Intro Kef1
description
Transcript of Intro Kef1
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2014
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1. & . , , . . ( ): : (), ( ), , ( ). , , , , , , , , , , , , , , , , , . . , . (population): , . , , . ( ), ( ),
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( ). (.. ), (.. ).
(variable): , . , (xi) i=1,2, ..., , , . , , . , X,Y,Z. (quantitative) , . ( min) Internet, ( ) , , , , , , /, , , , , . . (qualitative) ( ) . , , , , , , , , . . . (discrete) (continuous). , , . , {1, 2, 3, 4, 5, 6, 7, 8}. {0, 1, 2, 3, 4, . }. {0, 0.5, 1, 1.5, 2, 2.5, , 9, 9.5, 10} .. (0,1) [0,). , min Internet , 15 min 300 min. , o , , , , , ( ), , /, , , . ( ) (nominal) (ordinal). . ,
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{ } , . {, , } , .
- , (sample). , (= o n xi ( n )). . , , . , (random sample), . , , , . , . , , .
. - .. , , (.. ) ( , 1 ,) (.. ).
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, , , , - -
: , , ( ) , , ..
(.) (.. Eurostat, OHE)
( ) , , . , ( ), . ( .. , ). , ( ) : ( ) , 50% ,
: .
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, , ( ) .
. (Random errors) . ( ) , . ( ) . . . (Systematic errors) , , .. , . , . / , , . . 30 100 , 100.000 . . . (Gross errors): , . .
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() . (census).
() , , , , . .
(Simple Random Sampling) . 1, 2, ... 10%- 15% . . (Systematic Sampling) , . - . : 1, 2, ..., (.. 10), (.. 5) 10, 15, 20 ... . (Stratified Sampling ) .
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, & , . , (frequency distributions) . X ( ) (frequency table). (frequency) fi , xi . xi X fi , . n , :
f1 + f2 + .. fn = n (relative frequency) (percent) pi fi xi n ( fi n ,
(cumulative frequency) Fi xi xi ,
Pi
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(..) X, fX (x) . FX (x) . (x1, f1), (x2, f2)..(xn, fn) f1, f2, ..fn, x1., x2, ..xn . , x1., x2,. xn . (barchart) . , ( , ) xi. ( fX (x) ). . , (pie chart) () . 5 . . 120 1.1. ( . ) 1.1: 120 .
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(..) X 5L . 1.1 ( 1 ). , , 1 2 , 3 4 4 . 1.1 . ; 2 3 ; . ( SPSS). 1.2: 120 1.1 fi, pi, Fi Pi).
1.2 X ( xi i = 1, . . . , 6) , fi xi , () pi , Fi Pi . 1.1 . 2 , 1 3 , 4, 5 6 .
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1.1: 120 1.1 .. X , X (. ), . , [ , ], (). - (groups), , . fi ( i ) , fi/n, n . . ri i (ri = r). .
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. . 5-6 30 15-20 300. . - . . () xmin () xmax (range)
R , r , ( ). xmin, xmax. ( ) ( ) ( ), [ , ). , , . . , , r . ( ) . , . -, . . . (histogram). fi, () pi, Fi, Pi i . , , . , (), , . ( )
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fX (x) .. X, . .. X, , . X. ( 30 ) ( ). .. X . .. X . (stem and leaf plot) (dotplot). ` ! 2 (
) !!! , .
. 1.3 ( ) 25 ( 20 ). ( . ) 1.3: ( ) .
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X . xmin = 4.5, xmax = 7.0
10 (k = 10)
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4.5. . 1.4 , , , . 1.4: fi, pi, Fi Pi.
25 ( [5.25, 6.0]). X , 1.2. . ( ) .
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1.2: 1.3.
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1. 2014. .
8 4 6,5 4 9 0 2 2 5 0 7 3 9 3 0 3 1 1 2 2 10 8 4 5 9 1 5 3 3 3 3 9 3 1 4 5 1 1 6 5 4 7,5 1 2 3 5 5 3 7 4 1 6,5 5 6 4 5 1 1 2 0 2 2 5 5 1 3 3 3 7 2 6 1 2 5 2 5 5 7 6 2 5 1 7 5 6 1 1 1 2 4 5 1 9 4 5 2 7 3 5 6 5 0 2 3 5 5 9 2 7,5 4
2. .
, , .
3.
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( ) . .. X (descriptive statistics). .. . . : (measures of location) (.. ) (variability measures) . . : (sample mean value) (arithmetic mean), (average), (sample median), (sample mode) . . x1, x2, . . . , xn, .. X . x
[ 1.1 ] n . ( ) , .
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1.3: .
. () n . n (n + 1)/2, n ( n/2 n/2 + 1)
[ 1.2 ] : 50% 50% .
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. . , . . ( ) . , . . , . . ( ) ( ).
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. , , . , . , . 1.4 .
1.4. . 600 mg , 500 700 ( 600), 900 300 ( 600). . , . : (sample range) R, / (sample variance) s2 (standard deviation) s. (percentiles) (interquartile range). R = xmax xmin . . xmin xmax . ( ). , .
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// . . xi 0 (1.2)
x x x . . n . n 1 n s2
[ 1.3 ] (1.3)
[1.4 ]
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s2 . s, s2. s .. X ( ) , X . *** x1, x2,.xn f1, f2, . fn , x1, x2,.xn f1, f2, . fn * () (n-1) , . ( ), n.
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(box plot) . . . p- (ppercentile) p% (0 p < 1). 75 , 75% 25% . 75 . 50- . (quartiles). 25- - (first or lower quartile) Q1, 75- (third or upper quartile) Q3. ( ). , , n 1 n/2 n/2 + 1 n, n 1 (n + 1)/2 (n + 1)/2 n ( ).
1.5: . . I = Q3 Q1 (interquartile range) (). I ( R)
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. , Q1 Q3 , xmin xmax, 5 (five number summary). 5 (box plot) 1.6. Q1 Q3 ( ) . xmin xmax.
1.6: , SPSS, ( (whiskers)) . . . ( Bq/g) 10 . 1.5. ( . ) 1.5: ( Bq/g) .
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X. 10 1.5
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. . ( , ). xmin = 0.40 Bq/g xmax = 2.10 Bq/g. R = 1.70 Bq/g, . s2
(1.5)
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0.5 Bq/g, ( ). 5 1.7 . , I = Q3 Q1 = 0.67 0.51 = 0.16 Bq/g. 5 . 1.8 . 2.10. , , Q3 = 0.67, 3I = 3 0.16 = 0.48.
1.7: 5 10 .
1.8: 10 .
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, . . . (, , ), . . () (leptokurtic), (platykurtic). (mesokurtic).
. . . ( %) , .
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. , . .
:
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1. 0-15% 2. -30 3. ( ). , . , . . ( ). . . . . . , . :
, .
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. . , , . ( . )
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3.
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. . . , 1999 .
. 5 2011,
http://users.auth.gr/dkugiu/Teach/ChemicalEngineer
. . . & . ,
1999.