Minds On

Analyzing graphs

Analyze the following two graphs. They both show the gold, silver, and bronze medals won in the 2018 winter Olympics in two different countries. Country A has 11 gold, eight silver, and 10 bronze. Country B has nine gold, eight silver, and six bronze.

What do you notice about the graphs? Justify your answers using evidence from the graphs. Which measure of central tendency can you use to explain the data?

Which measure of central tendency (mean, median, mode) can you use to explain the data? Now, also consider the 2016 Summer Olympics medal counts for these two countries. Country A had four gold, three silver, and 15 bronze medals. Country B scored 46 gold, 37 silver and 38 bronze medals.

This bar graph is titled Country A. The x-axis is labelled type of medal and the y-axis is labelled number of medals. The bar for gold is 4 medals high, the bar for silver is 3 medals high and the bar for bronze is 15 medals high The second bar graph is titled Country B. The x-axis is labelled type of medal and the y-axis is labelled number of medals. The bar for gold is 46 medals high, the bar for silver is 37 medals high and the bar for bronze is 38 medals high.

What do you notice about these two graphs? Justify your answers using evidence from the graphs.

What statements can you make about all 4 graphs?

Did any of the data surprise you?

Which measure/s of central tendency can you use to explain which country performed better?

Throughout this learning activity, you can record your thoughts digitally, orally, or in print.

Action

Measures of central tendency review

For each measure of central tendency, describe when and how it is used as well as how to calculate it. Use the Measure of Central Tendency Organizer in your notebook or use the following fillable and printable document to organize your ideas.

Measure of Central Tendency Organizer

Mean

Median

Mode

Press the ‘Activity’ button to access Measure of Central Tendency Organizer. 

Activity(Open PDF in a new window)

Press the ‘Hint’ button to check your answers.

Mean is the average of a data set. It is found by adding all the numbers together in a data set and dividing by the amount of numbers in the set.

Median is the value that falls in the middle of the data set when all of the numbers are in consecutive order. If there is an even amount of data and two numbers fall in the middle, the average of those two numbers is calculated.

Mode is the most frequently occurring number in the data set.

Record your responses in a method of your choice.

  1. What do the measures of central tendency tell us about a data set?
  2. How can we use the measures of central tendency to compare different sets of data?

Using measures of central tendency to compare data

Each measure of central tendency gives a representation of the data set in one term. Mean, median, and mode are used at different times and for different reasons, but they will all represent the data set. If you are comparing two different graphs or two different data sets, you can create a representation of each data set to compare.

Let’s compare the following graphs. Both graphs show the number of plays/streams for two popular songs on a music app each week.

After examining the graph, which song do you think is more popular? Why?

Now, let’s determine some of the measures of central tendencies to directly compare them.

Press ‘Mode’ to reveal a hint.

There is no mode because none of the data set is repeated for either song.

Press ‘Mean’ to reveal a hint.

Calculate the mean for each song. Which one is higher?

Press ‘Median’ to reveal a hint.

Determine the median for each song. Which one is higher?

Based on comparing the measures of central tendency, which song do you think is better or more popular? Has your answer changed now that you used more information?

These two graphs or data sets can be easily compared because they both have the same number of terms in the data set. They are also looking at the exact same population (listeners of the same music app).

Reflect on the following questions and record your responses in a method of your choice.

  1. Could you compare these songs using the measures of central tendency if Song A only had data for 5 weeks, while Song B had data for 10 weeks?
  2. Could you compare these songs using the measures of central tendency if the data for each song was determined from a different music app?
  3. Could you compare these songs using the measures of central tendency if both 1 and 2 were true?

Your best and most appropriate comparison will always be when there is the same number of terms and the same population. As those variables change, data becomes a bit more difficult to compare.

Results may be drastically different depending on sample size. If you ask three people what their favourite song is, it is a lot more likely for everyone to have the same answer than if you ask 15 people what their favourite song is. The accuracy of data may be affected by the number of responses. However, mean helps to account for this a little bit because it incorporates the number of terms into the calculation. It is OK to compare data sets with a different number of values if the population is the same.

Results may be drastically different depending on sample size. If you ask three people what their favourite song is, it is a lot more likely for everyone to have the same answer than if you ask 15 people what their favourite song is. The accuracy of data may be affected by the number of responses. However, mean helps to account for this a little bit because it incorporates the number of terms into the calculation. It is OK to compare data sets with a different number of values if the population is the same.

Compare graphs

Analyze the following graphs and determine the mean, median, and mode to compare the graphs.

The graphs show the number of participants in a park cleanup for the given years by School A and School B. What conclusions can you draw? Are you able to appropriately compare these graphs even though they are focusing on different populations?

Analyze the following graphs and determine the mean, median, and mode to compare the graphs. This time there are three data sets to compare. The graphs show social media usage for three diverse age groups within City A. What conclusions can you draw? Are you able to appropriately compare data even though there are a different number of values in each data set?

Consolidation

Animal tracking

A conservation group tracked animals that were spotted in a local forest during the winter months. The results from five days of data gathering were graphed.

What conclusions can you draw from this graph?

Determine the measures of central tendency and decide which of the measures best represents the data. Why?

Reflection

Reflect on and answer the following questions:

  1. Why is it important to use the measures of central tendency to compare different graphs?
  2. Which measure of central tendency do you believe best represents a set of data? Explain your thinking.
  3. What skills are you practicing by analyzing and comparing different graphs and data sets?

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

I feel…

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.

Connect with a TVO Mathify tutor

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