Intro Kef1

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ΣΗΜΕΙΩΣΕΙΣ ΣΤΑΤΙΣΤΙΚΗΣ Ανδρεάνα Ασημοπούλου Επικ. Καθηγήτρια Τμήματος Χημικών Μηχανικών Α.Π.Θ. Σεπτέμβριος 2014

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Transcript of Intro Kef1

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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 ) .

  • , & , . , (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

  • (..) 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 .

  • (..) 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 .

  • 1.1: 120 1.1 .. X , X (. ), . , [ , ], (). - (groups), , . fi ( i ) , fi/n, n . . ri i (ri = r). .

  • . . 5-6 30 15-20 300. . - . . () xmin () xmax (range)

    R , r , ( ). xmin, xmax. ( ) ( ) ( ), [ , ). , , . . , , r . ( ) . , . -, . . . (histogram). fi, () pi, Fi, Pi i . , , . , (), , . ( )

  • fX (x) .. X, . .. X, , . X. ( 30 ) ( ). .. X . .. X . (stem and leaf plot) (dotplot). ` ! 2 (

    ) !!! , .

    . 1.3 ( ) 25 ( 20 ). ( . ) 1.3: ( ) .

  • X . xmin = 4.5, xmax = 7.0

    10 (k = 10)

  • 4.5. . 1.4 , , , . 1.4: fi, pi, Fi Pi.

    25 ( [5.25, 6.0]). X , 1.2. . ( ) .

  • 1.2: 1.3.

  • 1. 2014. .

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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

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    . () n . n (n + 1)/2, n ( n/2 n/2 + 1)

    [ 1.2 ] : 50% 50% .

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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 . ( ). , .

  • // . . xi 0 (1.2)

    x x x . . n . n 1 n s2

    [ 1.3 ] (1.3)

    [1.4 ]

  • s2 . s, s2. s .. X ( ) , X . *** x1, x2,.xn f1, f2, . fn , x1, x2,.xn f1, f2, . fn * () (n-1) , . ( ), n.

  • (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)

  • . , 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) .

  • X. 10 1.5

    . n

    . . ( , ). xmin = 0.40 Bq/g xmax = 2.10 Bq/g. R = 1.70 Bq/g, . s2

    (1.5)

  • 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 .

  • , . . . (, , ), . . () (leptokurtic), (platykurtic). (mesokurtic).

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  • . . . , 1999 .

    . 5 2011,

    http://users.auth.gr/dkugiu/Teach/ChemicalEngineer

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    1999.