a

x x x x 1 x 2 Ý; x. x = x 1 + x 2 + Ý + x = 10 1; 1; 3; 3; 4; 5; 8; 8; 8; 9 1 + 1 + 3 + 3 + 4 + 5 + 8 + 8 + 8 + 9 10 = 50 10 = 5

. 1 1 Ý Ý # 2 2 Ý Ý & 7 7; 9; 15; 21; 33; 44; 56 21 8 7; 9; 15; 20; 22; 26; 27 28 20 + 22 = 42 2 2 = 21

1 2 3

=

1 2 3

. 10 1; 1; 3; 3; 4; 5; 8; 8; 8; 9 8 3 8

4 3 1 2 3 Q 1 Q 2 Q 3

1 Q 1 2 Q 2 3 Q 3 1 2 Q 2 3 2 4 3 Q 1 5 3 Q 3 1 Ý {z } Q 1 2 Ý, {z } Q 1 Ý {z } Q 3, Ý {z } Q 3

1 Q 1 3 Q 3 Q 3 Q 1 Q 3 Q 1 2

1 Q 1 3 Q 3 ( ) ( ) ( ) 1 1 Q 3 Q

x x 1 x 2 Ý; x x x 1 x x 2 x Ý ; x x 0

1 2 2 s 2 s, x x 1 x 2 Ý; x x s 2 = (x 1 x) 2 + (x 2 x) 2 + Ý + (x x) 2 = 1 P (x k x) 2 F (x 1 x) 2 + (x 2 x) 2 + Ý + (x x) 2 s = C = stadard deviatio x cm s 2 cm 2 s cm x 6 4; 5; 7; 8; 8; 10 x 4 + 5 + 7 + 8 + 8 + 10 = 42 6 6 = 7 s 2 = (4 7)2 + (5 7) 2 + (7 7) 2 + (8 7) 2 + (8 7) 2 + (10 7) 2 6 = 9 + 4 + 0 + 1 + 1 + 9 = 24 6 6 = 4 s = B 4 = 2

x s x x 2 x 2 s 2 = x 2 (x) 2 (x ) = (x 2 ) (x ) 2 s 2 = (x 1 x) 2 + (x 2 x) 2 + Ý + (x x) 2 = (x 1 2 + x 2 2 + Ý + x 2 ) 2 x (x 1 + x 2 + Ý + x ) + (x) 2 = x 1 2 + x 2 2 + Ý + x 2 = x 1 2 + x 2 2 + Ý + x 2 = x 2 (x) 2 2x x 1 + x 2 + Ý + x + (x) 2 2 (x) 2 + (x) 2 $ Û x 1 + x 2 + Ý + x = x < x 6 4; 5; 7; 8; 8; 10 x = 4 + 5 + 7 + 8 + 8 + 10 = 42 6 6 = 7 x 2 x 2 = 42 + 5 2 + 7 2 + 8 2 + 8 2 + 10 2 6 = 318 = 53 6 s 2 = x 2 (x) 2 = 53 49 = 4 = 16 + 25 + 49 + 64 + 64 + 100 6

2 x y (x; y)

2 1 2 2 2 3 2

2 5 A B C D E É A Ê É B Ê É C Ê É D Ê É E Ê 1 A B A, A 2 C D C, C 3 E

2 2

2 x y x y s xy 2 x y (x 1 ; y 1 ) (x 2 y 2 ) Ý; (x ; y ) x y s xy = (x 1 x)(y 1 y) + (x 2 x)(y 2 y) + Ý + (x x)(y y) = 1 P (x k x)(y k y)

2 x y (x 1 ; y 1 ) (x 2 y 2 ) Ý; (x ; y ) 3 x = 1 P x k y = 1 P y k xy = 1 s xy s xy = xy x y =(xy ) (x ) (y ) P x k y k sxy = 1 = 1 = 1 P (x k x)(y k y) P (x k y k yx k xy k + x y) P x k y k y 1 P x k x = xy y x x y + 1 x y = xy x y 1 P y k + 1 P x y (2016 ) (2016) (2018)

2 x y 1 x y 2 x y 3 0 x y A = Q(x; y) j x > x y > y i B = Q(x; y) j x < x y > y i C = Q(x; y) j x < x y < y i D = Q(x; y) j x > x y < y i (x k y k ) 2 A x k x > 0 y k y > 0 (x k y k ) 2 B x k x < 0 y k y > 0 (x k y k ) 2 C x k x < 0 y k y < 0 (x k y k ) 2 D x k x > 0 y k y < 0 (x k y k ) 2 A [ C (x k x)(y k y) > 0 (x k y k ) 2 B [ D (x k x)(y k y) < 0 s xy = (x 1 x)(y 1 y) + (x 2 x)(y 2 y) + Ý + (x x)(y y) A [ C (x k y k ) s xy B [ D (x k y k ) s xy y y B C x A D x

r 2 x y s x s y s xy r = = s xy s x s y r = F (x 1 x)(y 1 y) + (x 2 x)(y 2 y) + Ý + (x x)(y y) F (x 1 x) 2 + (x 2 x) 2 + Ý + (x x) 2 (y 1 y) 2 + (y 2 y) 2 + Ý + (y y) 2

