math iv 1st term
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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. <ernative 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>