Question

explain whether a circle graph would change if the amount of data in each category was doubled. choose the correct answer below. a. since each category doubled its count, the circle graph will double in size. b. since each category doubled its count, each interior angle in the circle will increase in size. c. since each category doubled its count, a second circle is needed to display all the data. d. since each category doubled its count, the count labels on the graph will change but the size and percentage for each section will not.

Explanation:

Step1: Recall Circle Graph (Pie Chart) Properties

A circle graph (pie chart) represents data as proportions (percentages) of a whole. The size of the circle and the relative angles of the sections depend on the proportion of each category to the total, not the absolute counts.

Step2: Analyze Effect of Doubling Each Category

If each category's count is doubled, the total also doubles (since total = sum of all categories). The proportion of each category remains the same (e.g., if a category was \( \frac{a}{T} \) before, it becomes \( \frac{2a}{2T} = \frac{a}{T} \) after, where \( T \) is the original total). Thus, the angles (proportions) and the size of the circle graph do not change in terms of relative representation. The count labels (if present) would change, but the percentage and angle for each section stay the same.

Now, evaluate each option:

• Option A: The circle graph's size doesn't double. Proportions are same, so size remains. Eliminate A.
• Option B: Interior angles depend on proportion, not absolute count. Since proportion is same, angles don't increase. Eliminate B.
• Option C: A second circle isn't needed. The same circle can represent the data as proportions are unchanged. Eliminate C.
• Option D: Count labels (absolute counts) change, but size (of circle) and percentage (thus angles) for each section do not. This matches the analysis.

Answer:

D. Since each category doubled its count, the count labels on the graph will change but the size and percentage for each section will not.