Introduction

In this lesson, you will learn how to interpret pie charts. First, what is a pie?

A pie is a food dish that usually contains either fruit, meat, or vegetables and has a bottom and sometimes a top made out of pastry. It is usually round and divided into triangle-like slices, starting from the center to the outside edge. The picture above is of a pumpkin pie.

This video illustrates the lesson material below. Watching the video is optional.

• Interpreting Pie Charts (09:04 mins) | Transcript

What is a Pie Chart?

A pie chart is a round graph that uses pie-shaped wedges to represent percentages of the whole. The entire pie chart is equal to 100%. The bigger the slice in the pie chart, the higher percentage of the whole it represents. The smaller the slice in the pie chart, the lower percentage. Here is an example of a pie chart:

Figure 1

This chart represents the favorite colors of a group of people. The largest percentage of people represented like the color blue, and the smallest percentage of people like the color yellow. This does not tell you how many people like blue, it just tells you that most people like blue.

Interpreting Pie Charts

Example 1
This pie chart shows 50% gold and 50% blue.

Figure 2

One possibility is that this pie chart could represent 2 gold things and 2 blue things; a total of 4 things.

Figure 3

The percent of blue things was found by taking \(2÷4=0.5\) or 50%. The percentage of gold things was found the same way: \(2÷4=0.5\) or 50%. These percentages are represented by the pie chart included above.

However, the same pie chart could also represent a scenario with 10 gold things and 10 blue things; a total of 20 things.

Figure 4

Once again, the percent of gold things is \(10÷20=0.5\) or 50%, which is also the same for the blue things. As you can see, the same pie chart can represent different data because the percentages are the same in both examples.

What this pie chart really shows is that compared to 100 total objects, fifty of them would be gold, and fifty of them would be blue, but that does not necessarily mean that you have 100 objects.

Example 2
This example represents a group of data with more variation: there is 10% green, 20% blue, 30% gray, and 40% gold.

Figure 5

This is a representation of objects where you have a total of ten objects: one is green, two are blue, three are gray, and four are gold.

Figure 6

One out of ten is green, meaning \(1÷10=0.1\) or 10% are green. If you follow this same pattern for each section, you will get the results displayed on the pie chart above:

• \(1÷10=0.1\) or 10% are green.
• \(2÷10=0.2\) or 20% are blue.
• \(3÷10=0.3\) or 30% are gray.
• \(4÷10=0.4\) or 40% are gold.

Even though this data is represented by the pie chart, as you saw in the previous example, this same pie chart could actually be created using different amounts of data. For example, instead of only 10 items, there could be 20 items.
 

Figure 7

Now there are two green, four blue, six gray, and eight gold. To get the percentages, follow the same pattern as above:

• \(2÷20=0.1\) or 10% are green.
• \(4÷20=0.2\) or 20% are blue.
• \(6÷20=0.3\) or 30% are gray.
• \(8÷20=0.4\) or 40% are gold.

Even though the amounts are different, the percentages are the same, so the data is still represented by the same pie chart used when there were only 10 items.

Example 3
All kinds of data can be compared and represented with a pie chart. The pie chart below represents Daniel’s daily activities. Daniel tracked all of the things he did in one day and calculated the percentages of time that he spent on each activity.

Figure 8

In this example, Daniel spent 25% of his time asleep. This means that out of a 24-hour day, 25% of that time was spent on sleep. In this pie chart, all of the percentages are included on each wedge, except for the brown piece, which represents Time with Family and Friends. Even though you do not have the percentage of this wedge, you know that the total of all the wedges adds up to 100%. If you add up all of the percentages you do know, and then subtract that total from 100, you will be able to find the percentage of Daniel’s day he spent with his family and friends.

\begin{align*} 25\%+1\%+4\%+5\%+35\%+15\%+6\% &=91\% \end{align*}

\begin{align*} 100\%−91\% =9\% \end{align*}

From this equation, you determine that the missing percentage was 9%. Now you know that Daniel spent 9% of his time with his family and friends.

There are other things you can learn from this pie chart as well. You can compare how much time Daniel spent on each of these activities, determining what he spent the most time on, or the least time on. For example, Daniel spent most of his time working.

Things to Remember

• Everything on a pie chart should add up to 100%.
• Even though a pie chart represents 100%, it does not always represent 100 things. It can represent any number of things.
• Pie charts can help you compare information.

Practice Problems

 

1. When compared to the other activities, in what activity does Daniel spend the greatest portion of his time? (
   Solution

   x

   Solution: Work
   
   Details:
   Daniel spends more time working than he does in any other activity. He works 35% of the time. 35% is greater than any other percentage illustrated on the graph.
   
   Suppose you divided the day into 100 equal parts, Daniel would spend 35 of those working. If you considered all of Daniel’s time in a day, it would be 100% of his time. He spends 35% of his time working.
   )
2. On what activity does Daniel spend the least amount of time? (
   Solution

   x

   Solution: Shower and Dress
   
   Details:
   The smallest slice of the pie chart represents the percentage of time Daniel spends showering and dressing. The chart indicates that Daniel spent 1% of his day doing these things.
   )
3. What percentage of time does Daniel spend either sleeping or working? (
   Solution

   x

   Solution: 60%
   
   Details:
   The total percentage of time Daniel spends either sleeping or working can be calculated by adding the percentage of time he spends sleeping to the percentage of time he spends working. Daniel spends 25% of his time sleeping and 35% of his time working. Combining these, you get:
   
   \(25\% + 35\% = 60\%\).
   
   Notice that more than half of his time is spent either sleeping or working. Half of his time would be represented by 50%. Since 60% is greater than 50%, he spends more than half of his time either sleeping or working.
   |
   Video Solution

   x

   
   (Pie Charts #3 (00:35 mins) | Transcript)
   | Transcript)
4. What percentage of time is Daniel with family and friends? (
   Solution

   x

   Solution: 9%
   
   Details:
   If you think about all the things Daniel can do in a day, all of this time must add up to 100%. When you think in terms of percentages, 100% represents the whole (or the entire amount.)
   
   Daniel spends 25% of his time sleeping, 1% showering and dressing, 4% in scripture study and prayer, 5% traveling, 35% at work, 15% cooking and eating, and 6% doing homework. Add these together to find the total percentage of time he spends on these activities:
   
   \(25\% + 1\% + 4\% + 5\% + 35\% + 15\% + 6\% = 91\%.\)
   
   The entire day is represented by 100%. So, if a full day is 100%, and 91% of the time is spent on other activities, the amount of time Daniel spends with family and friends:
   
   \(100\% − 91\% = 9\%.\)
   )
5. How many hours does Daniel spend at work? (
   Solution

   x

   Solution: 8.4 hours
   
   Details:
   In a full day, there are 24 hours. This represents 100% of the time Daniel has. The portion of the day that Daniel spends at work is 35%.
   
   You want to know what portion of Daniel’s day is spent at work. In math, including with story problems, the word “of” can be a hint that you need to multiply. Notice what happens when you express the sentence “Daniel spends 35% of 24 hours at work.” In this case, the word “of” suggests multiplication.
   
   You can convert this percentage to hours by multiplying 35% by 24 hours. Before you do this multiplication, it is helpful to rewrite 35% as 0.35.
   
   Divide 35 by 100 to get 0.35. (Note: 35% and 0.35 are two ways to represent the same value.)
   
   Multiply this by the total number of hours in a day:
   
   \(0.35 × 24\) hours = \(8.4\) hours.
   
   Daniel spends 8.4 hours each day at work.
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   Video Solution

   x

   
   (Pie Charts #5 (01:03 mins) | Transcript)
   | Transcript)

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