Circle Graphs

Circle Graphs exercise

• Explain how to draw a circle graph.

  Hints

  Each partition of a circle graph looks like a slice of pie.

  $100\%$ corresponds to the whole circle, with a corresponding central angle of $360^\circ$.

  $\frac12$ corresponds to $50\%$, which corresponds to $180^\circ$.

  Solution

  On the right-hand side you see the resulting circle graph, also known as a pie graph.

  Here are the steps needed to get to this graph:

  1. Determine the percentage of each location. For example, $2$ people out of a total of $8$ people want to go to a campground. That's $\frac28\times 100\%=25\%$.
  2. Calculate the central angle of the corresponding sector for each location. So for the campground, that would be $\frac28\times 360^\circ=\frac{720^\circ}{8}=90^\circ$.
  3. Divide the circle into sectors, each sector with the correct central angle corresponding to a location.

• Label the circle graph.

  Hints

  The central angle as well as the sector of the circle for the car and skateboard are the same.

  The percentage of people who want a particular mode of transportation is the ratio of the number of people who want that particular mode of transportation and the total number of people.

  Multiply this relation with $360^\circ$ to get the central angle.

  Solution

  Let's practice the construction of a circle graph step by step.

  What do we already know? $3$ people decide to go by plane, $2$ by car and $2$ by skateboard. Together we have $7$ people.

  First, we determine the regarding percental part as follows:

  • Plane: $\frac37\approx 0.4286=42.68\%$ To get the percent we multiply with $100$.
  • Car: $\frac27\approx 0.2857=28.57\%$
  • Skateboard: $\frac27\approx 0.2857=28.57\%$

  Next, we calculate the regarding central angle by multiplying the fraction above with $360^\circ$:

  • Plane: $\frac37\cdot 360\approx154.28^\circ$
  • Car: $\frac27\cdot 360\approx102.86^\circ$
  • Skateboard: $\frac27\cdot 360\approx102.86^\circ$

  Last, we draw sectors of the circle with the given central angles as you can see beside.

• Determine the angles for the circle graph.

  Hints

  If you sum all angles you get $360^\circ$.

  To get each angle multiply the relation between the number of persons deciding for the regarding meal and the total number with $360^\circ$.

  The total # of all people is the sum of the different numbers.

  Solution

  Here you see the circle graph to the meal problem. How do we get it?

  We know that $3$ people decide for barbeque, $2$ for turkey and $5$ for pizza. So we have $10$ people in total.

  Now we can consider that $360^\circ$ corresponds to the total number, and thus, the regarding sectors correspond to the relation between the number and the total number. In other words, we have to multiply each such relation with $360^\circ$ to get the central angle of the corresponding sector:

  • Barbeque: $\frac{3}{10}\times 360^\circ=108^\circ$
  • Turkey: $\frac{2}{10}\times 360^\circ=72^\circ$
  • Pizza: $\frac{5}{10}\times 360^\circ=180^\circ$ This sector is easy to recognize: it's the half of the whole circle.

• Interpret the circle graph.

  Hints

  Just look at the percental part. This corresponds with the number of friends prefering the regarding sport.

  For example, if the total number is $20$, $25~\%$ stands for $5$ people.

  The size of the sectors corresponds with the percental part of the regarding prefered sport.

  Solution

  Let's turn the scope.

  Here you see a circle graph showing the results of Paul investigation.

  His friends, we can't get the total number from the graph, prefer the following sports

  • Baseball $37.5\%$
  • Basketball $37.5\%$
  • Soccer $25\%$

  So, three different sports are given. We can't determine the number of people prefering the regarding sport but we can see the percental part.

  Using this graph we see that as many people prefer baseball as basketball. The regarding sectors have the same size. The smallest sector is this one representing soccer. So least of Paul's friends prefer soccer.

• Find the right circle graph.

  Hints

  Pay attention to the number of sectors. There are four different destinations.

  Keep the relations in mind; the sector corresponding to the highest percent number must be the biggest one.

  Because $12.5\%<37.5\%$, you must have the same order for the corresponding sectors.

  Solution

  On the right side of the picture beside you see the resulting circle graph, also known as pie graph.

  How can you decide which one matches with the given problem?

  • Check the number of sectors. Because there are $4$ destinations there must be also $4$ sectors.
  • You can see the percent numbers. Those have to correspond to the sectors. $25\%$ stands for a quarter circle. The sector to $37.5\%$ must be bigger and this one to $12.5\%$ smaller.

• Decide which circle graph corresponds to each table.

  Hints

  Remember, the sum of the percent is always $100$.

  Determine for each given table the percentage corresponding to the given sport.

  For this, first sum all given numbers to find the total number.

  Next, divide the given number by the total number and multiply it by $100$ to give you the percentage.

  Let's have a look at an example:

  • Let the total number be $20$.
  • The number at any position is $5$.

  So we get the percentage as follows: $\frac{5}{20}\times 100\%=25\%$.

  Two circle graphs don't have a match.

  Solution

  To match each table with the corresponding circle graph, we have to determine the percentages of each sport. Then we can compare the circle graphs.

  We match the circle graphs to the tables from left to right.

  For the first table, we get the total number $20+20+40=80$ and thus the following percentages:

  • Ice hockey: $\frac{20}{80}\times100\%=25\%$
  • Soccer: $\frac{40}{80}\times100\%=50\%$
  • Baseball: $\frac{20}{80}\times100\%=25\%$

  This matches the corresponding circle graph with the same percentages.

  Now we look at the second table. The total number is $9+5+6=20$ and thus we get the following percentages:

  • Ice hockey: $\frac{9}{20}\times100\%=45\%$
  • Soccer: $\frac{5}{20}\times100\%=25\%$
  • Baseball: $\frac{6}{20}\times100\%=30\%$

  This matches the corresponding circle graph with the same percentages.

  The next table: The total number is $25+10+15=50$ and thus we can conclude the following percentages:

  • Ice hockey: $\frac{25}{50}\times100\%=50\%$
  • Soccer: $\frac{10}{50}\times100\%=20\%$
  • Baseball: $\frac{15}{50}\times100\%=30\%$

  This matches the corresponding circle graph with the same percentages.

  So there is still one table left: First, we sum the numbers to get the total number $5+8+7=20$ and calculate the percentages next:

  • Ice hockey: $\frac{5}{20}\times100\%=25\%$
  • Soccer: $\frac{8}{20}\times100\%=40\%$
  • Baseball: $\frac{7}{20}\times100\%=35\%$

  This matches the corresponding circle graph with the same percentages.