Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf ·...

25
Chap. 1 £ª5O

Transcript of Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf ·...

Page 1: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

Chap. 1 £££ããã555ÚÚÚOOO

Page 2: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

p³'-k�úi

I ¯Kµ��éÝCW�®NÈ�÷¿Ý§=��Ó�þe§éW�®�Ý���É��\±��"

I )û�{µ½ÏÄ�W�®��§ÿþÙ�ݧ(��Ý��35½��þ5�S"

I Uì5½§�ÝY²�L0.40´Ø�±�É�þ�"Ä���, ±��ªÇ©ÙãÚ��ã"

Page 3: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

L�Úã/�{

½½½555êêêâââ®®®ooo

I ªê©Ù(frequency distribution)µL«3A�pØ­U|O¥�z�|�N�ê8(=ªê)"

I ~fµeL�Ñ50g不<�ÀJ5«É�HØ��êâµCoke Classic (cc), Diet Coke (dc), Dr. Pepper (dp),Pepsi (p) Ú Sprite (s)"

cc s p dc cc cc p dc cc dccc cc cc dc p cc cc dp dp scc dc p dc p cc p p cc pcc cc p dp p p s cc cc ccs dp dc dp p cc p s cc dc

Page 4: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

ØØØ���ïïïgggêêê���ªªªêêê©©©ÙÙÙ

Ø� ªê

cc 19dc 8dp 5p 13s 5oO 50

R �è:

>data=c("cc","s","p","dc","cc","cc","p","dc","cc","dc","cc","cc","cc","dc","p","cc","cc","dp","dp","s","cc","dc","p","dc","p","cc","p","p","cc","p","cc","cc","p","dp","p","p","s","cc","cc","cc","s","dp","dc","dp","p","cc","p","s","cc","dc")>table(data)datacc dc dp p s19 8 5 13 5

Page 5: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

½5êâ®o

I �éªê©Ù(relative frequency distribution): ¤á|O��N�êÓoê�'~§=

�éªê = z�|�ªê���ê

I z©êªê©Ù(percent frequency distribution): �éªê¦±100"

I Ø�ïgê��éªêÚz©êªê©Ù

Ø� �éªê z©êªê

cc 0.38 38dc 0.16 16dp 0.10 10p 0.26 26s 0.10 10oO 1 100

Page 6: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

½5êâ®o

I ^/ã(bar graph)µ�«ã/�{§£±½5êâ�ªê©Ù§�éªê©Ù½öz©êªê©Ù" ã/�î¶L«êâ�|O§p¶±�z�|�ªê§�éªê½öz©êªê"

I Ø�ïªê�^/ã

cc dc dp p s

05

1015

R �èµ>barplot(table(data))

Page 7: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

½5êâ®oI \/ã(pie chart)µ�«£±½5êâ�ªê©Ù§�éªê©Ù½öz©êªê©Ù�ã/�{" r���y©eZ÷/Ü©§©O�L�|��éªê"

I Ø�ïªê�\/ã

cc

dc

dp

p

s

38%

16%

10%

26%

10%

Page 8: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

R �èµ

>pie(table(data))text(0.2,0.5,"38%")text(-0.4,0.2,"16%")text(-0.4,-0.3,"10%")text(0,-0.5,"26%")text(0.4,-0.1,"10%")

Page 9: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

½þêâ®oI c""O�m(Uê)

12 14 19 1815 15 18 1720 27 22 2322 21 33 2814 18 16 13

I ªê©Ùµ|ê§|°§|�"|êµpØ­U|��ê§���5�20�|"êâ�Nê8���§�5�6|§�êâ� Nê8���§Ï~À��õ�|ê§Ù8�´võ�|5w«êâ�CÉ"

I |°µ���z|O�°Ý�Ó§=

Cq|° = êâ���-êâ���|ê

.

