Compare the following heights in

inches:

Boys Girls

72 61

74 64

70 65

68 66

69 68

70 67

68 65

69 63

67 62

70 65

71 66

  67

  64

  66

Computational Computational Formulas and IQR’sFormulas and IQR’s

Computational Computational Formulas and IQR’sFormulas and IQR’s

Computational Formula:

22

2

1

xx

nsn

This is an easier computational formula that contains no rounding.

Let’s try it!

7

18

22

34

42

x

You try one!

4

8

12

18

22

34

38

x

Is the standard deviation affected by

outliers?

5

7

5

8

9

5

7

5

8

29

The standard deviation is sensitive to extreme

values.

67

65

68

70

74

60

61

64

67

68

The following data represents the heights of some students in my class.

a. Find the mean & st. dev.

b. What % are within 1 st. dev. Of the mean?

c. What % are within 2 st. dev. Of the mean?

IQR – Interquartile Range

• This is the measure of variability that is not affected by outliers.

• It’s based on quartiles.

25%25% 25%

25%

1Q 2Q 3Q

1Q

2Q

- This is the median of the lower ½ of the sample.

3Q

- This is the median.

- This is the median of the upper ½ of the sample.

3 1IQR Q Q

18 24 25 27 27 29 30 33 34

Find IQR

12 13 16 18 22 24 27 40

Find IQR

8 10 11 14 16 20 22 26 28 32

Find IQR

4 5 6 6 7 10 22

If normal distribution – then you can estimate the

standard deviation with the IQR.

1.35

IQRStandard

Deviation

*Can also be use to check to see if a distribution is normal – if much larger then it’s skewed.

Homework• Worksheet

• Use the new formula to compute the standard deviation.

Now for the Lab!