STANDARD DEVIATION AND VARIANCE
 
 

SAMPLE

  

POPULATION

 

Example:

24 29 35 39 43 48 55

= 39

 

USEFUL ALTERNATIVE FORMULA for Sample   when mean is messy
   

#6

2  4  4  5  7  8  8  9  10  12  13  16

  
 

 Use calculator for second part of #6
 

GROUPED DATA
   #14
 

Age	x	Students	xf	x^2	x^2f
0-2		23
3-5		33
6-8		63
9-11		68
12-14		19
15-17		10
18-20		1
21-23		0

 
 
 
 
 

UNDERSTANDING STANDARD DEVIATION

 

MOST data falls within 4s

That is:  within plus or minus (2) of mean

 
 

RANGE ~ 4s

That is:   (High - Low) ~ 4s

  
 
 
 
 

CHEBYSHEV'S THEOREM        True for ANY type of distribution

  Proportion of data within k standard deviations is at least 1 - 1/k^2

                    k = 2            then   1 - 1/4 = 3/4
 
                    k = 3            then    1 - 1/9 = 8/9

                    k = 4            then    1 - 1/16 = 15/16

EMPIRICAL RULE - If Distribution is approximately bell shaped,
                        then 68-95-99  Rule
   

Discuss Shifting Data and how affects mean and Standard Deviation