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.
