### Video Transcript

Which set of data could be represented by the given box-and-whisker plot?

We have five sets of data (A), (B), (C), (D), and (E) to choose from. Well, the first thing we want to do is we want to identify from our box-and-whisker plot what each of the sections are. So first of all, what we have at the end of our whiskers is the minimum value on the left-hand side and the maximum value on the right-hand side. So, therefore, we can identify that the minimum value of our data set has to be 72 and the maximum value of our data set has to be 80.

And then inside of our box, what we have is a line and a point. And this point is the median. So, we can say this is the median value. And what we have with the median is the middle value if we line our data set up in order. And what we have with the median is the middle number if we line our data set up in order. And we could see that the median from our box-and-whisker plot is 76. And then we have at either end of the box, we have our lower quartile and upper quartile, which are 74 and 78, respectively, with our box-and-whisker plot.

So now, what we need to do is decide which set of data could be represented by our box-and-whisker plot. Well, the first bit of information we can use, which is the most straightforward, is the fact that we know the minimum value must be 72 and the maximum value must be 80. If we look at the data set (A), this is correct. So, this could be the correct answer. But if we take a look at data set (B), we can see that with data set (B), we’ve got a minimum value of 71 and a maximum value of 80. So therefore, it cannot be data set (B).

Again, when we look at data set (C), we can see that the maximum value is 80, and this time, the minimum value again is 71. So therefore, this cannot be the correct data set. However, data set (D) could be the correct data set because what we have here is the minimum of 72 and maximum of 80 that we’re looking for. And for data set (E), this can’t be the correct date set. This time, we’ve got the correct minimum cause we have 72; however, the maximum is 81. So therefore, we’ve shown this cannot be the correct data set. So therefore, we need to choose between (A) and (D). But how are we going to do that?

Well, what we’re gonna do to try and separate the date sets (A) and (D) is use the median. And as I’ve already said; to use the median or find the median, what we need to do is line our data sets up in numerical order, which I’ve done here. Then, what we want to do is find the middle value. However, if we want to find the middle value of our data set, what we’re gonna look for is actually a value or piece of data that’s halfway between the fourth and fifth values because as I said we’ve got an even number. But how we’re going to do this? Well, what we need to do if we want to find the halfway point between two bits of data is add them together and then divide it by two.

If we do that for data set (A), we’ll have 76 plus 78 then divided by two will give us 77, so we’d have a median of 77. However, if we do that to data set (D), we’ve got 76 plus 76 divided by two, which gives us a median of 76. Well, the median we’re looking for is in fact 76 from our box-and-whisker plot. So therefore, we can rule out data set (A). So therefore, we can say that the data set which could be represented by the box-and-whisker plot that we’ve been given is the data set (D).

And what we could do is just double-check this is the case by checking the lower and upper quartile. Well, to find the lower and upper quartile, what we need to do is find the halfway point of first of all the lower part of our data set, the part of data that’s before the median, then the halfway point between the upper part of our data, which is the bit after the median point. Well, if we wanted to work out the lower quartile, then we can see that this will actually lie between 72 and 76. So, we’d add these two together. But if we add 72 and 76, we’re gonna get 148 then divide this by two gives us 74. So, that’s our lower quartile. And that does agree with the one that we’ve got from our box-and-whisker plot.

And we can see that the upper quartile, without doing any calculation, is gonna be equal to 78. And that’s because the values that are at either side of the upper quartile are 78. So therefore, it’s going to be 78 between them. So that matches what we’re looking for with our box-and-whisker plot. So therefore, we can definitely confirm the data set which could be represented by the given box-and-whisker plot is data set (D).