In polk middle school, 45% of the students are 6th graders, 35% of the students are 7th graders and the remainder are 8th graders. Would a circle graph of this data that had 3 sections each with a central of 120% be misleading?
yes, since it would imply sections of equal size.
To determine whether the circle graph would be misleading, we need to analyze the given data and consider the principles of constructing a circle graph.
First, let's calculate the percentage of 8th graders in Polk Middle School. Since the percentages of 6th and 7th graders are already given, we can subtract their percentages from 100% to find the percentage of 8th graders.
Percentage of 8th graders = 100% - (45% + 35%)
Percentage of 8th graders = 100% - 80%
Percentage of 8th graders = 20%
Therefore, 20% of the students at Polk Middle School are 8th graders.
Now, let's analyze whether a circle graph with three sections, each with a central angle of 120%, would be misleading.
In a circle graph, each section represents a part of the whole. The size of each section is determined by the percentage it represents.
In this case, if we were to allocate 120% to each section (representing 6th, 7th, and 8th graders), it would be misleading because the total central angle (360%) exceeds what a circle can accommodate. A circle graph should always add up to 360 degrees (or 100%).
Since the percentage of 8th graders is 20%, they should ideally be represented by a section with a central angle of 20% × 360 degrees = 72 degrees.
Similarly, the 6th graders and 7th graders should be represented by sections whose central angles reflect their respective percentages.
Therefore, a circle graph with three sections, each with a central angle of 120%, would create an inaccurate representation of the data and be misleading.