Explore 5 – Interpreting a Pie Chart

The pie chart shows the percentage distribution of the Food and Drug Administration's (FDA) Budget to different programs for the fiscal year 2021. The total budget amount was $6.1 billion.

FDA FY 2021 Budget by Program

Pie chart showing how the FDA's $6.1 billion budget for fiscal year 2021 is allocated across programs including Human Drugs, Foods, Medical Devices, Biologics, Tobacco, Animal Drugs & Feeds, and Toxicological Research.

1. What is the sum of the percentages on the pie chart?

Solution: Adding all the percentages, it is 101%. The percentages on a pie chart must sum to 100%, so this difference must be due to rounding the percentages shown on the chart.

2. Which program received the most money? How much did it receive?

Solution: Human Drugs has the largest slice and received 33% of the funding: 33% of $6.1 billion = 0.33($6.1 billion) = $2.013 billion.

3. Which program received the least money? How much did it receive?

Solution: The smallest slice represents Toxicological Research that received 1.1% of the funding: 1.1% of $6.1 billion = 0.011($6.1 billion) = $0.0671 billion =$67.1 million.

4. How much money was designated for Foods?

Solution: Foods was allocated 18.4% of the budget: 18.4% of $6.1 billion = 0.184($6.1 billion) = $1.1224 billion.

5. How much money was designated for Tobacco?

Solution: Tobacco was allocated 11.3% of the budget: 11.3% of $6.1 billion = 0.113($6.1 billion) = $0.6893 billion =$689.3 million.

6. How much more money did Human Drugs receive than Foods?

Solution: Human Drugs received 33% of the budget, while Foods received 18.4%. That's a difference of 33% – 18.4% = 14.6% and 14.6% of $6.1 billion = 0.146($6.1 billion) = $0.8906 billion =$890.6 million.

7. A student claims that 1/3 of the money was designated for Human Drugs. Is the student's claim correct? Explain your reasoning.

Solution: 33% = 0.33, while 1/3 = 0.33333…, so since these are very close and the percentages on the pie chart are rounded, the student is correct.

Explore 6 – Interpreting Pie Charts

The two pie charts show the water use percentages of different categories in Utah. The first pie chart shows all categories of water use in Utah. The second pie chart shows all categories of non-irrigation water use.

Utah Water Use (All Categories) and Non-Irrigation Water Use

Two pie charts side by side. The first shows all categories of water use in Utah, with irrigation comprising 81%. The second breaks down non-irrigation water use, with residential use comprising 51%.

1. What percentage of Utah water is used for non-irrigation?

Solution: Irrigation uses 81% of Utah's water leaving 100% – 81% = 19% for non-irrigation use.

2. What percentage of non-irrigation water is used for non-residential purposes?

Solution: Residential uses 51% of Utah's non-irrigation water leaving 100% – 51% = 49% for non-residential purposes.

3. True or False (Justify your answer): The residential water use is about 1/2 of the non-irrigation water use in the second pie chart. Therefore, the percentage of residential water use should be about half of the non-irrigation water use in the first pie chart.

Solution: True. The blue slice representing Residential use of non-Irrigation water on the second chart is 51%, which is very close to 1/2 = 50%. Also, the percentage of non-irrigation water use is 19% according to the first pie chart. Since residential water use is half of the non-irrigation water use according to the second pie chart, half of 19% is 9.5%, which is close to 10%, which matches the residential water use percentage in the first pie chart.

4. If Utah were to cut its water use, which sector should be mandated to cut its water use? Explain your reasoning.

Solution: 81% of all water goes towards irrigation. That is the first sector that should be cut. 51% of the non-irrigation water is used by residential customers. That could also be cut to save water.

Explore 7 – Interpreting a Histogram

U.S. Box Office Revenue (2012–2021)

Histogram showing box office revenue in billions of dollars for each year from 2012 to 2021. Each bar is labeled with its revenue value.

The histogram shows the box office revenue for movies in the US from 2012–2021 in billions of dollars.

1. Which year had the lowest box office revenue?

Solution: The lowest revenue is shown by the shortest bar, which is $9.7 billion in 2014.

2. Which year had a box office revenue of $10.9 billion?

Solution: We look for the bar that has 10.9 written near the top: 2019.

3. What is the mode of the revenues?

Solution: We have to look at the revenues and decide which revenue occurs most often: 10.7 occurs in 2016 and in 2018, so the mode is $10.7 billion.

4. What is the median revenue?

Solution: The median is the middle value so we order the revenues from lowest to highest: $9.7;\ 10;\ 10.2;\ 10.4;\ 10.6;\ 10.7;\ 10.7;\ 10.9;\ 11.1;\ 11.3$ Since there are 10 values, the median will be halfway between the 5th and 6th data values: $\frac{10.6 + 10.7}{2} = 10.65$ The median revenue is $10.65 billion.

5. Is a histogram the appropriate graph to illustrate this data? Explain your reasoning.

Solution: Each bar represents the sum of all box office revenues across the US per year so is a calculated amount (continuous) that has been rounded to a tenth of a billion dollars. Year represents time, which is continuous. So a line graph would be an appropriate graph.

Reflect

A student claims that each bar in a bar graph is a data point, where the value associated with a bar is the value of the data point. Do you agree? Explain your reasoning.

Practice Example

Incarceration Rates: Utah, U.S., and NATO Countries

Bar graph comparing incarceration rates per 100,000 population for Utah, the United States, and other founding NATO member countries. Utah and the U.S. are highlighted as outliers.

1. What does this bar graph show?
2. Why does the box around most of the countries exclude Utah and the United States?
3. Why is Utah shown in orange?
4. Which country has the lowest incarceration rate?
5. How many times higher is the US incarceration rate compared to the Utah rate?
6. How many times higher is the US incarceration rate compared to the Canadian rate?
7. What is the median rate of incarceration for NATO countries?

This chapter is adapted from Numeracy by Utah Valley University, licensed under CC BY-NC-SA 4.0.