.MCAD 308000000 \  docDocumentMmcObject[11 d2_graph_format graphData% axisFormat)L)Ltrace2D&&&&&&&&& & & & & &&& dim_formatTmasslengthtimecharge temperature luminosity substanceNumericalFormatQdii shpRectVmcDocumentObjectState\ mcPageModelK?XU???mcHeaderFooterI@I CHeaderFooterJ@J@J@JMbP?MbP? TextState? TextStyle>@ Arial0,0,128Serial_ParPropDefaultW?Normalfont_style_listO font_styleP  VariablesTimes New Roman@P  ConstantsTimes New Roman@P TextArial@P Greek VariablesSymbol@P User^1Arial@P User^2 Courier New@P User^3System@P User^4Script@P User^5Roman@P User^6Modern@P User^7Times New Roman@P SymbolsSymbol@P Current Selection FontArial@P Undefined Font@P HeaderArial@P FooterArial@P Rotated Math FontTimes New Roman* TextRegion* docRegionGshpBoxU ] QQ CharacterMap-RangeMap;@wAPPLIED QUANTITATIVE RESEARCH PAD/PDD/UST601 COMPUTER LAB#2: DISTRIBUTION OF SAMPLE MEANS AND THE CENTRAL LIMIT THEOREM ChrPropMap7w RangeElem<w  ChrPropData8 RangeData=~ MathSoftText 128,0,128 ParPropMap9w 0@NormalArial ?eqRegionB@U8J@@tree @ p@A@@ @@@B@@d@A\m@C@@@A@D@@@@C@E@@t@D1@F@@@D6@G@@@@C@H@@@@G@I@@t@H1@J@@@H6@K@@@G@L@@d@Kj@M@@@Kj@N@B@U@O@@ p@P@@ @O@Q@@d@P\s@R@@{@P@S@@@R@T@@@@S@U@@t@T1@V@@@T6@W@@@@S@X@@@@W@Y@@t@X1@Z@@@X6@[@@@W@\@@d@[j@]@@@[@^@@p@@]@_@@@^@`@@d@_j@a@@@_\m@b@@@]2@c@B@U8v I@d@@ p@e@@@d@f@@d@e\m@g@@@e@h@@+@@gSerial_DisplayNodeX@i@@@g _n_u_l_l_@j@B@U^ @k@@ p@l@@@k@m@@d@l\s@n@@@l@o@@+@@n@X@p@@@n _n_u_l_l_@q*@U!;0:+i+i-A|We generate next random numbers 1, 2, 3, 4, 5, 6 from the uniform distribution by using runif(N,1,7), which returns a vector of N random numbers between 1 and 7 having the uniform distribution. To generate just integers in that interval we apply the function floor to runif(N,1,7). The function floor(x) returns the greatest integer that is less than or equal to x. For example:7nX|@r Root EntryaB.dK8aCContents9OlePres000>#R KQ MS Sans Serif T1c$Arial `YYDArial `YYDA@@A@XA@@A _n_u_l_l_A*@U_jh -COPYRIGHT @KAUFMAN, 19997A<A8A~9A<A :@W?1A!</A"<A#0@NormalArial A$*@U5--~-~-AIn this table, column number t represents the results of the t's sampling. Next we graph the results of the 5'th and 15'th sampling. We show on the same graph: (mean + one standard deviation) and (mean - one standard deviation) to illustrate that for this uniform distribution 2/3 of the data is expected to fall in this interval. We use the MathCAD descriptive statistics functions mean and Stdev.7A%<A&8A$ MathSoftTextA'<A(8A$ MathSoftTextA%A)<5A*8A$ MathSoftTextA'A+@@@A=A?@@@A>A@@@tA?6.1AA@@A?0.9AB@@A>AC@@dAB _n_u_l_l_AD@@AB _n_u_l_l_AE@@ A=AF@@ @AEAG@@ @AFAH@@@AGAI@@dAHdiceAJ@@ AHAK@@dAJjAL@@AJ5AM@@AGAN@@@AMAO@@dANmeanAP@@pANAQ@@4APAR@@dAQdiceAS@@AQ5AT@@AMAU@@dATStdevAV@@pATAW@@4AVAX@@dAWdiceAY@@AW5AZ@@AFA[@@@AZA\@@dA[meanA]@@pA[A^@@4A]A_@@dA^diceA`@@A^5Aa@@AZAb@@dAaStdevAc@@pAaAd@@4AcAe@@dAddiceAf@@Ad5Ag@@AEAh@@dAgmeanAi@@pAgAj@@4AiAk@@dAjdiceAl@@Aj5Am@@A@B@U B?@@ pB@@@ B?BA@@dB@mBB@@B@BC@@tBB0BD@@BBBE@@dBDBINBF@@BD1BG@B@U  3 BH@@ pBI@@ BHBJ@@@BIBK@@dBJintBL@@BJmBM@@BIBN@@@BMBO@@@BNBP@@dBOmBQ@@BOBINBR@@BN5BS@@BM1BT@B@U   BU@@ pBV@@ BUBW@@@BVBX@@eBW0intBY@@BWBINBZ@@BV6B[*@U   '~~-@mIn the interval (2.5,2.75) there are 3 data points, while in the interval (3.,3.25) there are 18 data points.7mB\ Root EntryaB.dK8yContents9OlePres000R KQ MS Sans Serif T1c$Arial@`YYDArial@`YYDBr@@Bn@XBs@@Bl _n_u_l_l_Bt@B@U u p )Bu@@ pBv@@BuBw@@dBvintBx@@BvBy@@@BxBz@@5ByB{@@<@BzB| BtB{B}< r7CVSOleClientItem ࡱ> Root EntryaB.dK8QDContents9OlePres000R KQ MS Sans Serif T1c$"Arial `YYDArial `YYDB~@@Bz@XB@@Bx _n_u_l_l_B*@U ,  * -COPYRIGHT @KAUFMAN, 19997B<B8B~9B<B:@W?1B</B<B0@NormalArial B*@U   J-@C We normalize the hist and dnorm functions by using the following:7ACB<B8BB