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### Outliers

Take away six matches to leave 10

- Take away four matchsticks to leave exactly four
- small equilateral triangles.

- Can you move two matches to make 7 squares.

- Take away two matches to leave two squares.

- Arrange four matches and a coin as shown below
- to represent a glass containing a cherry.

By moving two matches only, remove the cherry

from the glass, but leave the glass intact.

How many moves to get the cherry outside of the fancy glass?

To be able to identify an outlier using the Inter Quartile Range

What is an outlier?

- In a set of numbers, a number that is much LARGER or much SMALLER than the rest of the numbers is called an Outlier.

Say we have the following data:1,2,5,5,7,8,10,11,11,12,15,20

- Find the median first. It’s the middle point.

- Then find the quartiles, Q1 and Q3. They are the middles of the lower and upper half, respectively.

- The last thing to do is determine whether there are outliers using the 1.5*IQR Rule

min Q1 Q3 max 1,2,5,5,7,8,10,11,12,12,18,25

M

1

5

9

12

18

25

-5.5

22.5

1.5IQR

IQR = 12 – 5 = 7

1.5IQR

5 - 1.5 * 7 = -5.5

12 + 1.5 * 7 = 22.5

25 is considered an outlier and will be a point in a boxplot and the ‘whisker’ ends at the last non-outlier data point.

Do any of these sets of data have outliers

- 21, 27, 31, 35, 29, 42, 45, 50, 54, 61, 69
- 108, 134, 141, 152, 153, 157, 159, 160, 160, 160, 161, 162, 167, 169, 173
- 4, 4, 4, 5, 5, 5, 7, 9, 11, 13, 15, 33
- 6, 7, 7, 8, 8, 9, 11, 12, 13, 15, 18
- 4, 4, 7, 7, 8, 8, 8, 9, 9, 11, 13
- HINT – Use the IQR

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