~X§c""O�m�5�|O§Cq|°�(33-12)/5=4.2§Ïd±5U��|°"

Page 10: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

½þêâ®o

I |�µ(�z��êâ�áu��|"~Xc""O�mêâ�5�|O§|°�5§K5�|��µ10∼14§15∼19§20∼24§ 25∼29§30∼34"

I c""O�mêâ�ªê§�éªê§z©êªê©Ù

"O�m/U ªê �éªê z©êªê

10∼14 4 0.20 2015∼19 8 0.40 4020∼24 5 0.25 2525∼29 2 0.10 1030∼34 1 0.05 5oO 20

Page 11: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

½þêâ®oI ��ã(histogram): �«~^�½þ.êâ�ã/£ã�ª"ïÄ�Cþ§ p¶µªê§�éªê½z©êªê

I c""O�mêâ���ãHistogram of days

days

Fre

quen

cy

10 15 20 25 30 35

01

23

45

67

Page 12: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

R �èµ

>days=c(12, 14,19,18,15, 15,18,17,20, 27,22,23,22, 21,33,28,14, 18,16,13)>hist(days,nclass=5)

I \Ȫê©Ù(cumulative frequency distribution): £±�u½�uz�|þ���êâ�Nê8§ Ø´z�|�ªê"

I c""O�mêâ�\È©Ù

"O�m/U \Ȫê \È�éªê \Èz©êªê

�u½�u14 4 0.20 20�u½�u19 12 0.60 60�u½�u24 17 0.85 85�u½�u29 19 0.95 95�u½�u34 20 1.00 100

oO 20

Page 13: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

I \È­�: £ã\È©Ù�­�"ïÄ�Cþ§ p¶µ\Ȫê§�éªê½z©êªê

I c""O�mêâ�\È­�

Page 14: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

R �èµ>x=c(10,14,19,24,29,34)>y=c(0,0.20,0.60,0.85,0.95,1.00)>plot(x,y,type="b",xlab=""O�m(Uê)",ylab="\È�éªê")

