Question

1. what does the stacked bar chart above tell that is not easy to read from the first column chart above?
2. what information do pie charts give that is not available in a column chart?
3. if you include the total with the parts in a pie chart why will the percentage for the total always be 50%?

Explanation:

Question 3

A stacked bar chart shows the composition of each category (total and parts) and how parts contribute to the whole. A regular column chart shows individual values but not the proportional contribution of each part to the total for each category. So the stacked bar chart makes it easy to see the relative proportion of each sub - category within each main category, which is hard to get from a regular column chart.

A pie chart is used to show the proportion of each category relative to the whole. In a pie chart, the sum of all the percentages is 100% (or the whole is represented as a circle), so it clearly shows the relative share (percentage) of each category out of the total. A column chart shows the magnitude of each category but not the proportion of each category relative to the total.

Step 1: Recall the nature of a pie chart

A pie chart represents a whole (total) as 100% (or a full circle, which is 360 degrees). The parts of the pie chart are the sub - categories that add up to the whole (100%).

Step 2: Analyze the error in the question's premise

The statement "the percentage for the total will always be 50%" is incorrect. The total in a pie chart is the sum of all the parts, and the percentage of the total (the whole) should be 100% because the parts (sub - categories) are portions of the whole. If we incorrectly include the "total" as a separate category along with the parts, we are double - counting the whole. Let the sum of the parts be \(P = 100\%\) (since they are parts of the whole). If we add the "total" \(T\) which is equal to \(P\) (because \(T=P\) as \(T\) is the sum of the parts), then the new total becomes \(P + T=100\%+ 100\% = 200\%\). Now, the percentage of the "total" (T) out of this new (incorrect) total is \(\frac{T}{P + T}=\frac{100\%}{200\%}=50\%\). But this is a misrepresentation because the total should not be added as a separate category in a pie chart as the pie chart already represents the total as the whole (100%).

Answer:

A stacked bar chart shows the relative proportion of each sub - category within each main category (how parts contribute to the whole for each category), which is not easy to read from a regular column chart.

Question 4