topic 1- mean mode median(qc)

7/21/2019 TOPIC 1- Mean Mode Median(qc)

1/64

BASIC STATISTICBASIC STATISTIC


2/64

Two Types of StatisticsTwo Types of Statistics

Descriptive statistics of a POPULATIONRelevant notation (Greek)

mean N population size sum

Inferential statistics of SA!PL"S fro#a pop$lation% Ass$#ptions are #a&e t'at t'e sa#ple

reects t'e pop$lation in an $niase& for#%Ro#an Notation

X mean n sample size sum


3/64

Concept Of Population andConcept Of Population and

SampleSample

Population

Sample


4/64

MEASURES OF CENTRA TEN!ENC"MEASURES OF CENTRA TEN!ENC"

FOR UN#ROUPE! !ATAFOR UN#ROUPE! !ATA

Mean

MedianMode

$


5/64

MeanMean

T%e mean for ungrouped dataiso&tained &' di(idin) t%e sum of all

(alues &' t%e num&e* of (alues in t%edata set+ T%us,

Mean fo* population data-

Mean fo* sample data-

.

N

x

=

n

xx =


6/64

E/ample 0E/ample 0

Ta&le 1+0 )i(es t%e 2332 total pa'*ollsof 4(e Ma5o* ea)ue Base&all 6MB7

teams+ Find t%e mean of t%e 2332 pa'*olls of

t%ese 4(e MB teams+

8


7/64

Ta&le 0Ta&le 0

9

MB Team

2332 Total Pa'*oll

6millions of dolla*s7Ana%eim An)els

Atlanta B*a(es

Ne: "o*; "an;ees

St+ ouis Ca*dinals

Tampa Ba' !e(ilRa's

82


8/64

Solution 0Solution 0

million78$5

390

===nx

x

=

T%us, t%e mean 2332 pa'*oll of t%ese 4(eMB teams :as >9= million+


9/64

E/ample 2E/ample 2

T%e follo:in) a*e t%e a)es of all ei)%templo'ees of a small compan'-

.1 12 80 29 1< $$ $< .9

Find t%e mean a)e of t%ese emplo'ees+

18,0.3+

>.$,99,$21,9$3+ Find t%e mode+

2.


26/64


Because eac% (alue in t%is data setoccu*s onl' once, t%is data set contains

no #o&e+

28


27/64

E/ample 9E/ample 9

T%e p*ices of t%e same &*and oftele(ision set at ei)%t sto*es a*e

found to &e >$$=8, >.31, >$$93, >.3., >$93 and >$


28/64


In t%is data set, eac% of t%e t:o (alues>$$93 occu*s t:ice and eac%

of t%e *emainin) (alues occu*s onl'once+

T%e*efo*e, t%is data set %as t:omodes- -,./and -,+0+

2=


29/64

E/ample =E/ample =

T%e a)es of 03 *andoml' selectedstudents f*om a class a*e 20, 0


30/64

Solution =Solution =

T%is data set %as t%*ee modes- 0


31/64

MEASURES OFMEASURES OF

!ISPERSION FOR!ISPERSION FOR

UN#ROUPE! !ATAUN#ROUPE! !ATARan)e

?a*iance and Standa*d !e(iation

Population Pa*amete*s and SampleStatistics

10


32/64

Ran)eRan)e

Findin) Ran)e fo* Un)*ouped !ata

Ran)e a*)est (alue Smallest ?alue

12


33/64

E/ample


34/64

Ta&le $Ta&le $

1$

State

Total A*ea

6s@ua*e miles7

A*;ansas

ouisiana

O;la%oma

Te/as

.1,0=2

$


35/64

Solution


36/64

?a*iance and Standa*d?a*iance and Standa*d

!e(iation!e(iation

T%e standa*d de(iation is t%e mostused measu*e of dispe*sion+

T%e (alue of t%e standa*d de(iationtells %o: closel' t%e (alues of a dataset a*e cluste*ed a*ound t%e mean+

18


37/64


!e(iation cont+!e(iation cont+

S%o*tcut Fo*mulas fo* t%e ?a*iance andStanda*d !e(iation fo* Un)*ouped !ata

%e*e is t%e population (a*iance and sist%e sample (a*iance+

( )

1and

!" 22

2

22

2

=

=

n

n

xx

sN

N

xx

19


38/64


!e(iation cont+!e(iation cont+

S%o*tcut Fo*mulas fo* t%e ?a*iance andStanda*d !e(iation fo* Un)*ouped !ata

T%e standa*d de(iation is o&tained &'ta;in) t%e positi(e s@ua*e *oot of t%e(a*iance+

Population standa*d de(iation-Sample standa*d de(iation-

1=

2ss=

2=


39/64

E/ample 03E/ample 03

11$,1=9,$


42/64


T%e follo:in) data a*e t%e 2332ea*nin)s 6in t%ousands of dolla*s7

&efo*e ta/es fo* all si/ emplo'ees of asmall compan'+

$=+.3 1=+$3 8.+.3

22+83 9


43/64


x x

$=+.31=+$3

8.+.3

22+83

9


44/64


( )

359#18$thousand359#18$0489.337

0489.3376

6

!40.309"02.977#17

22

2

2

===

=

=

=

N

N

xx

$$

T%us, t%e standa*d de(iation of t%e2332 ea*nin)s of all si/ emplo'ees oft%is compan' is >0=,1.


45/64

MEAN, ?ARIANCE AN!MEAN, ?ARIANCE AN!

STAN!AR! !E?IATION FORSTAN!AR! !E?IATION FOR

#ROUPE! !ATA#ROUPE! !ATAMean fo* #*ouped !ata?a*iance and Standa*d !e(iation

fo* #*ouped !ata

$.


46/64

Mean fo* #*ouped !ataMean fo* #*ouped !ata

N

mf=

$8

n

mfx =

Calculatin) Mean fo* #*ouped !ata

Mean fo* population data-

Mean fo* sample data-

%e*e mis t%e midpoint andfis t%ef*e@uenc' of a class+


47/64


Ta&le 1+= )i(es t%e f*e@uenc'dist*i&ution of t%e dail' commutin)

times 6in minutes7 f*om %ome to :o*;fo* all2. emplo'ees of a compan'+

Calculate t%e mean of t%e dail'

commutin) times+

$9


48/64

Ta&le =Ta&le =

$=

!ail' Commutin)Time 6minutes7

Num&e* of Emplo'ees

3 to less t%an 03

03 to less t%an 23

23 to less t%an 13

13 to less t%an $3$3 to less t%an .3

$

topic 1- mean mode median(qc)

Documents