Page 15: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

£ãÚOµê��{

~~~fff

I Small Fry Design úiÏLÝþ�G±u¦�²þÏ�Ú]7ê�5ýÿ�^y7Ú i�AÂá±G��Cz"úi��8Iµ�G±u¦�²þÏ�Ø�L45U§�L60U��G± u¦�]7êØA�LAÂá±�5%"

I úi^£ãÚOþ5ïþ�G±u¦�Ï�µ²þê 40U¥ ê 35U¯ê 31UÚO®ow«§�k3%��G±u¦7��L60U

Page 16: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

£ãÚOµ ��Ýþ

I ²þê(mean)µéêâ¥% ��Ýþ"��²þêµx̄¶oN²þêµµ"

I Pxi, i = 1, 2, · · · , n L«*ÿ��§@o��²þê�µ

x̄ =∑ni=1 xin

= x1 + x2 + · · ·+ xnn

.

I e¡5g,�?5 Æ)�¤1µx1 = 76§x2 = 84§x3 = 72§x4 = 76§x5 = 62§K

x̄ =∑5i=1 xin

= 76 + 84 + 72 + 76 + 625 = 74.

I b�oN¥kN��N§ÿþ��Xi, i = 1, 2, · · · , N§KoN²þêµ

µ =∑Ni=1Xi

N.

Page 17: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

£ãÚOµ ��Ýþ

I ¥ ê(median)µéêâ¥% ��Ýþ"ò¤kêâUì,Sü�§ u¥m�ê�"(a)*ÿê�Ûê�§¥ ê´ u¥m�@�ê�¶(b)*ÿê�óê�§¥ ê´ u¥m�ü�ê��²þ�"35 Æ)�¤1¥§¥ ê�76"

I ¯êµêâ8¥ÑyªÇ�p�êâ�"35 Æ)�¤1¥§¯ê�76"

I z© ê(percentile)µ1pz© ê÷v^����ê�§��kp%�*ÿ��u½�u T�§���k(100− p)%�*ÿ��u½�uT�"O�1pz© ê§1. rêâU,Sü�¶2. O��ê i = (p/100)n¶3. eiØ´�ê§K��ui�e���êéA ��ê�¶ei´�ê§ K�1i�Ú1i+ 1�êâ�²þ�"

I o© êµ125§50§75z© ê"

Page 18: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

£ãÚOµCɧÝ�Ýþ

I Ø �Ýþ§·����Äêâ�Cɧݧ�=lѧÝÝþ"~ü[,�¬øAû§§�10g �À¤I��m©O´µøAû Aµ9§11§11§10§10§10§11§10§10§11øAû Bµ7§8§7§10§10§10§11§12§13§15´�§§��²þ�À¤I��mÑ´10U"

Page 19: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

£ãÚOµCɧÝ�ÝþI �À¤I��m��ã

Page 20: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

£ãÚOµCɧÝ�Ýþ

I 4�(range)µ���-���"`:§N´O�¶":§´ÉÉ~�K�"øAû Aµ4�=11-9=2øAû Bµ4�=15-7=8

I o© êmå(inter quartile range)µIQR=13o© ê-11o© ê=Q3 −Q1"´�§IQR Ò´¥m�50%�êâ�4�"øAû AµIQR=11-10=1øAû BµIQR=12-8=4�ã(Box plot)

I ��(variance): Ýþ¤kêâ�CɧÝ"

oN��µσ2 =∑N

i=1(Xi−µ)2

N "

����µs2 =∑n

i=1(xi−x̄)2

n−1 "

øAû Aµs2 = (9−10)2+(11−10)2+···+(11−10)2

9 ≈ 0.456øAû Bµs2 = (7−10)2+(8−10)2+···+(15−10)2

9 ≈ 6.678"

Page 21: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

R �èµ> a=c(9,11,11,10,10,10,11,10,10,11)> b=c(7,8,7,10,10,10,11,12,13,15)> group=c(rep(1,length(a)),rep(2,length(b)))> boxplot(c(a,b)~group)

�À¤I��m�ã

Page 22: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

£ãÚOµCɧÝ�Ýþ

I IO�µoNIO� σ =√σ2¶��IO� s =

√s2"

øAû Aµs ≈ 0.675øAû Bµs ≈ 2.584"

I CÉXê(coefficient of variation)µ(IO�²þê

× 100)%"øAû Aµ s

10100% = 6.75%øAû Bµ s

10100% = 25.84%"

Page 23: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

£ãÚOµ©Ù/G

I êâ�©Ù/�Ì��êâ©Ù´Ä顧 �§ÝXÛ§©ÙÍ�§Ý�"(1)  Ý£Skewness¤µ£ãCþ��©Ù/�é¡5�ÚOþ"ÙO�úª�µ

βs = µ3σ3 = E(X − E(X))3

(E((X − E(X))2))3/2

�©Ù�é¡©Ù�§�Ko ���§ Ý��u0¶�©Ù�Øé¡©Ù�§�Ko �Ø��§ Ý��u0½�u0"  Ý��u0L«� ���§¡�� ½m ¶ Ý��u0L«K ���§¡�K ½� " Ýýé���§ L«êâ©Ù/�� �§Ý��"

Page 24: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

£ãÚOµ©Ù/G

I (2) ¸Ý£Kurtosis¤µ£ãCþ��©Ù/�Í�§Ý�ÚOþ"ÙO�úª�µ

βk = µ4σ4 = E(X − E(X))4

(E((X − E(X))2))2 − 3

�êâ©Ù�IO��©Ù�Í�§Ý�Ó�§¸Ý��u0¶¸Ý�u0L«êâ�©Ù'IO��©Ù²�§�²¸©Ù¶¸Ý�u0L«êâ�©Ù'IO��©Ù�Í�§�k¸©Ù"

Page 25: Chap. 1 £££ªªª555ÚÚÚOOOstaff.ustc.edu.cn/~zfw/nonpara/chapter1.pdf · £ªÚOµŒ−’{~~~fff I SmallFryDesignœiˇLÝþŽG–uƒ˙†þˇ†Ú] 7Œ 5ýÿ„^y7ÚiłA´Æ–G

£ãÚOµ��

æ�/«�ûÆ�¥ôÖóû+na¬(MBA)Æ êâ" ¯Kµ

I éz�Cþ�£ãÚO©Û§éuæ�ûÆ�§ùêâUJø�o#�&Eº

I ®oêâ'�µ(1) �IÆ)ƤÚIÆ)Ƥ�É"(2) �¦ó�²�ÚØ�¦ó�²��Æ�ÙÆ)å���É"(3) �¦=�ÿÁÚØ�¦=�ÿÁ�Æ�ÙÆ)å���É"

I å��Ƥk'íº

I éêâ�Ñã/©Û.