Circle/Pie Graphs and Review: Mean, Median, Mode

Circle/Pie Graphs

What are they?

A pie chart, also known as a circle chart, is special chart that uses “pie slices” to show relative sizes of data.

Example 1

The first 200 visitors to a state park were asked about their favorite park activity. The results are shown in this circle graph.

Which of the following is closest to the number of these 200 visitors who was hiking was their favorite activity?

A. 25 visitors

B. 40 visitors

C. 50 visitors

D. 75 visitors

In order to tackle problems with pie charts, we must able to understand the relative sizes of the pie slices. Camping takes up approximately 40%, hiking and swimming both around 25%, and fishing around 10%. We can make this estimate since the swimming slice and hiking slices both make 90 degree angles (a circle is 360 degrees so 90 degrees is 25% of the circle). The question is asking for hiking, and since hiking is 25% of the total, 200, our answer is 50 visitors.

Answer: C. 50 visitors

Example 2

The sixth-grade class held elections for class president. This graph shows the results of the election.

Create a circle graph that represents the same set of data.

From the graph, we can estimate that Haley had 45 votes, Ishmael had 80 votes, Juan had 45 votes, and Rema had 120 votes. In total, this is 290 votes.

Next, we can divide each value by the total in order to find what percent of the pie chart it will represent. Haley is 45/290 = 16%, Ishmael is 80/290 = 28% , Juan is 45/290 = 16%, and Rema is 120/230 = 41% (These percentages add to over 100% due to rounding).

Then, to figure out how many degrees for each “pie slice”, we multiply each percentage by 360 (for the degrees in a circle)/ Haley’s slice is 58 degrees, Ishmael is 101, Juan is 58 degrees, and Rema is 148 degrees (again, this number is slightly above 360 due to rounding).

Using the angle measurements and a protractor, the pie chart should look like the following:

Review: Mean, Median, Mode

What are they?

Mean - another word for “average”

Median - the “middle value” in a list of numbers

To find the median, the numbers you are working with most be listed from smallest to largest

Mode - the value that occurs most often

If no number in a list is repeated, there is no mode

There can be multiple modes in a list of numbers

Example 1

Find the mean, median, and mode for the following list of values:

13, 18, 13, 14, 13, 16, 14, 21, 13

  • Mean

    • To find the mean, simply add all the numbers and divide by the total of numbers in the list. In this case, the mean is (13+18+13+14+13+16+14+21+13)/9 = 15

      • Answer: Mean = 15

  • Median

    • To find the median, we need to reorder the numbers from smallest to largest like this: 13, 13, 13, 13, 14, 14, 16, 18, 21

    • Since there are 9 numbers, we know that the middle value will be the 5th number

      • Answer: Median = 14

  • Mode

    • The mode is the number that is repeated the most often in a list. The number 13 shows up the most in our list (4 times).

      • Answer: Mode = 13

Example 2

This list shows the number of text messages 5 friends sent last week: 13, 60, 61, 63, 64. The most appropriate measure of center for this data is the...

A. Mean because all the numbers are close to one another in value

B. Median because all the numbers are close to one another in value

C. Mean because 13 text messages is much lower than the other numbers

D. Median because 13 text messages is much lower than the other numbers

Generally, when there is a number in a list of values that is significantly smaller or larger than the other numbers, it is a good idea to use the median. This is because the median ignores the extremes and focuses on the “middle” values. In this case, D is the best answer choice, because it addresses how 13 text messages is much lower than other numbers 60, 61, 63, and 64.

Answer: D. Median because 13 text messages is much lower than the other numbers

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