School
DAILY LESSON LOG
Teacher STATISTICS & PROBABILITY
I. OBJECTIVES A# Co"!e"! S!a"dard B# Per7or*a"ce S!a"dard C# Lear"'" Co*:e!e"c'e= O;%ec!'ve ($r'!e !he LC Code 7or each)
CCNHS – SENIOR HIGH SCHOOL DEPARTMENT (SHS) Mr# $arre" Erro%o LPT
Teach'" Da!e a"d +AN,AR +AN,ARY Y -./ 012 3 Mo" . T'*e 4r'
MONDAY
T,ESDAY
$EDNESDAY
GRADE
S!ra "d STATISTICS STA TISTICS AND PROBABILITY
56ar!er
THIRD
TH,RSDAY
The lear"er ' a;le !o a::l9 6'!a;le a*:l'" a"d a*:l'" d'!r';6!'o" o7 !he a*:le *ea" !o olve real.l'7e :ro;le* '" d'
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A! !he e"d o7 !he leo" !he lear"er *6! ;e a;le !o3 1. fnd the mean and variance o the sampling distribtion o the sample mean.
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A! !he e"d o7 !he leo" !he lear"er *6! ;e a;le !o3
A! !he e"d o7 !he leo" !he lear"er *6! ;e a;le !o3
1. illstrate the Central !imit Theorem.
1. solve problems involving sampling distribtions distribtions o the sample mean.
M=0SP.IIIe.0
M=0SP.IIIe.7.
Sampling and Sampling $istribtions
Sampling and Sampling $istribtions
Sampling and Sampling $istribtions
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1. Statistics and Probability, 1st Ed., pp. 110 – 118 2. Statistics, CMO 03, 2015 Ed., pp. 139 - 10
1. Statistics and Probability, 1st Ed., pp. 110 – 118 2. Statistics, CMO 03, 2015 Ed., pp. 139 - 10
III. !E%&"I"' &ESO(&CES A# Re7ere"ce 1. Teacher’s Guide pages 2. Learner’s Materials pages 3. Textbook pages
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4. Additional Materials ro! Learning "esource #L"$
4RIDAY
The lear"er de*o"!ra!e 6"der!a"d'" o7 8e9 co"ce:! o7 a*:l'" a"d a*:l'" d'!r';6!'o" o7 !he a*:le *ea"#
M=0SP.IIId.>
II. CO"TE"T
T'* e
Grade level Lear"'" Area
1. Statistics and Probability, Probability, 1st Ed., pp. 110 – 118 2. Statistics, CMO 03, 2015 Ed., pp. 139 - 10
portal B# O!her Lear"'" Reo6rce
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!!!.analy"#$at%.co$
!!!.analy"#$at%.co$
!!!.analy"#$at%.co$
IV. )&OCE$(&ES A# Rev'e?'" :rev'o6 leo" or :ree"!'" !he "e? leo" B# E!a;l'h'" a :6r:oe 7or !he leo"
C# Pree"!'" ea*:le= '"!a"ce
. Introdction
Rev'e? !he co"ce:! d'c6ed d6r'" !he @r! d'c6'o"
Rev'e? !he co"ce:! d'c6ed la! *ee!'"
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Conc#pts& -M#an o' Sa$plin( )istrib*tion -+arianc# o' Sa$plin( )istrib*tion -ar rap% #pr#s#ntation
Conc#pts& -/nnit# Pop*lation -C#ntral i$it %#or#$
Conc#pts& -Mor# disc*ssions on C#ntral i$it - Probl#$ Solin( and applications
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E*ample+ )roblem # %&onsider a population consisting o nos. 1'2'3'4 and (. )uppose sa!ples o si*e 2 are dra+n ro! the population. ,escribe the sa!pling distribution o the sa!ple !eans.
E*ample+
E*ample+
)roblem , -I"I"ITE )O)(!%TIO"/
)roblems+
1. hat is the !ean o the sa!pling distribution o the sa!ple !eans 2. hat is the /ariance o the sa!pling distribution o the sa!ple !eans 3. &o!pare these /alues to the !ean and /ariance o the population. 4. ,ra+ the histogra! o the sa!pling distribution o the population !ean. )olution0 1. &o!pute the population
1.4 A population has a !ean o and a standard de/iation o (. A rando! sa!ple o 1 !easure!ents is dra+n ro! these population. ,escribe the sa!pling distribution o the sa!ple !eans b co!puting its !ean and standard de/iation. ote0 # s%all ass*$# t%at t%# pop*lation is innit#.
