Median: The middle of what? Grade 10’s misconceptions

Teaching the concept of median to my grade 10 class on Thursday 21/08/2014 I made the following interesting observation:

How the problem became evident:

I was trying to explain why it is important to divide the data into two equal parts and made the following drawing:

Median

Me: “This is two different sets of data with two different medians. What is the difference between the two sets of data if we look at the median?”

And I am waiting for an answer. (The data is spread evenly for the fist one but more “clustered on the left / more spread on the right for the second set.)

Me: ” Ok, here’s a hint for you: remember the median divides 50% of the data to it’s left and 50% of the data to it’s right. Now, what is the difference between the two sets of data if we look at the median?”

Again a great silence! And then it hits me: “So who of you feel that the first line is correct and the second line were drawn correctly?”

And almost all the hands went up.

Me (already anticipating the answer): “Why is it wrong?”

A learner: ” The median is not in the middle.”

The problem:

Learners view the median as the middle and in line 2 the median is not in the middle. The challenge is to let them understand that the middle of the data is not always the middle between the minimum and maximum.

How I addressed the issue:

I then complete a survey of their shoe sizes as follow:

Median2

 

This helped them to see that median is the middle of the data and do not have to be the middle of the line.

Please share more ideas.

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