Slides : การวัดแนวโน้มเข้าสู่ส่วนกลาง (มัธยฐาน ฐานนิยม ค่าเฉลี่ย)

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rn-a1~ tbu 11ua.Jb~16f6f1un~1-3 'II(Measure of Central Tendency) ~ ..:. .:1 Ql .11.1 ~ u~: o tl I .11.1 ~blJ'U1iifl1'3'l-i1 VI1tb't1'Utl el-3!1 ela.J ~'U1'.1fl~1-3 el-3A1tl ela.J 'II 'II 'II Ql1. a.J iii'.lfiil'U (Median) d3 .0::.2. fiil'U'Ui'.la.J (Mode) d3 I3. AlI b%~1.':1.1 d (Arithmetic Mean 'l-i'ael Mean) I ..:. I .:1 ..:.Ql ..:. Ql ..:.Vl1fl~1-3b~tl AmVI, a.J~Ola.J b~tJAmVI, Al b%~1'.1 b~tJAmVI

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c~httlnl~ : 1 2 3 4 5 .d oq.,.QIb'a~~~1@l'lJ1JelaJ~ : 1 2 4 5 6 ~ q., I q., .:.. a-Ji~~114bcn1n'1J 4 cl.3 o I q., 2=V11tb'VIU~3Jfi£1~1U d3

. .. ={911tb'IIIU~3\"H' itltli11-t 4.5 ungrouped data(~ltbl.nl-3)~-eo--.. 1 2 3 4 5 6 7 8 f(~a~~ .. 66 63 63 ~ 60 60 60 / 60 3 61 1=Vl0 1tb'VIU-I 33QJlfi£1~1U N+1 - 8 + 1 = 4.-~ 62 1 63 2 22 66 1• 62 + 61 - 61.5- -• • 2

(n-am~e13oia1aJu~nu~.:~A113J~(~1e1rl1~ ~.:J~1~1UU£J3J .o:lfl. 2 3 4 4 6 5 -.... mode = 4 - b'5tlfl unimodalil. 2 3 4 4 6 2 -.... mode = 2, 4 - .o:l b'5tlfl bimodalA. 1 2 3 4 -1aJ~ mode.:1. 7 9 7 6 6 7 9 9 6 -1aJ~ mode

~b~.1e1.1lQfll'lt'5fl'.:5Ifl \"~\ ' I IA el1U11 '6lffl3.J1' (sigma) i=l 4 = Lxi i=2 4 = L Xi yi i=l

@niJ~1!Gi (practice~=1. X + X + X + X + X 567892. f X + f X + f X = 11 22 332222+ + +3. X 1X X X- 2 3 4 222=4. (x - y ) + (x - y ) + (x - y )11 22 33

4L: x~ =i=1 4L (xi - Yi ) = (x 1 - Y1) + (x 2 - Y2) + (x3 - Y3) + (x 4 - Y4)i=1

l ~fl1.l!J11Gl {practice)) I :31. ~Qi i= l. _ __2 i =l....;.._;;......_ WX+ WY + WX+ WX i =l - 1 1 2 -\" \"'2 3 3 4 43. TJ; + Wz +1~ + ~ - ~ I; I; - +- + ··· +- Q1 Q2 Q5

( 3. ~1n~1~b~t~AmVI (arithmetic mean) )~!lela..!~ : X , X , ••• , X '~~ 1 2 n n LxLXi - -i=l nn

(GA\•1el~I1~ 1i.Jfel3J~ : 2 4 6 8 10 'II I~ OJ.:JVI1 ~I1b%.~o::l ~ (mean) 11el.:JA1.f1el3J~'[email protected]:U:l 'II Q -- 2 + 4 + 6 + 8 + 10 5 -- 30 5 (= 6)

fl'5m~el3~~aUq)flUq).:JA11a.J~I tb'JJ'JJbaJ~~fl~a.J i1

-c~'be1~h~) <il~'ln A1b%~1'..1 (mean) 11el~~e13Ja~Glit j'.x . 'II 'i Il X . j~ 18 l 99 9 210 10 10 r- - 10 3 30 \ 11 1 11 Lf= 6 L fx=59L xn = 59= 9•8 L f. X. 59 6 i=l I I - 6 = 9.8 ll Lf. i=l I

A ~ ~~uu I I Jl'l.x.l ~1<il@ln611~ A'n3-15 ifj 6 56 mi dpoint (X ) 3 144 80-4 (§!l- 2] +i 125-9 710-14 1215-19 17 5 8520-24 22 2 44 _ L:J@amdpomt)L f =30 :Lfx = 335)(- L: f .\r = 3f o5 = 11.17.9.1~~~

( ~1n~1~b~t~AmVItb1J1J~b~1-h'Viun (weighted arithmetic mean) )tin-am~el3J~um~:'\"h~A113J6hA'ru1a.it't'hnu v~ A.- 0 Ql w : bb't1UU1'Vi'UflX= w1x 1+ w2x2 + ... + wnxn w1 + w2 +... + wn n- ?1=:1wi xi - Lwx n Lw L w1. i=1

@bt~~~~ . .~rn-a'VIIbn-a~b%~tlb~u~bu~I.:J'VI~.:J~t~.:~m-a~hw:~u~hb%~tJ bb'l.J'l.Jrb.:~~I'VI,Xn.:. bfl'5Gl X1~1 Ql c 2 ... X l 3 ... w3l1'lf1 el.:Jfl ~'lf 1 Ql A 4 ... x 2 ... w IIUAGiAGiGf 22 'II B 3 ... x 1 ... waam 33 .'l-X 2.::.:: wixi = (2 X 3) + (4 X 2) + (3 X 1) i=l n 3+2 +1 L W; i=l = ( 2.83).9.1~~~ ~.2[1

3QJlfi£1~1U (median) = 575 ../ j d3~lUU£13..1 (mode) = 550 ../d3I I .:I = 775 XA1b%6i£1 (mean)

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( A11a.J6f~a.QJ'iVfUfoi'3:'Vi•11~ mean, median, mode )f Xmean = median = mode

mode mean

f r- f f .....-- \I-- .---- IJ ~ l/ X