krit.club logo

Statistics - Interpret stacked and 100 percent stacked bar graphs for data comparison

Grade 9CBSE

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

🔑Concepts

•

A stacked bar graph represents multiple sub-categories of data for a single entity as segments within a single bar. The total height of the bar corresponds to the sum of all individual values. To find the value of a specific segment, subtract its lower boundary value from its upper boundary value: V=ytop−ybottomV = y_{top} - y_{bottom}.

Stacked bar graph showing segments A and B. Segment A goes from 0 to 100, and segment B goes from 100 to 180.
•

A 100% stacked bar graph shows the relative proportion of each category within a whole. Every bar is normalized to the same total height representing 100%100\%. This graph is useful for comparing the percentage distribution across different groups, regardless of the absolute size of the groups.

100% stacked bar graph showing two groups X and Y, both reaching the 100% mark with different internal distributions.
•

When interpreting data, look for changes in the 'mix' of components. In a stacked bar, if the total height increases but one segment remains the same height, that segment's percentage contribution to the whole has decreased.

•

Stacked bar graphs are preferred over multiple separate bar graphs when the total volume (the sum) is as important as the individual contributions of the components.

📐Formulae

Total Height of Bar=∑i=1nValue of Componenti\text{Total Height of Bar} = \sum_{i=1}^{n} \text{Value of Component}_i

Value of Specific Segment=yupper limit−ylower limit\text{Value of Specific Segment} = y_{\text{upper limit}} - y_{\text{lower limit}}

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

\text{Total Percentage for any bar in 100% Stacked Graph} = 100\%

💡Examples

Problem 1:

A stacked bar graph shows the production of Wheat and Rice in two years. In 2022, the Wheat segment starts at 00 and ends at 4040 units, and the Rice segment ends at 7575 units. In 2023, the Wheat segment ends at 3535 units and the Rice segment ends at 8080 units. Which year had higher Rice production?

Solution:

For 2022: Rice production = 75−40=3575 - 40 = 35 units.
For 2023: Rice production = 80−35=4580 - 35 = 45 units.
Since 45>3545 > 35, the year 2023 had higher Rice production.

Explanation:

To find the value of a stacked segment that does not start at the origin, subtract the value at the start of the segment from the value at the end of the segment.

Problem 2:

A 100% stacked bar graph shows that in School A, 60%60\% of students are Boys, while in School B, 55%55\% of students are Boys. If School A has 500500 students and School B has 800800 students, which school has more Girls?

Solution:

School A Girls Percentage: 100%−60%=40%100\% - 60\% = 40\%.
Number of Girls in School A: 40100×500=200\frac{40}{100} \times 500 = 200.
School B Girls Percentage: 100%−55%=45%100\% - 55\% = 45\%.
Number of Girls in School B: 45100×800=360\frac{45}{100} \times 800 = 360.
School B has more girls.

Explanation:

Even though School A might look like it has a 'larger' segment if only looking at percentages, the absolute number depends on the total population of each category (school).

Problem 3:

Calculate the total revenue from a stacked bar where 'Product X' contributes ₹120₹ 120 and 'Product Y' is represented by a segment starting at 120120 and ending at 300300.

Solution:

300 (Total height)−120 (Product X)180 (Product Y)\begin{array}{r} 300 \text{ (Total height)} \\ - 120 \text{ (Product X)} \\ \hline 180 \text{ (Product Y)} \end{array} The total revenue is the value at the top of the bar, which is ₹300₹ 300.

Explanation:

In a sub-divided/stacked bar graph, the top-most point on the y-axis for a bar represents the cumulative total of all components in that bar.

Problem 4:

The following stacked bar graph represents the number of students enrolled in 'Art' and 'Science' courses over two years. In 2021, the Art segment ends at 120120 and the Science segment ends at 300300. In 2022, the Art segment ends at 150150 and the Science segment ends at 350350. Calculate the increase in the number of Science students from 2021 to 2022.

Stacked bar graph for years 2021 and 2022 showing enrollment segments for Art and Science.

Solution:

  1. In 2021, the Art segment goes from 00 to 120120. The Science segment starts at 120120 and ends at 300300.
  2. Science students (2021) = 300−120=180300 - 120 = 180.
  3. In 2022, the Art segment goes from 00 to 150150. The Science segment starts at 150150 and ends at 350350.
  4. Science students (2022) = 350−150=200350 - 150 = 200.
  5. Increase in Science students = 200−180=20200 - 180 = 20.

Explanation:

To find individual component values in a stacked bar graph, we calculate the difference between the top and bottom values of that specific component's segment.

Problem 5:

A 100% stacked bar graph compares the expenditure of two families. Family P spends 40%40\% on Food, 30%30\% on Rent, and the rest on Others. Family Q spends 35%35\% on Food, 45%45\% on Rent, and the rest on Others. If Family P's total expenditure is Rs 50,00050,000, find the absolute amount they spend on 'Others'.

100% stacked bar for Family P showing 40% Food, 30% Rent and the remaining segment for Others.

Solution:

  1. For Family P, the total percentage is always 100%100\%.
  2. Percentage spent on 'Others' = 100%−(Food%+Rent%)100\% - (\text{Food}\% + \text{Rent}\%)
  3. Percentage for Others = 100%−(40%+30%)=100%−70%=30%100\% - (40\% + 30\%) = 100\% - 70\% = 30\%.
  4. Absolute amount spent on Others = 30%30\% of Rs 50,00050,000.
  5. Amount = 30100×50000=15000\frac{30}{100} \times 50000 = 15000.
  6. Family P spends Rs 15,00015,000 on Others.

Explanation:

In a 100% stacked bar graph, we first determine the percentage of the segment of interest and then apply it to the total value provided for that specific bar.