1.) The average time it takes a group of college students to complete a certain examination is 46.2 minutes. The standard deviation is 8 minutes. Assume that the variable is normall distributed. a.) !hat is the probabilit that a randoml selected college students "ill complete the examination in less than 4# minutes$ ANS. 0.3446 or 34.46%
)teps0 1. 5denti the gi/en inor!ation. 6 7 ' 8 7 (' and n 7 1
b.) %f &' randoml selected college students take the examination( "hat is the probabilit that the mean time it takes the group to complete the test "ill be less than 4# minutes$
2. 9ind the !ean o the sa!pling distribution. :se the propert
μ x 7 6.
ANS. 0.0023 or 0.23%
c.)
!ean.
x μ N
μ x 7 6 7 /1
7 #1;2;3;4;($<(
3. 9ind the standard de/iation o the sa!pling distribution. :se the propert that
7 -#11 2. &o!pute the population /ariance. =T>0 ?roduce a table. 2
σ
X μ N
5
7
2
7 1<( 7 0
16
7
5 4
7 #0>
3. ,et. the nu!ber o possible sa!ples o si*e n 7 2. n
C r
7 1 #)o' there are 1
sa!ples$ 4. List all possible sa!ples and !eans. Sa*:le 1' 2 1' 3 1' 4 1' ( 2' 3 2' 4 2' ( 3' 4 3' ( 4' (
Mea" 1.( 2. 2.( 3. 2.( 3. 3.( 3.( 4. 4.(
)teps0
(. &onstruct the sa!pling distribution o sa!ple !eans. Sa*:le Mea"
2.4 The heights o !ale college students are nor!all distributed +ith !ean o @ inches and standard de/iation o 3 inches. 5 @ sa!ples consisting o 2( students each are dra+n ro! the population' +hat +ould be the expected !ean and standard de/iation o the resulting sa!pling distribution o the !eans
1. 5denti the gi/en inor!ation. 6 7 @' 8 7 3' and n 7 2(
4re6e"c9
X
7
1.( 2. 2.( 3.
1 1 2 2
2. 9ind the !ean o the sa!pling distribution. :se the propert
μ x 7 6.
3.( 2 4. 1 4.( 1 To!al 1 . &o!pute the !ean o the sa!pling distribution o the sa!ple !eans #
μ x
7
X
X
P(
X
P(
)
X
20010
2
P(
13.78
μ
14.11
)
2
μ
2.
1<1
2.(
1<(
3.
1<(
1.( 1. .( .
2001
X
X
1<1
correction actor i 7 2 and n 7 1.
7
)
1.(
%9ind the nite population
$.
X
2.2(
.22(
1.
.1
.2(
.(
.
.
7
2
X μ
25
1<1 3 1<1 7 1#/1 1<( 5 1<( 1<( 1<1 1<1 )roblem , -I"ITE #11 )O)(!%TIO"/
-#11 2# &o!pute the /ariance o the sa!pling distribution o the sa!ple
σ x
7
P(
1.( 2. 2.( 3. 3.( 4. 4.( To!al
!eans #
3
Pro;a;'l'!9
X
μ x
3. 9ind the standard de/iation o the sa!pling distribution. :se the propert that
$.
Sa*:le Mea"
here0
μ x 7 6 7 /
7
.B@
7
3.( 4. 4.(
1<(
.(
.2(
.(
1<1
1.
1.
.1
1<1
1.(
2.2(
.22(
To!a l
#1 1
1#2>1
@. &onstruct the histogra!.
D# D'c6'" "e? co"ce:! a"d :rac!'c'" "e? 8'll F
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Concepts and defnitions+
Concepts+
#) The :o:6la!'o" d'!r';6!'o" is the probabilit distribution o the population data.
1./ %f random samples of sie n are
0#) 5n general' the probabilit distribution o a sa!ple statistic is called its a*:l'" d'!r';6!'o"#
Concepts+
dra"n from a population( then as n becomes larger( the sampling distribution of the mean approaches the normal distribution( regardless of the shape of the population distribution. *+entral ,imit Theorem) 2.) The /ariance o the
sa!pling distribution o the 3.$ Po:6la!'o" Mea" – the a/erage o the co!plete set o /alues.
