Minds On

Examining a set of data

What conclusions can we make from the mean, median, and mode of a data set?

An image of a baker putting sprinkles on cupcakes topped with vanilla cream.

Use the following questions to explore a set of data that represents the number of cupcakes sold at a bakery to nine customers. Throughout this learning activity, you can record your thoughts digitally, orally, or in print.

  • The mean number of cupcakes sold is nine.
  • The median number of cupcakes sold is seven. Knowing only this information, what conclusions can you make?
  • The mode of the cupcakes sold is two. Knowing only this information, what conclusions can you make?

Now that you have the mean, median, and mode of the data set you explored in the previous section, check out the following list of cupcakes sold at the bakery:

2, 2, 2, 3, 7, 8, 14, 17, 26

  • Does the actual data match some of the conclusions you made using the mean, median and mode?
  • What does this tell us about the measures of central tendency and how they can tell the story of the data?

Action

Task 1: Let’s reflect

Image is decorative so no alt is needed.

Review the data from the Minds On. Which measure of central tendency is the most appropriate measure used to describe the data? Explain your thoughts.

Task 2: What is an outlier?

An image of a graph on a tablet showing an outlier that falls away from all the other data points.

A data value or a data point that exists outside the overall pattern of the data is called an outlier. It’s important to identify potential outliers because they can influence the mean, median, and mode

Let’s explore how outliers can affect a data set.

Let’s go shopping

Examine the following data set. The amounts represent the cost of the items purchased at a store over a one hour time period.

$9.00, $9.50, $15.50, $15.50, $20.50, $29.00, $89.25

Respond to the following prompts to explore how an outlier can affect a data set.

  • Determine the mean, median, and mode of this data. Record your responses using a method of your choice.
  • Notice that the outlier in the data is $89.25. It is an outlier because it is so much higher than the other amounts. Eliminate the outlier and calculate the mean, median, and mode again.
  • Describe how the mean, median, and mode changed when you removed the outlier. Record your thoughts.

Outliers affect the mean value of the data but have little effect on the median or mode of a given set of data.

Press ‘Answers’ to reveal the sample solutions.

  • The mean of the data set is $26.89 - the sum ($188.25) divided by the number of numbers (7).
  • The median of the data set is $15.50.
  • The mode of the data set is $15.50.
    • If the outlier is removed, the data set would be: $9.00, $9.50, $15.50, $15.50, $20.50, $29.00
    • The mean would be the sum ($99) divided by the number of numbers (6). The mean is $16.50.
    • The median of the new set would be $15.50.
    • The mode would be $15.50.
  • The median and mode didn’t change when I removed the outlier. The mean became a value that was more like the other numbers in the set and more like the median and the mode. Before, the mean was way off the other measures of central tendency and was even higher than almost all the values in the data set, except the largest value.

Extend your understanding

If the store owner wants to get an idea of how much money was spent over that one-hour period, what would the most appropriate measure of central tendency be, the mean, the median or the mode? Explain your thoughts.

Consolidation

Task 1: Reflect and connect

Use the following questions to reflect on your learning.

Explain your thoughts and record your responses using a method of your choice.

  • Does mean, median, or mode always represent the data in the most appropriate way?
  • When might median be a more appropriate measure than mean?
  • If you were making conclusions about numerical data, which would you try to find first: mean, median, or mode?

Task 2: Collect data and make conclusions

  • Research and find a data set that contains at least ten values (e.g., sports data, sales data, etc.)
  • Determine the mean, median, and mode of this data set.
  • Determine which measure of central tendency best represents your data set.

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.

Independent practice

Complete the Data Set Worksheet in your notebook or using the following fillable and printable document.

Press the ‘Activity’ button to access the Data Set Worksheet.

Activity (Open PDF in a new window)