Download Stat 101 Lesson 6

Measures of Variability
Chapter 2
(Page 60)
(Page 60)
Measures of Variability –shows the spread of
the data.
(Page 60)
Range – the difference between the largest and the smallest
measurements.
Range = 9.4 – 5.6 = 3.8
The range is easy to calculate, easy to interpret and is an
adequate measure of variation for small sets of data.
(Page 62)
Variance of a Population – is the average of
the squares of the deviations of the
measurements about their mean µ.
( x i   )
 
N
2
2
The population standard deviation – is equal
2
to the positive square root of  .
 
2
Page 61
2

(
x


)
2
i
 
N
( xi   )
xi
( xi   ) 2
22.80
 
 4.56
5
2
    4.56  2.14
2
Variance of a Sample – is the sum of the squared
deviations of the measurements about their mean
2
x.

(
x

x
)
2
i
s

n 1
2

(
x

x
)
22.80
2
i
s 

 5.7
n 1
4
Sample Standard Deviation – is the positive square
2
root of s .
s
s2 
5.7  2.39
(Page 63)
5, 7, 1, 2, 4
 x 2 i  25  49  1  4  16  95
( xi ) 2  (5  7  1  2  4) 2  (19) 2  361
2
(

x
)
361
2
i
x i 
95 
95  72.2 22.8
2
n
5
s 



 5.7
n 1
5 1
4
4
Answer 2 – 15
Page 65