Lesson Video: Pie Charts Mathematics

In this video, we will learn how to use pie charts to analyze data, communicate information, and draw conclusions from this data.

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Video Transcript

In this video, we will learn how to use pie charts to interpret data and make conclusions. We will begin by looking at a definition of a pie chart.

A pie chart is a chart in the shape of a circle divided into sectors whose areas are proportional to the quantities they represent. The whole circle represents the whole. That is, the sum of all the sectors represents the whole or the total. If the quantities in each sector are expressed in percentages, the sum of all the sectors is 100 percent. If, on the other hand, the quantities are expressed by their central angle, the sum of all the sectors is 360 degrees. This will vary from question to question. In some cases, the numbers inside the pie chart will correspond to quantities. Other times they will be fractions or percentages. Finally, they could also be angles.

We will now look at some questions of all the different types.

The pie chart shows the results of a survey of how students travel to school. What is the most common method of travel?

The most common answer in any pie chart will be denoted by the largest sector. This is because the areas of each sector are proportional to the quantities they represent. It is clear from the pie chart that the largest sector corresponds to taxi. Therefore, this is the most common method of travel to school.

Whilst it is not required in this question, we can see from the pie chart that the sector for taxi corresponds to half of the circle. This means that one-half or 50 percent of the students travel to school by taxi. The metro sector corresponds to one-quarter of the circle. This is equal to 25 percent of the students. Whilst the actual values aren’t given, it appears that the sector for bus and walking are equal. Therefore, they correspond to one-eighth of the circle. This is equal to 12.5 percent.

We could also convert these percentages or fractions into the central angles as the angles in a circle add up to 360 degrees. The angle for taxi will be 180 degrees; for metro, 90 degrees; and for bus and walking, both 45 degrees. It is always worth checking at this point that our angles sum to 360 degrees and our percentages sum to 100.

Our next question involves interpreting the data given in a pie chart.

James works in a bookstore. He made the following pie chart to represent the sales of different types of sports books. Which book sold 17 units?

We can see from the pie chart that the bookstore sold 22 books on baseball. They sold 24 books on tennis. 17 books were sold on football. There were 18 basketball books sold. The final sector of our pie chart tells us that 19 books were sold on bowling. We’re asked which book sold 17 units. The correct answer is therefore football.

Our next question is a pie chart involving percentages.

The pie chart shows the results of a survey of what fruits students prefer. Given that 30 students completed the survey, how many students prefer peaches?

We can see from the pie chart that the percentage of students that prefer peaches was 40 percent. As there were 30 students surveyed in total, we need to calculate 40 percent of 30. There are lots of ways of calculating this. One way would be to convert the percentage into a decimal first. As the word percent means out of 100, we can convert from a percentage to a decimal by dividing by 100. Therefore, 40 percent is equivalent to 0.4. The word “of” in mathematics means multiply. We need to multiply 0.4 by 30. 0.4 multiplied by 10 is equal to four. Therefore, 0.4 multiplied by 30 is equal to 12. 12 of the 30 students in the survey prefer peaches.

An alternative method to calculate 40 percent of 30 would be to turn the percentage into a fraction. 40 percent is the same as 40 over 100, so we would need to multiply this by 30. We could simplify the fraction by dividing the numerator and denominator by 10. 30 and 10 are also divisible by 10, leaving us with four multiplied by three. Once again, we get an answer of 12 students.

A third method would be to calculate 10 percent of 30 first. We know that to find 10 percent, we divide the quantity by 10. And 30 divided by 10 is three. We can then multiply this answer by four to calculate 40 percent of 30. All three of these methods give us an answer of 12 students.

In our next question, we need to calculate the missing value in the pie chart.

The pie chart shows the results of a survey to find the most popular subject in a school. What percentage of students picked mathematics?

We know that the sum of all percentages in a pie chart is 100. This means that we can begin by adding the percentages we know: 26, 19, 16, and 15. This is equal to 76. So 76 percent of the students did not pick mathematics. In order to calculate the percentage that did, we need to subtract this number from 100. 100 minus 76 is equal to 24.

We can therefore conclude that 24 percent of the students picked mathematics. We know that this answer is a sensible one, as the sector for mathematics looks approximately one-quarter of the circle, and one-quarter is equal to 25 percent.

The penultimate question in this video involves converting percentages to fractions.

The pie chart shows the results of a survey of what fruit students prefer. What fraction of students prefer oranges or peaches?

We are told in the pie chart that 40 percent of students prefer oranges, 20 percent prefer apples, and 15 percent prefer bananas. As the sum of all our percentages must equal 100, we can begin to calculate the percentage that prefer peaches by adding 40, 20, and 15. This is equal to 75. So 75 percent of students do not prefer peaches. Subtracting this from 100 gives us 25. So 25 percent of the students prefer peaches. We want to find those students that prefer oranges or peaches. This will be equal to 40 percent plus 25 percent. 40 plus 20 is equal to 65. We can therefore conclude that 65 percent of students prefer oranges or peaches.

This is not the end of the question, however, as we were asked to give our answer as a fraction. As percentages are out of 100, this is equivalent to 65 out of or over 100. We can then simplify the fraction by dividing the numerator and denominator by five. 65 divided by five is 13, and 100 divided by five is 20. The fraction of students that prefer oranges or peaches in its simplest form is 13 over 20 or thirteen twentieths.

Our final question involves interpreting a pie chart where the central angles are given.

The pie chart shows the results of a survey in which 100 students were asked to give their favorite flavor of crisp. How many students chose ready salted?

In this question, we are given the central angle of each sector of the pie chart. We can see that 72 degrees represents ready salted. We know that the angles in a pie chart sum to 360 degrees. This means that 72 degrees out of 360 degrees represents ready salted. 72 and 360 have lots of common factors including two and nine. The highest common factor is 72. This means that we can divide the numerator and denominator by 72. As 360 divided by 72 is equal to five, the fraction 72 over 360 in its simplest form is one-fifth. One-fifth of the 100 students chose ready salted.

In order to calculate a fifth of a number, we can divide the number by five. Using the bus stop method, we can see that 100 divided by five is equal to 20. This means that the number of students that chose ready-salted crisps was 20. Whilst we’re not asked to in this question, we could use this answer to calculate the number of students for each other flavor.

The angle for chicken was the same as for ready salted. Therefore, 20 students chose chicken-flavor crisps. 144 is double 72, and double 20 is 40. Therefore, 40 students chose cheese and onion. 36 degrees is a half of 72 degrees. Therefore, 10 students chose salt and vinegar and prawn cocktail as 10 is one-half of 20. We could check our answers by finding the sum of our five values. 20 plus 40 plus 10 plus 10 plus 20 is equal to 100. As the total number of students was 100, we also know that these values are the percentages. One-fifth is equal to 20 percent. So 20 percent of students chose ready salted.

We will now summarize the key points from this video on pie charts. As mentioned at the start of the video, a pie chart is a circular chart divided into sectors whose areas are proportional to the quantities they represent. The quantities in each sector of the pie chart can be written as numbers, fractions, percentages, or angles. If the quantities are written as fractions, they must sum to one. If they are written as percentages, they must sum to 100 percent. If the central angles are labeled, they must sum to 360 degrees. The sum of the sectors must always represent the whole or the total.

As well as finding missing values and working out calculations, we can interpret and draw conclusions from any pie chart.