The purpose of this Warm-up is to encourage students to review how to calculate mean and median.

Some students may forget to sort the data when finding the median. Ask them, “What is a median? What does it tell you about the data?” Some students may not remember how to find the median when there is an even number of data values. Ask them, “What does the median tell you about the data? How could we find a middle number between these two values?”

The goal of this activity is to review how to calculate mean and median and to identify common mistakes in the calculation of mean and median. In the discussion, ask students to recall what information the mean and median reveal about the data.

• “What does the mean tell you about the data?” (On average, where the center of the data is.)
• “What does the median tell you about the data?” (Half of the numbers are greater than or equal to the median, and half are less than or equal to the median.)

Some common mistakes to avoid:

• Not putting the numbers in order when finding the median.
• If two numbers are in the middle, not adding them and dividing by two to find the median.
• Finding the middle number on the horizontal axis rather than in the data.
• Rounding the mean or median (if it must be calculated) to the nearest whole number.

The purpose of this activity is to get students to calculate the median and IQR, and to investigate how those values are affected by outliers.

The data sets in this lesson are small enough that finding summary statistics like measures of center or measures of variability are not necessary. The entire data set could be assessed fairly easily and does not need further analysis. The sets are small here for the purposes of practicing calculating and understanding the statistics. In reality, finding such statistics are much more useful when the data set is much larger. For example, some devices will find heart rate every 10 minutes, giving more than 1,000 values for a week, which might be analyzed to determine health information about a person. It would be difficult to understand all of the data by looking at a table or even a data display. Having some summary statistics, such as mean or median, would be useful to understand a person’s heart rate for the week.

In this activity, an optional graphic organizer is provided in the blackline master to help students compute the interquartile range. The boxes that are shaded are not to be used, and the position of the open boxes are meant to highlight the useful data for calculating the value for the row. For example, to compute the first quartiles, students use the average of the second and third values, so those boxes are left open to indicate that this data are useful.

The purpose of this activity is to get students to calculate and describe the mean absolute deviation. Students are given a data set and an organizer for calculating the MAD. Then they consider questions that are intended to get them thinking about MAD more conceptually as a measure of variability.