Screencast 1 Effects on the median and mean when data points change

Transcript

INSTRUCTOR
In this screencast, I’m going to talk about calculating the mean and the median from the stemplot and showing how the mean and the median change when some of the data changes. So I’m going to start off with a stemplot. And the stemplot I’ve got here is a stemplot of the prices of the small flat screen televisions that are shown in Activity 1 in Subsection 1.2 of Unit 2.
And the first thing I’m going to do is calculate the median. And we note first that we’ve got 20 data points in our batch. And so the median is the average of the 10th and 11th largest values.
So it’s just a question of finding out from the stemplot what the 10th and the 11th largest values are. And we can do that by counting down from the top value in our stemplot. That’s 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
But we could also have counted from the bottom of the stemplot. Again, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. And notice, it’s come at the same two numbers, as it should. So for these data, the median is 150 plus 150 over 2, which is £150, taking into account this key for this stemplot.
Now the mean is just the sum of all the numbers divided by the number of numbers. And going through stemplot, we can write down what all the numbers are. So the lowest number is 90. The next one is 100. Next one is 120. And so on, so forth, until we get to 240 and 250 and 270.
And that’s all divided by the number of numbers, which is 20. And the sum on top of the fraction happens to be 3240. That’s divided by 20, and that comes to £162. So the mean of the television prices is £162, and the median is £150. So the mean is £12 bigger than the median.
Now, what happens if some of the data changes? For example, what happens if a couple of the prices for the televisions goes up? And in particular, what happens if the prices of the most expensive televisions go up? So instead of having a television that costs £250 and a television that costs £270, we actually had a couple of televisions that cost £350 and £400? What difference does this make to the median and the mean?
Well, notice that the two values we work the median out from haven’t changed. So we can just write that down immediately. The median is £150, just as it was before.
So what about the mean? Well again, we’ve got to work out the sum of all the data points and divide by the number of numbers. For most of the numbers, they haven’t changed. So most the numbers in the sum don’t change. But the last two have – so instead of 250, we’ve now got 350, and instead of 270, we’ve got 400. Again, that’s divided by 20. That’s equal to 3470 over 20, which equals 173.5, or we can say that’s £174 to the nearest pound.
So what we notice here that when the data is changed, the median has stayed the same. We say that the median is a resistant measure. It’s been resistant to a change in the data. On the other hand, the mean is bigger. We say that the mean is a sensitive measure. It has been sensitive to changes in the data.

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