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Video: Finding the Median of a Data Set

Tim Burnham

The points that each player scored during a basketball game are shown in the table. Find the median of the points scored.

02:23

Video Transcript

The points that each player scored during a basketball game are shown in the table below. Find the median of the points scored for each player. And we can see that Patricia scored four points, Donna scored ten, Helen scored seventeen, Bonnie scored eight, Lisa scored fifteenth, and Laura scored fourteen.

Now the definition of the median in this question would be is if we lined up all the scores from smallest to the biggest which would be the one bang smack in the middle. It’s an attempt to be a measure of the most typical piece of data for that data set, so not one of the extremes, not the biggest not the smallest, but the one that’s most in the middle. So the first thing that we need to do is to put all of these numbers in order from smallest up to biggest. Well four is the smallest number and eight is the second smallest number. Then we have ten, so that’s the third smallest number. And then fourteen, so that’s the fourth smallest number, then fifteen, and then seventeen. So let’s write them out in order.

And there we have six numbers all in ascending order or from smallest to largest. Well the next problem that we encounter is the fact that there isn’t actually a middle number. If we chose this number, it would have two numbers to the left and three numbers to the right, so it’s not quite in the middle. And if we chose this number, it’s got three numbers to the left and two numbers to the right, so it’s not quite in the middle either.

We’re looking for a number which is in the three and a half position. Because then that would have three numbers to the left and three numbers to the right. So what we’re actually looking for is the number that’s midway between the third and fourth number. So the way we’re gonna do that is we’re gonna find the number that’s halfway between ten and fourteen. And the way we are gonna do that is to find the mean of those two numbers, so we’re gonna do ten add fourteen and divide by two. And ten and fourteen is twenty-four, so that’s twenty-four divided by two, which is twelve. So the answer is the median number of points scored is twelve.