Question

Draw a circle graph showing each percent. Students in an English course can earn an \(\mathrm{A}, \mathrm{a} \mathrm{B}, \mathrm{a} \mathrm{C}\) or an F. The following table shows the results of a class. $$\begin{array}{c|c} \mathrm{A} & 12 \% \\ \hline \mathrm{B} & 25 \% \\ \hline \mathrm{C} & 45 \% \\ \hline \mathrm{F} & 18 \% \end{array}$$ (GRAPH CANT COPY)

Short answer

Answer: The angle measure representing the percentage of students who received a grade of C is 162 degrees.

Step-by-step solution

Convert percentages to degrees

Since there are 360 degrees in a circle, we need to convert the given percentages to their corresponding angular measures. To do this, we multiply the percentage by 360 and divide by 100: A: \(\frac{12\% \times 360^\circ}{100} = 43.2^\circ\) B: \(\frac{25\% \times 360^\circ}{100} = 90^\circ\) C: \(\frac{45\% \times 360^\circ}{100} = 162^\circ\) F: \(\frac{18\% \times 360^\circ}{100} = 64.8^\circ\) (Note: the sum of the angles may not exactly equal 360 due to rounding errors, but it should be extremely close.)

Draw the circle and divide it to represent percentages

Using a compass, draw a circle of an appropriate size for your graph. We will begin at the top of the circle and draw angles using a protractor in a clockwise direction. Start with a small mark at the top of the circle to indicate the 0-degree point. For the "A" section, measure 43.2 degrees from the 0-degree point and draw another small mark on the circle. Then, use a straightedge to draw a line from this new mark to the center of the circle to create a segment representing the A grades. For the "B" section, measure 90 degrees from the end of the "A" section (the previous mark) and draw a small mark on the circle. Connect this mark to the center of the circle with a straightedge to create a segment representing the B grades. Proceed with the same method for the "C" and "F" sections, making sure to measure the correct angle and connect the marks to the center of the circle. For "C," measure 162 degrees from the end of the "B" section, and for "F," measure 64.8 degrees from the end of the "C" section.

Label the segments with their respective grades and percentages

Lastly, label each segment with the corresponding grade and percentage. Write "A: 12%" in the A section, "B: 25%" in the B section, "C: 45%" in the C section, and "F: 18%" in the F section. Ensure that the labels are clear and easy to read. Now, the circle graph is complete and accurately represents the percentages of students who earned each grade in the English course.

Key concepts

Converting Percentages to Degrees

Understanding the relationship between percentages and degrees is crucial when creating a circle graph because a circle graph represents data in a round format divided into slices, akin to a pie, where each slice corresponds to a portion of the whole.

To convert a percentage to degrees, we use the fact that a circle has a total of 360 degrees. Here's the conversion process in a nutshell: you multiply the given percentage by 360 and then divide by 100. For example, if you have a section that is 25% of the total, you calculate the angle by multiplying 25% (0.25 as a decimal) by 360 degrees, resulting in a 90-degree angle for that section of the circle graph.

This method ensures that you assign an angle size to each percentage that is proportionate to its share of the total 100%. A common mistake to avoid is merely estimating the angles without calculating - this can lead to an inaccurate representation of data.

Graphing Percentages

Once you've converted the percentages into degrees, the next step is graphing those percentages on the circle. To graph percentages accurately, you'll need two tools: a compass for drawing a perfect circle and a protractor for measuring the angles.

Start by using the compass to draw your circle graph. Then, make a small mark at the top of the circle to represent the starting point, which is typically the 0-degree point. From there, use your protractor to measure out the angle for each category.

Drawing Each Section

Place the protractor's center point at the center of the circle, align the 0-degree mark with the starting point, and measure out the angle you previously calculated. Draw a mark at the angle that corresponds to your first category, then connect this mark to the center of the circle with a straight line to form the first 'slice'.

Repeat this process for each percentage category around the circle, always starting from the outer end of the previous slice. To ensure precision, it's best to work in a clockwise direction and continue marking and drawing each section in sequence. In this way, you'll construct a visual representation where each slice's size is proportional to its percentage of the whole.

Interpreting Data in a Circle Graph

Interpreting data from a circle graph can offer insights into how different categories compare to each other at a glance. Each 'slice' of the circle represents a percentage of the whole, and by looking at the sizes of the slices, you can generally tell which categories are larger or smaller.

However, to accurately read a circle graph, you need to pay attention to the labels indicating what each slice represents, including its percentage value. In more intricate graphs, the colors or patterns should have a key or legend to aid interpretation.

Analyzing the Data

When analyzing the data, compare the sizes of the slices to each other: a larger slice means a larger percentage. For instance, in a circle graph showing grades, you can quickly see which grades are most common or least common.

Remember that circle graphs are best when you need to understand proportions or compare parts to a whole, rather than when precise values are necessary. They are a powerful tool for visual learners, providing a snapshot of data distribution that can be immediately understood and utilized for various applications, from business insights to classroom assessments.