whole, and segments within the bar represent the components of that total. It is particularly useful for comparing the total size of categories while showing the internal breakdown.

A stacked column chart showing two categories, each divided into two vertical components.
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To construct a stacked column, determine the cumulative values for each category. If category XX has parts aa, bb, and cc, the first segment ends at aa, the second at a+ba+b, and the third at a+b+ca+b+c.

Diagram
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Stacked columns can also be expressed as 'Percentage Stacked Bars' where the total height of every bar is 100%100\%. This allows for a comparison of the relative proportions (shares) of components across different totals.

Two bars of equal total height representing 100 percent, each divided at different internal points to show varying proportions.

📐Formulae

Total Height=∑i=1nComponent Valuei\text{Total Height} = \sum_{i=1}^{n} \text{Component Value}_i

Segment Percentage=Component ValueTotal Value×100%\text{Segment Percentage} = \frac{\text{Component Value}}{\text{Total Value}} \times 100\%

Upper Boundary of Segment k=∑i=1kValuei\text{Upper Boundary of Segment } k = \sum_{i=1}^{k} \text{Value}_i

💡Examples

Problem 1:

A family spends Rs 5000 on Food and Rs 3000 on Rent. Represent this as a stacked column chart where the total height reflects the total expenditure.

A stacked column representing a total of 8000, with a bottom segment of 5000 for Food and a top segment of 3000 for Rent.

Solution:

  1. Calculate Total: 5000+3000=80005000 + 3000 = 8000.
  2. Draw a rectangle for 'Food' from base 00 to height 50005000.
  3. Draw the next rectangle for 'Rent' starting at 50005000 and ending at 5000+3000=80005000 + 3000 = 8000.

Explanation:

The stacked column shows that the total expenditure is Rs 8000. The portion of the bar from 0 to 5000 represents Food, and the portion from 5000 to 8000 represents Rent.

Problem 2:

Convert the following production data for two years into a percentage stacked bar chart: Year 1 (Wheat: 40 tons, Rice: 60 tons), Year 2 (Wheat: 90 tons, Rice: 30 tons).

Two bars of equal height. The first bar is split at 40 percent. The second bar is split at 75 percent.

Solution:

For Year 1: Total = 100100. Wheat = 40100×100=40%\frac{40}{100} \times 100 = 40\%. Rice = 60%60\%. For Year 2: Total = 120120. Wheat = 90120×100=75%\frac{90}{120} \times 100 = 75\%. Rice = 30120×100=25%\frac{30}{120} \times 100 = 25\%.

Explanation:

In a percentage stacked bar, all bars have a total height of 100 units. Year 1 shows a 40-60 split, while Year 2 shows a 75-25 split.