Transcript Lesson 3 - Computational Formulas and IQR

COMPUTATIONAL
FORMULAS AND IQR’S
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:
Objective
•Calculate standard
deviation, variance
and IQR.
Relevance
•To be able to analyze a
set of data and see how
far each value is above or
below the mean of the
set.
Computational Formula
• This is an easier computational formula that
contains no rounding.

 x

2
s 
x
2
2
n 1
n
Example – Find Var and St Dev
𝒙𝟐
𝒙
8
49
64
22
484
34
1156
42
1764
7
 x2  3517
 x  113
s2 
2



x
 x2 
n 1
n

2

113
3517 
5
4
 240.8
s  240.8  15.5
You Try One!
𝒙
𝒙𝟐
4
16
64
144
324
484
1156
1444
8
12
18
22
34
38
 x  136
s2 
2



x
 x2 
n 1
n

 x  3632
2
2

136 
3632 
7
6
 164.95
s  164.95  12.8
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


74

60

61


64

67




68
The following data represents the
heights of some students in my
class.
a. Find the mean & standard deviation.
x  66.4
s  4.14
b. What % are within 1 standard
deviation of the mean? ()
x  1s :
66.4  4.14  62.26
66.4  4.14  70.54
7
 70%
10
c. What % are within 2 standard
deviations f the mean? () 10
x  2s : 58.12  74.68
10
 100%
IQR – Interquartile Range
• This is the measure of variability
that is not affected by outliers.
• It is 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 )
Q1 = 24.5
Q3 = 31.5
IQR = 31.5 – 24.5 = 7
Find IQR
12 13 16 18 22 24 27 40
Q1 = 14.5
Q3 = 25.5
IQR = 25.5 – 14.5 = 11
Find IQR
8
10 11 14 16 20 22 26 28 32
IQR = 15
Find IQR
4
5
6
IQR = 15
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.
Which Measure Should You Report?
Shape
Central
Tendency
Dispersion
(Spread)
Symmetric
Mean
Skewed
Left or Right
Median
Standard
Deviation
IQR
NOTE: When told to “describe the distribution” you
will give the shape, the center and the spread of the
distribution using the above categories as a guideline.
Homework
• Worksheet
• Use the new formula to compute the
standard deviation.
• Now – time for the lab!