Outliers in 1, 11, 12, 13, 14, 15, 16 Step by Step

Step by step

The question

Question: find the outliers in 1, 11, 12, 13, 14, 15 and 16.

1, 11, 12, 13, 14, 15, 16

An outlier is a number far away from the others.

outlier: far from the others

1 Put them in order

First we put them in order, smallest first: 1, 11, 12, 13, 14, 15 and 16.

= 1, 11, 12, 13, 14, 15, 16

2 Find the quartiles

7 numbers: 3 on each side of the middle one.

The median is 13.

The median cuts the list in two halves, 3 numbers each.

The median itself is in neither half.

Careful!

The median is not counted in the halves.

Each half has 3 numbers.

Careful: the median is in neither half

Q1 is the middle of the lower half: 11.

Q3 is the middle of the upper half: 15.

3 Find the IQR

The IQR is Q3 minus Q1: how wide the middle half is.

15 minus 11 is 4.

IQR = Q3 − Q1 = 15 − 11 = 4

4 Find the fences

The rule: an outlier is more than 1.5 IQRs outside the box.

1.5 times 4 is 6.

1.5 × IQR = 1.5 × 4 = 6

The low fence: Q1 minus 6.

11 minus 6 is 5.

low fence = Q1 − 6 = 11 − 6 = 5

The high fence: Q3 plus 6.

15 plus 6 is 21.

high fence = Q3 + 6 = 15 + 6 = 21

5 Find the outliers

On a number line: the fences in red, and a dot for each number.

1 is outside the fences.

So the outlier is 1.

= outlier: 1

6 Check

Let's check each one against its fence.

1 is less than 5.

So it is right!

1 < 5

Let's look back.

First: put them in order.

Then: find the quartiles.

Then: find the IQR.

Then: find the fences.

Then: find the outliers.

Last: check.

Answer