2 x y r = x y x y 2 r = (x 1 x)(y 1 y) + (x 2 x)(y 2 y) + Ý + (x x)(y y) C (x 1 x) 2 + (x 2 x) 2 + Ý + (x x) 2 C (y 1 y) 2 + (y 2 y) 2 + Ý + (y y) 2 r (x 1 x)(y 1 y) + (x 2 x)(y 2 y) + Ý + (x x)(y y) r = F F (x 1 x) 2 + (x 2 x) 2 + Ý + (x x) 2 (y 1 y) 2 + (y 2 y) 2 + Ý + (y y) 2

r 1 1 r 1 2 r 1 3 r 1 Ã! Ã! r Ì 1 r Ì 0 r Ì 1

2 x y x y a b 1 ax + b = a x + b 2 x + y = x + y 3 x y = x y 1 x x 1 x 2 Ý; x x = x 1 + x 2 + Ý + x ax + b ÝÝ1 ax + b = (ax 1 + b) + (ax 2 + b) + Ý + (ax + b) z } { = a(x 1 + x 2 + Ý + x ) + b + b + Ý + b x 1 + x 2 + Ý + x = a + b = a x + b (Û 1) 2 x x 1 x 2 Ý; x y y 1 y 2 Ý; y x = x 1 + x 2 + Ý + x x + y y = y 1 + y 2 + Ý + y x + y = (x 1 + y 1 ) + (x 2 + y 2 ) + Ý + (x + y ) = (x 1 + x 2 + Ý + x ) + (y 1 + y 2 + Ý + y ) ÝÝ2 = x 1 + x 2 + Ý + x + y 1 + y 2 + Ý + y = x + y (Û 2) 3 2 x y x + y = (x 1 y 1 ) + (x 2 y 2 ) + Ý + (x y ) = (x 1 + x 2 + Ý + x ) (y 1 + y 2 + Ý + y ) = x 1 + x 2 + Ý + x y 1 + y 2 + Ý + y = x y (Û 2)

x s x 2 s x a b 2 ax + b s ax+b s ax+b 1 s 2 ax+b = a 2 2 s x 2 s ax+b = a s x 1 x x 1 x 2 Ý; x x s 2 x = 1 P (x k x) 2 ÝÝ1 ax + b s ax+b 2 = 1 = 1 = 1 = 1 = a 2 P P P P 1 Q(ax k + b) ax + b i 2 Q(ax k + b) (ax + b)i 2 # Û ; Qa(x k x )i 2 a 2 (x k x ) 2 P (x k x ) 2 = a 2 s x 2 (Û 1) 2 1 s ax+b = C a 2 s x 2 = a s x

2 x y s xy a b c d 2 ax + b cy + d s (ax+b)(cy+d) s (ax+b)(cy+d) = ac s xy x x1 x 2 Ý; x y y 1 y 2 Ý; y 2 x y x y s xy = 1 P (x k x)(y k y) ÝÝ1 2 ax + b cy + d s (ax+b)(cx+d) = 1 = 1 = 1 = ac P P P 1 Q(ax k + b) ax + b iq(cy k + d) cy + d i Q(ax k + b) (ax + b) iq(cy k + d) (cy + d) i Qa(x k x)iqc(y k y)i P (x k x)(y k y) = ac s xy (Û 1) # Û ;

2 x y r xy a b c d 2 ax + b cy + d r (ax+b)(cy+d) 1 ac = 0 r (ax+b)(cy+d) = 0 2 ac > 0 r (ax+b)(cy+d) = r xy 3 ac < 0 r (ax+b)(cy+d) = r xy 2 x y sx s y s xy 2 ax + b cy + d s ax+b s cy+d s (ax+b)(cy+d). ac = 0 s(ax+b)(cy+d) = 0 r (ax+b)(cy+d) = 0 ac Ë 0 r (ax+b)(cx+d) = s (ax+b)(cy+d) s ax+b s cy+d = ac s xy a s x c s y # Û ; = acs xy ac s xy ac > 0 = X ac < 0 ac s xy ac s x s = s xy y s x s = r xy y ac s xy ac s x s = s xy y s x s = r xy y