# DI Bar Graphs: Stacked Bars

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## DI Bar Graphs: Stacked Bar Graphs

The following chart gives the revenue share of different companies in the tech sector in Cuckooland. :

In 2001, the company that grew the quickest grew by 100%, what was the growth rate of the company that had the least growth rate?

1. 50%
2. 25%
3. 20%
4. 33%

Choice D

## Detailed Solution

Note that we can answer this question even if we do not know the overall numbers in 2000 and 2001. Let the total revenues of the entire industry be X in 2000 and Y in 2001.

FINY has grown from 22.9% of X to 21.1% of Y, which is nothing but ${ \frac{21.1}{22.9}}$% * $\frac{Y}{X} - 1$ expressed as a percentage.

Likewise, growth of PRIWO would be $\frac{19.3}{17.1}$% * $\frac{Y}{X} - 1$. And so on for the rest.

So the company that grew the quickest would be the one that had the maximum ration of 2001 revenue share to 2000 revenue share. Only the shares matter, X's and Y's do not matter.

So, to find the company that grew quickest, all we need to do is find the highest of ${ \frac{21.1%}{22.9%}, \quad\frac{19.3%}{17.1%},\quad \frac{21.1%}{25.7%},\quad \frac{14%}{14.31%}, \quad \frac{10.5%}{8.6%}, \quad \frac{14%}{11.4%} }$. Of these ${ \frac{14%}{11.4%} }$ is the highest.

Now, we know that CENTURE saw the highest growth and that this growth number was 100%. Or, CENTURE saw its revenues double.

Or 14% of Y = 11.4% of X * 2

Or ${ \frac{Y}{X} = \frac{2 \times 11.4}{14} =1.629 }$

To find out the company that saw the least growth rate, we need to find the least among the listed fractions. Or the least among Or ${ \frac{21.1%}{22.9%}, \quad \frac{21.1%}{25.7%},\quad and \frac{14%}{14.31%} }$. This is clearly ${ \frac{21.1%}{25.7%} }$.

Or, the company that saw the least growth rate is SCT.

SCT’s growth rate is ${ \frac{21.1}{25.7 }}$% * $\frac{Y}{X} - 1$. Or ${ \frac{21.1%}{25.7%} \times 1.629=0.33 }$.

Or, SCT grew by 33%. Correct Answer: Choice D

In stacked bar charts (and pie charts) the relative shares very often underpin the more important ideas. A bunch of key pointers –
1. For measuring which component has growth the maximum and minimum, actual numbers are not required.
2. We need actual numbers only to measure actual growth rates.
3. A company that has seen its share shrink could also have seen actual growth (like SCT above) and vice versa.
4. If we know overall growth rate from one year to another, we can compute individual growth rates

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