2
is0
2
2
2.1 4.$ Sa*:le Mea" C the a/erage o the set o sa!ples obtain ro! the population.
σ
sa!ple !eans
σ x 7
σ N n ∙ n N 1 #nite
population$ 2
2
2.2 5.) The mean of the sampling distribution of is alwas e!ual to the mean of the population. Thus(
σ x 7
population$
σ n
#innite
3.$ The standard de/iation o the sa!pling distribution o 2
-ence( if "e select all possible samples *of the same sie) from a population and
the sa!ple !eans
calculate their means( the mean of all these sample means "ill be the
3.1
same as the mean population.
population$
-The sample mean(
of the
x
is called an
estimator of the population mean(
σ X
+here0
7
σ
is0
σ N n ∙ n N 1 #nite
N n N 1 #nite pop.
correction actor$
3.2
σ X
7
σ n #innite
population$ =T>0 "entral limit
E# D'c6'" "e? co"ce:! a"d :rac!'c'" "e? 8'll F0
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E:la'"3 #ro! the exa!ple$
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1. Do+ do ou co!pare !ean o the sa!ple !eans and the !ean o the population 2. Do+ do ou co!pare /ariance o the sa!ple !eans and the /ariance o the population
4# Develo:'" *a!er9 (Lead !o 4or*a!'ve Ae*e"! 0)
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)roblems+
)roblems+
)roblem+ 1. A population has a normal
1. )ee page 121-123' proble!s E'&',' nite population.
1. )ee page 124' proble! >' nu!bers 1 to (' innite population.
distribution. A sample of sie n is selected from this population. /escribe the shape of the sampling distribution of the sample mean for
each of the follo"ing cases. a. n 7 04
G# 4'"d'" :rac!'cal a::l'ca!'o" o7 co"ce:! a"d 8'll '" da'l9 l'v'"
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b. n 7 11
A::l'ca!'o"3 1. %# 'ollo!in( dat# (i# t%# a(#s 6in y#ars4 o' all si7 $#$b#rs in t%# 'a$ily. 55 53 28 25 21 15 a. rit# t%# pop*lation distrib*tion. b. Calc*lat# t%# pop*lation $#an.
H# Ma8'" e"eral'a!'o" a"d a;!rac!'o" a;o6! !he leo" I# Eval6a!'" lear"'"
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c. Calc*lat# t%# sa$pl# $#an o' 'o*r n*$b#rs 55, 53, 28 15. #n#rali"# t%# conc#pts disc*ss#d
V. &E3%&4S VI. &E!ECTIO" A# No# o7 lear"er ?ho ear"ed 1 '" !he eval6a!'o"# B# No# o7 lear"er ?ho re6're add'!'o"al ac!'v'!'e 7or re*ed'a!'o" ?ho cored ;elo? C# D'd !he re*ed'al leo" ?or8J No# o7
#n#rali"# t%# conc#pts disc*ss#d
# &ecitation0 Seator2
+# Add'!'o"al ac!'v'!'e 7or a::l'ca!'o"
#in'orc# t%# conc#pts disc*ss#d and sills practic#d
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NON.$ORING HOLIDAY NO SCHED,LE
&ecitation0 Seator2
Seator2
lear"er ?ho have ca6h! 6: ?'!h !he leo"# D# No# o7 lear"er ?ho co"!'"6e !o re6're re*ed'a!'o"# E# $h'ch o7 *9 !each'" !ra!e'e ?or8ed ?ellJ $h9 d'd !hee ?or8J 4# $ha! d'Kc6l!'e d'd I e"co6"!er ?h'ch *9 :r'"c':al or 6:erv'or ca" hel: *e olveJ G# $ha! '""ova!'o" or local'ed *a!er'al d'd I 6e=d'cover ?h'ch I ?'h !o hare ?'!h o!her !eacherJ
)repared b5+
Chec2ed b5+
CES%& 3. $E! &OS%&IO J&.0 CE S7S T#1
E&6I" !. )(&CI%0 $%!! 7ead0 CC"7S#S7S
%pproved+
C%!IC4 $. %&&IET%0 )h$ )rincipal I
