1.. . , , , , (, , , . .). , , , : , , (, ), (, , , ).
, , . .
; , , , , , . .
:
- . 2 .
. . .
. , , , .
. , .
. , 100 ( 100).
.
21,9; 21,4; 27,7; 17,0; 12,3; 21,7; 23,4; 25,7; 21,2; 20,3;
23,8; 24,1; 26,9; 21,4; 20,7; 18,5; 22,5; 23,0; 18,5; 25,7;
20,1; 21,3; 15,7; 24,8; 19,3; 22,2; 22,9; 14,9; 26,1; 20,5;
14,6; 27,8; 22,4; 16,7; 22,9; 25,3; 22,7; 19,7; 15,2; 21,3;
22,1; 20,5; 19,7; 24,5; 29,6; 22,3; 19,1; 23,5; 25,9; 17,2;
15,5; 18,1; 23,9; 25,4; 20,4; 13,2; 19,6; 24,4; 18,2; 24,8;
24,2; 20,9; 20,1; 16,5; 20,9; 23,2; 27,2; 21,1; 26,3; 18,6;
17,2; 17,8; 31,2; 25,0; 20,7; 18,3; 23,7; 16,1; 16,2; 21,6;
23,0; 20,7; 25,3; 13,9; 17,3; 21,8; 14,1; 19,0; 21,9; 18,7;
28,5; 21,2; 19,9; 24,8; 22,7; 16,4; 20,6; 23,5; 22,2; 19,5.
, , . . .
(min) = 12,3 , (max)=31,2 . (/), :
(1)
, , . : 30 60 68 , 61 100 78 , 101 912 . 10 .
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. 1,89, K = 2.
. min = 12,3 (12), . (2 ), (14). , 16, 18, 20, 22 . .
, , . , 0,1 . 0,1 , : 12,0 13,9, 14, 0 15,9, 16,0 17,9 . . (W). (12+14):2=13, (14+16):2=15, (12+1=113 . .).
, , , (. 1). , , , . f.
1.
1. 100
f | f | ||||
12,0-13,9 | 22,0-23,9 | ||||
14,0-15,9 | 24,0-25,9 | ||||
16,0-17,9 | 26,-27,9 | ||||
18.0-19.9 | 28,0-29,9 | ||||
20.0-21,9 | 30,0-31,0 |
∑f =n=100
, -, . (∑f) (). ∑ff =n=100.
,
, .
:
(W), 13 15 17 19 21 23 25 27 29 31
(f) 3 6 10 15 24 19 14 6 2 1
( ). , , : ( ) , ( ) . , , . , , , , , (. 1).
. 1 :
,
, '(. 2). , . , (. 3).
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. 2. . 3.
.
.
, . () .
. 231 ( . ):
(). 0123 4 5 6 7 8 9 10
(q). 10 9 8 7 6 5 4 3 2 1 0
(ni)... 0 4 3 33 45 56 44 28 14 3 0
n=∑ nii =231
.
:
= (41+32+333+454+565+446+287+148+93+
100): 231 = 1178:231 =5,1 .
231 : =1117:(10 231)=0,51.
231 : q=1 - =1 - 0,51=0,49
(, q ).
(+q)n, .
:
0 1 2 3 4 5 6 7 8 9 10
. (.) 043 33 45 56 44 28 14 3 1
. (.) 0 2 10 27 48 57 48 27 10 2 0
( = q=0,5) . (. 4).
. 4. 10 .
I- ,.
, 1 ., 10 . (, , , , - ).
, , .
. 100 4 . 10 . :
( +).. 0123
()..................................... 90 6 3 1
100
. 76 - ( ). . - : 5, 4, 4, 2, 8, I, 6, 4, 3, 4, 4, 4 , 4, 5, 2, 4, 7, 4, 6, 5, 6, 4, 5, 4, 4, 8, 4, 5, 4, 4, 5, 4, 3, 4, 5, 4, 5, 4, 4, 7, 3, 4, 5, 4, 5, 4, 4, 5, 3, 4, 4, 4, 4, 7, 5, 3, 6, 4, 9, 4, 4, 6, 4, 2, 6, 4, 2, 4, 5, 4, 4, 4, 4, 3, 4.
=76. : lim=l9 ( ).
, . , 1 , . . 9 . :
( ) (w) 1 2 3 4 5 6789
( ) (/) 1 4 6 39 13 7 3 2 1
( ). ( ) .
, , 19 19,1 19,12 .
. 5. :
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; .
. 6.
. 7.
. (). (1, 2 ...9). , . . ( ). , (. 5).
, , , . (. 6).
(. 7) . . (, ).
2.
. .
. , . , . : , .
: , , , .
(X) . , (x1+2+3+n) ():
(3)
∑x . (2) X.
: 1 5, 2 6, 3 3, 4 7, 5 4 . (2).
. X . .
- . . :
= + (3), (4)
; , .
(. 2).
(). , . =21 . , (2) .
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2 , .