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
Compare the following
heights in inches:
Computational
Formulas and IQR’s
Computational Formula:
s 
2
x
2
x



n 1
2
n
This is an easier computational
formula that contains no
rounding.
Let’s try it!
x
7
18
22
34
42
You try one!
x
4
8
12
18
22
34
38
Is the standard deviation
affected by outliers?
5
5
7
7
5
5
8
8
9
29
The standard deviation is
sensitive to extreme
values.
67
65
68
70
The following data represents the
heights of some students in my
class.
a. Find the mean & st. dev.
74
60
61
64
b. What % are within 1 st. dev. Of the
mean?
67
68
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%
Q1
Q1
Q2
Q3
Q2
25%
Q3
- This is the median of the lower ½ of the sample.
- This is the median.
- This is the median of the upper ½ of the sample.
IQR  Q3  Q1
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.
Standard Deviation
IQR
1.35
*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!