8/10/2019 Math IV 1st Term

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Math IV 1st TermI. Intro

a. Major Divisionsi. Descriptive

• Concerned with collection, classifcation, and

presentation o data to be able to summarieand describe the !roup characteristics

• Conclusion can be !otten usin! mean, median,

or modeii. Inerential

• Drawin! conclusion or jud!ment aboutpopulation based on representative sampleta"en

b. #teps in #tatistical Investi!ationi. Collection o Data $ !atherin! numerical dataii. %rocessin! o Data $ or!aniin! data to show

si!nifcant characteristicsiii. %resentation $ in orm o tables, etc.iv. &nal'sis o Data $ method o drawin! rom !iven

data relevant ino rom which numericaldescription can be ormulated

v. Interpretation $ tas" o drawin! conclusions romanal'ed data

c. T'pes o Datai. %rimar' $ rom ori!inal sourceii. #econdar' $ rom e(istin! records)boo"s

d. Classifcation o #tatistical Datai. *ominal

• *umerical in name onl'

• *umbers assi!ned to somethin!

• +(. #in!le 1, Married -

ii. rdinal

• Indicate ran" order

• +(. rder o fnish in race, place in competition

iii. Interval

•

*umbers represent e/ual units betweenmeasurements

• Can0t be

iv. 2atio

• *umbers represent e/ual units between

measurements and there is an absolute eropoint

• Can be

• +(. Income, distance

v. Discrete

• 3uantifable b' whole number

• Done b' coutin!

• 4ow man'5

• +(. *umber o students

vi. Continuous

• 6suall' results in measurements

• Can assume infnitel' man' values that

correspond to point on a line)interval

• 4ow much5

• +(. 4ei!ht, wei!ht, winnin! timeII. #ample and %opulation

a. #lovin0s 7ormula

• #ample $ subset o the population

• %opulation $ entire !roup

III. 7re/uenc' Distribution Tablea. Terms

• 8oundar' $ actual number

• 9imit $ lowest)hi!hest number included in theclass

• Class Mar" :(; $ midpoint o the class

• 7re/uenc' <  

• Cumulative 7re/uenc' :C ; $ add the re/uencie

until n is reachedb. 2an!e

• 2 4i!hest #core $ 9owest #core

• =rouped Data> 2 6pper 8oundar' $ 9ower

8oundar'c. *umber o Class Intervals :?;

• #tur!e0s 7ormula

•

? 1 @ A.Alo!• &lwa's whole

d. Class Bidth

• C 2)? 

•  T'picall' whole number

e. Table

#core

( :(;

C

 

( < ( :(<(;- :(<(;-

IV. Measures o Central Tendenc'a. Mean

• (  :(;)n

b. Median• Median Class :mc; n)- E C 

c. Mode

• Modal class is class with hi!hest  

• D1  o modal class $ o lower class

• D-  o modal class $ o hi!her class

V. Measures o %osition  F 2ound<oG onl' when un!rouped

a. 3uartile• H e/ual parts

• 6n!rouped> 3"  "n)H

• =rouped

• n")H, then loo" at cumulative re/uenc' to

determine the class to useb. Decile

• 1 e/ual parts

• 6n!rouped> D"  "*)1

• =rouped>

8/10/2019 Math IV 1st Term

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• n")1, then loo" at cumulative re/uenc' to

determine the class to usec. %ercentile

• 1 e/ual parts

• 6n!rouped> %"  "*)1

• =rouped>

• n")1, then loo" at cumulative re/uenc'

to determine the class to useVI. Measures o Variabilit'

a. 2an!e 4# < 9#b. Variance

• %opulation J- :class mar" :(; $(;-)n

• #ample s-  :class mar" :(; < (;-):n<1;

• =rouped> :(<K;-)n sample> :( < x;-):n <1;

c. #tandard Deviation

• #/uare root o variance

VII. L<testa. L #core

• #tandard #core

• a statistical measurement o a scores

relationship to the mean measured b'

standard deviations•

b. *ormal Distribution

• & histo!ram where data is distributed with no

bias let or ri!ht

• 8ell curve

• Mean Median Mode

• #pread o a normal distribution is controlled b'

standard deviation

• NOP o values are within 1 standard deviation o the mean

• QRP o values are within - standard deviations

o the mean

• QQ.SP o values are within A standard deviations

o the meanc. L Test

• 6sed when lar!e samples sies more than A

are involved and variance and standarddeviation is "nown

i. T'pes1. L<test or sin!le proportiono 6sed to test a h'pothesis on a specifc value

o the population proportion-. L<test or diGerence o proportionso 6sed to test the h'pothesis that two

populations have the same proportionA. L <test or sin!le meano 6sed to test a h'pothesis on a specifc value

o the population mean

H. L<test or sin!le varianceo 6sed to test a h'pothesis on a specifc value

o the population varianceR. L<test or testin! e/ualit' o varianceo 6sed to test the h'pothesis o e/ualit' o tw

population variancesd. T test

• & amil' o continuous probabilit' distributions

• 7or less than A sample sie

i. T'pes

1. ne #ample < used to compare a sample meawith the "nown population mean

-. Two #ample < used to compare eitherindependent samples or dependent samples

 Bhere>(1 Mean o frst set o values(- Mean o second set o values#1 #tandard deviation o frst set o values

#- #tandard deviation o second set ovaluesn1 Total number o values in frst setn- Total number o values in second set

VIII. 4'pothesis Testin!

• ( or sample

• K or population

a. *ull 4'pothesis 4

• ne tr'in! to disprove

• Can be , E,

b. &lternative 4'pothesis 41 or 4a

• ne tr'in! to prove ri!ht• Can be U, , W

c. T'pes o +rror

 T'pe 1 T'pe -4  True 7alse

41 7alse TrueDecision 41 4

d. 4'pothesis Testin!i. #teps1. #tate the null and alternative h'pothesis-. #elect the test to be used and level o

si!nifcance

• L test i population, T test i sample

A. #tate the decision ruleH. Compute or appropriate test statistic and

ma"e decisionR. Interpret Decision

I. +/uations to 2emember>