Question Video: Verifying the Outliers of a Data Set Mathematics • 8th Grade

Video Transcript

The numbers of matches won by 12 teams in the national league are 11, five, six, six, nine, 10, 19, 14, 11, nine, nine, and six. Is it true or false that 19 is an outlier of the data?

To identify whether 19 is an outlier or not, we’ll need the interquartile range. And to do that, we’ll have to identify quartile one and quartile three. This means our first step is to put the data in order of size. Now, we have our 12 data points in size order.

We know that the median will come in the middle of these 12 data points and that the median is quartile two. 𝑄 one is the middle of the lower half of the data. Since there are six data points below the median, 𝑄 one will be located between the third and fourth. And similarly, 𝑄 three is the middle of the upper half of the data. There are six points above quartile two. And that means 𝑄 three will be located in the middle of those. It will be between the ninth and 10th value.

Because the third and the fourth value is six, we would call quartile one six. And because the ninth and 10th values are the same, quartile three is equal to 11. The interquartile range equals 𝑄 three minus 𝑄 one. For us, that’s 11 minus six. And so, we have an IQR of five. To find out if 19 is, in fact, an outlier, we’ll use the 1.5 times IQR rule. This rule tells us that a value is an outlier if it’s greater than 𝑄 three plus 1.5 times the IQR or less than 𝑄 one minus 1.5 times the IQR.

Since we’re looking at a data point that’s above 𝑄 three, we’ll look for the greater-than option. And that means we want to know is 19 greater than the quartile three plus 1.5 times the interquartile range? The IQR is five. 𝑄 three is 11. 1.5 times five is 7.5, plus 11 equals 18.5. 19 is greater than 18.5. And so, we can say it’s a true statement that 19 is an outlier of this data set.