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Analyzing Data - Problem 1

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

A box and whisker plot is typically used to divide our data into quarters. How they actually work is, you arrange your data in ascending order, which I’ve already done here, and we look for the median. We look for the spot where there is the same number of terms on either side. In this case 1, 2, 3, 4, our median is going to lie directly between 87 and 83, so our median is going to be 85. We go to our number line and mark 85.

So then we have split or data into half, we have half on one side, half on the other. We then find the median of both of those halves. Looking for the upper half, we find the median of that, so that is going to lie in between 91 and 97. The median is just going to be the average, if it doesn’t fall directly on a number, so that gives us a median of 94. Doing the same thing on the other side, we end up with the median directly between 76 and 82, giving us a median of 79.

What we do here is we draw two boxes. We draw a box from our 85, our centre median up until 94, which will be right in here and also one from the 85 down to the 79, which is going to be right around in here. Each of these represents a quarter of the data.

We then draw a line segment from the end of the box to the last point of data, so we draw from our 94 to our 98. It will be something like this, and then from the 79 down to the 70. It’s called a box and whisker plot because you have these boxes and then those little lines look like whiskers. And how this comes in handy is, a quarter of our data comes into play in each of these regions. This is the lower quarter. This is the second lower quarter, this is the top upper quarter and the upper quarter. Often times you’ve heard these referred to as quartiles.

Basically all a box and whisker plot does is, divide your data up into quarters. You have lower quarter, upper quarter and two in between, and we find it just by finding the medians of the whole thing and then divvy up each of the halves into medians as well.

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