Intro Kef1

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  • .

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    2014

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    1. & . , , . . ( ): : (), ( ), , ( ). , , , , , , , , , , , , , , , , , . . , . (population): , . , , . ( ), ( ),

  • ( ). (.. ), (.. ).

    (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). . ,

  • { } , . {, , } , .

    - , (sample). , (= o n xi ( n )). . , , . , (random sample), . , , , . , . , , .

    . - .. , , (.. ) ( , 1 ,) (.. ).

  • , , , , - -

    : , , ( ) , , ..

    (.) (.. Eurostat, OHE)

    ( ) , , . , ( ), . ( .. , ). , ( ) : ( ) , 50% ,

    : .

  • .

    , , ( ) .

    . (Random errors) . ( ) , . ( ) . . . (Systematic errors) , , .. , . , . / , , . . 30 100 , 100.000 . . . (Gross errors): , . .

  • &

    () . (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. .

    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.

  • ( ) . .. 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 . ( ) , .

  • 1.3: .

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

    [ 1.2 ] : 50% 50% .

  • . . , . . ( ) . , . . , . . ( ) ( ).

  • . , , . , . , . 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,