## Lesson: Mean, Median, and Mode

Developing the Concept

Now that you've introduced your students to what happens when outliers or new data are added or deleted from a data set, it is time for them to explore this further on their own. Continue to stress the use of proper vocabulary during the lesson.

**Materials:** pencil and paper for each student

**Wrap-Up and Assessment Hints**

One way to deepen students' understanding of mathematical concepts is to ask them open-ended questions instead of closed questions. For example, we usually give students a set of data and ask them to find the mean, median, and mode of the data. Instead, we should open up that question by asking students to find 10 numbers that have a mean of 35, a mode of 33, and a median of 36. The answer is not unique and requires students to have a firm grasp of the three concepts. Have students explain how they got their answer. A sample answer follows.

Since the mean is 35 and there are 10 numbers, the sum of all the data points must be 10 x 35, or 350.

Since the mode is 33, I decided to have three 33s in my data set and make sure no other number was repeated more than twice.

33, 33, 33Since the median is 36, I know the average of the fifth and sixth numbers is 36, so I made them both 36.

33, 33, 33, 36, 36Four of the five remaining scores have to be greater than 36, and one has to be less than 36. I added the numbers 37, 37, 38, and 39 to the set.

33, 33, 33, 36, 36, 37, 37, 38, 39Since the sum of these 9 numbers is 322, the remaining number must be 28 if the mean is to be 35.

28, 33, 33, 33, 36, 36, 37, 37, 38, 39