Infectious Respiratory Disease

Teaching Activities

Mean, Median, Mode, and Range

Part 1: Mean, median, mode, and range are common concepts used in math, science, and daily life to present data. Students need an understanding of these concepts to understand and interpret data, make informed decisions, and solve real world problems. The following activities will be completed over multiple class days.

Students will first need to understand the vocabulary being used. While they have seen this vocabulary in multiple grades previous to high school, I find they do not generally remember them and rarely remember the required process for calculations. The first activity will introduce students to the vocabulary, concepts, and basic calculations with numbers smaller than those that will be used throughout other activities. Students will be randomly given a playing card. On the board, there is a chart with four columns labeled Summer, Spring, Winter, and Fall. I will tell students that we are pretending there is a new highly contagious respiratory virus. The suit of their card will tell in which season they contracted the virus: Summer=heart, Spring=diamond, Winter=spade, Fall=club. We will create a class graph displaying how many students “contracted the virus” in each season. Make sure to explain to the students that this is NOT how real viruses spread, randomly and with 100% infection rate, but that we are just doing this to start with small numbers. 

Introduce the following terms, their definitions, and perform the calculation using the values from the graph in the previous step.

Mean- the average of a set of numbers

Add all the numbers and divide them by the quantity of numbers.

Median - the middle number in a sorted set of numbers

Order all the data from least to greatest and find the middle number

Mode- the number that appears most frequently in the number set.

Range -  the difference between the highest and lowest numbers

Subtract the smallest number from the largest number.

Outlier - data point (number) that is very different that the others

When students have had trouble with this in the past, I’ve listed the ages of everyone in the classroom, including myself and then pointed out how my age is the outlier. This demonstration can be extended by finding the mean, median, and mode of the age data and demonstrating how my age makes the mean much further from their ages, while the mode and median stay similar.

Mean, median, and mode all show centering of data in different ways. It is important to note differences in each of these values and discuss what could be causing them to be higher/lower than the others. Mean is heavily influenced by outliers while mode and median are not as impacted.

Now that students have worked through a simple example with me, they will work with me to determine the mean, median, mode, and range of the values on the following chart.

Figure 1: Number of new cases of coronavirus (COVID-19) in the United States from January 20, 2020 to November 11, 2022, by week (World Health Organization, 2022)¹⁰

Before finding the actual numbers, have students note patterns and trends they notice. Are there any obvious outliers? Point out the exceptionally high numbers of January and February 2022. Why do students suppose these weeks were so high? Point out that this is a time of the year when infectious respiratory diseases like the flu are often high and so it makes sense that COVID-19 would also follow that pattern. Also, community wide strategies, like quarantine and wearing masks, were no longer common which likely kept the January and February 2021 numbers from being as high. 

We will choose the first date range, January 2021-December 2021. Create a table of the chosen data. I will walk through the steps allowing students time to find the answer and then check them against my answers.

Groups of students will determine the mean, median, mode, and range of March 2020-October 2022 and once the group agrees on their answers, will check with the teacher.

Part 2: Now that students have found these data pieces, they will do some research to determine the effectiveness of masks in preventing infectious respiratory disease. Since masks are more effective in the prevention of influenza, we will find those data points. Students will be challenged to find the number of confirmed flu cases in the 2019-2020, 2020-2021, and 2021-2022 flu seasons, by month. They will then determine the mean, median, mode, and range of each of these seasons and of all of them as a combined data set.

When looking at bar graphs of these three flu seasons, it is obvious that there is a significant drop in the amount of flu cases from the 2019-2020 flu season to the 2020-2021 season. Discuss with students what they believe could have contributed to this dramatic change. Point out that by the 2020-2021 season, most public places and schools (at least here in Texas) were open, so while some people may have still been in quarantine, most were not. What else could have led to the decrease in cases? Most people were still being required to wear masks in public. Not only did it slow the spread of COVID-19, but it slowed the spread of influenza.

Part 3

Students will create box plots of their data. Box plots tend to be more difficult for students than many other displays. This is likely because we do not see them much outside of the science and math communities. But there is a reason that these academic areas use these particular charts. They mitigate some of the effects of outliers. They do not completely discard the outliers, but place emphasis on the second and their quartiles of data.

A box plot is a visual representation of a data set's 5 figure summary. The following terms will need to be explicitly taught.

Minimum- smallest data point in the set

First Quartile (Q1) - the point that separates the lowest 25% from the rest of the data set

Second Quartile (Q2) -also called the median of the data set, divided the lower 50% and the higher 50%

Third Quartile (Q3) - the point that separates the highest 25% from the rest of the data set

Maximum - the largest number in a data set

How to create a Box plot.

1. Order all data points from smallest to greatest.
2. Identity the minimum (smallest) and maximum (largest) and place them on the number line (see figure 2)
3. Determine the median of the data set and label its position on the number line as well.
4. Determine Q1 by finding the median of the lower half of the data set, all the points from the minimum to the median. Label this Q1.
5. Determine Q3 by finding the median of the larger half of the data set, all the points from the median to the maximum. Label this Q3.
6. Draw a box on the number line that begins at Q1 and ends at Q3.  (See Figure 2)

Figure 2: A box plot is a visual representation of a data set dividing the data into sections each containing approximately 25% of the data points.¹¹

Explain to students that box plots are important because they visually display the distribution of data. Sources will often talk about the average or the median as these single figures are easy to understand and quick to communicate, but they really don’t tell the whole story. If students are able to either find or create a box plot of the data, they have access to an even greater understanding of the information presented to them.

Part 4

Students have had the chance to look up data and talk about it in terms of mean, median, mode, and range. Now we need to talk about the sources from which we get our data. Students see most of their news on social media and, to a lesser extent, television. They need to think critically about the source/person posting the data and the organizations that the data came from originally. Sometimes graphics are made up and posted with no actual research to back them up.

Depending on student level, this activity can be assigned to individual students, student groups, or as a whole group activity. For my foundational level students, we will work as a class.

Ask Google or another search engine “What percentage of people wore face masks in 2020?” and select the image results. (If a teacher is concerned about what might pop up in the search they could create a list of links to images or compile images on a document to display.) Choose different graphics and ask students what they notice. Point out where the source is listed and how they can find out more about the source. Remember, that even if a graphic says that data is from a reputable source, such as the Center for Disease Control (CDC), if it was not published directly from that organization, it is a good idea to fact check. With increased social media usage, false information is more easily spread, even unintentionally. People often share posts without fact checking them. Demonstrate ways of fact checking a post or statistic shared. Did it site a source? Is it a reputable source? Can we verify if the source actually released that data?

Alternatively, the teacher could find the posts ahead of time and display them on slides (with links) for the students. This would be an effective way to steer them to accurate posts, false posts, and posts that are technically true but misleading in the way they were presented. The sides should include information about where they were published (facebook, instagram, etc) and by whom.