bdm lecture 8

7/25/2019 BDM Lecture 8

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The formula

You may need to sit down for this!

WARNING

= { (x - ) 2/ n}

This is the symbol forthe standard deviation


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BPS - 5th Ed. Chapter 2 2

Standard eiation "ormulatypical deviation from the mean

# standard deiation $ s%uare root of thearian&e '

sn

x xi

i

n

=

=1 1

2

1( )( )


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(arian&e and Standardeiation) E*ample

+eta,oli& rates of men &al./20hr.1

342 3 362 330 307 383064

16007

200,11

7

1439186714601614136216661792

=

=

++++++=x


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(arian&e and Standardeiation

E*ample from Te*tObservations Deviations Squared deviations

1792 17921600 = 192 (192)2= 36,864

1666 1666

1600 = 66 (66)

2

= 4,3561362 1362 1600 = 238 (238)2= 56,644

1614 1614 1600 = 14 (14)2= 196

1460 1460 1600 = 140 (140)2= 19,600

1867 18671600 = 267 (267)

2

= 71,2891439 1439 1600 = 161 (161)2= 25,921

su! = 0 su! = 214,870

xxi

ix ( ) 2xx

i


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67.811,35

17

870,2142=

=s

calories24.18967.811,35 ==s


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Semi-wor9ed e*ample" :e are ;oin; to try and


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To calculate the standard deviation weconstruct a table like this one:

(x - ) 2

(x - ) 2=(x - ) 2/n =(x - ) 2/n =

(x - )x

=* $ $ =*/n $

There should be enouh s!a"e

here to fit in the number ofvalues# $% there are &'

tem!eratures so leave &' lines#

x = temperature --- = mean temperature --- = square root = total of --- 2= squared --- n = number of values


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To calculate the standard deviation we construct atable like this one:

(x - ) 2

(x - ) 2=(x - ) 2/n =(x - ) 2/n =

(x - )x

=* $ $ =*/n $

ext e rite the values (tem!eratures) in"olumn x (they "an be in any order)#

593279822

3


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(x - ) 2

(x - ) 2=(x - ) 2/n =(x - ) 2/n =

(x - )x

=* $ $ =*/n $


*dd them u! (x)

5932798223

+al"ulate the mean (1

50!0 = 550


10/16

(x - ) 2

(x - ) 2=(x - ) 2/n =(x - ) 2/n =

(x - )x

=* $ $ =*/n $


5932798223

50!0 = 550

next

,,,,,,,,,

,

rite the mean tem!erature ( ) inevery ro in the se"ond "olumn#


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(x - ) 2

(x - ) 2=(x - ) 2/n =(x - ) 2/n =

(x - )x

=* $ $ =*/n $


5932798223

50!0 = 550

now

,,,,,,,,,,

.ubtra"t ea"h value (tem!erature) from the mean# tdoes not matter if you obtain a neative number#

'0-2-1201-1-1

-2


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(x - ) 2

(x - ) 2=(x - ) 2/n =(x - ) 2/n =

(x - )x

=* $ $ =*/n $


5932798223

50!0 = 550

and

then

,,,,,,,,,,

'0-2-1201-1-1

-2

.uare (2) all of the fiures you obtained in"olumn 1 to et rid of the neative numbers#

'&3040&3444

0


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(x - ) 2

(x - ) 2=(x - ) 2/n =(x - ) 2/n =

(x - )x

=* $ $ =*/n $


5932798223

50!0 = 550

then

,,,,,,,,,,

'0-2-1201-1-1-2

'&3040&34440

*dd u! all of the fiures that you"al"ulated in "olumn 0 to et (x - ) 2#

80


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(x - ) 2

(x - ) 2=(x - ) 2/n =(x - ) 2/n =

(x - )x

=* $ $ =*/n $


5932798223

50!0 = 550

and

,,,,,,,,,,

'0-2-1201-1-1-2

'&3040&34440

80

5ivide (x - ) 2by the total number ofvalues (in this "ase &' 6 eather stations)

8


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(x - ) 2

(x - ) 2=(x - ) 2/n =(x - ) 2/n =

(x - )x

=* $ $ =*/n $


5932798223

50!0 = 550

finally

,,,,,,,,,,

'0-2-1201-1-1-2

'&3040&34440

80

Ta7e the suare root () of the fiure to obtain thestandard deviation# (8ound your anser to the nearestde"imal !la"e)

8


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>nswer

2"8#$

bdm lecture 8

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