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.
