USING STATISTICAL FUNCTIONS ON A SCIENTIFIC CALCULATOR

Transcription

1 USING STATISTICAL FUNCTIONS ON A SCIENTIFIC CALCULATOR Objective:. Improve calculator skills eeded i a multiple choice statistical eamiatio where the eam allows the studet to use a scietific calculator.. Helps studets idetify where ad what their problem may be. Target group: This worksheet is for studets who do ot have a soud mathematical backgroud ad are doig a statistics module; studets who did maths literacy at school; studets who have a supplemetary for a statistics eam. FUNCTION (ormal mode) CASIO f-99es PLUS SHARP EL-53WH MY NOTES FROM QL WORKSHOP Proper fractios 4 4 = 4 b a c 4 = 4 Improper fractios = b a c 3 = 3 3 (the aswer is 3 3 ) Mied fractios = b a c b a c 3 = 4 3 SD = 3 3 df b a c aswer 3 3 Covertig betwee fractios ad decimals Follows from above 3 3 SD aswer SD aswer 4 3 Follows from above 3 3 b a c aswer b a c aswer 4 3 Quatitative Literacy (QL) UNISA Durba Learig Cetre, Dr Piley Ka Seme St

2 4 Havig difficulty simplifyig without the use of a calculator? Did you kow it is much quicker to do it metally tha reach for a calculator?! Try doig a worksheet or QL workshop o FRACTIONS! factorial! 5! The factorial otatio is used to represet the product of the first atural umbers, where 0 5 = 0 The butto with orage above it egages the orage colour stats fuctios above each umerical pad butto. 5 df 4 =0 The orage df butto egages the orage colour stats fuctios i the left had corer of each umerical pad butto. Fractios usig! 5! 3! 5 = df 4 3 df 4 = 0 Fractios with two factorials i the 0! deomiator 7!3! Permutatios Pr (o repeats; order is importat) Pr! ( r)! 9! 9P 6 (9 6)! 0 3 ( 7 ) = 0 Brackets NB! Why? 9 6=60480 Before pushig equal the scree will have9p 6. Else 9 ( 9 6 ) = df 4 ( 7 df 4 3 df 4 ) = 0 Brackets NB! Why? 9 df 6 6=60480 After pushig equal the scree will have9p 6. Else 9 df 4 ( 9 6 ) df 4 = Combiatios Cr (o repeats; order is NOT importat) 9 6=84 Before pushig equal the scree will have9c 6. Else 9 df 5 6=84 After pushig equal the scree will have9c 6. Else Quatitative Literacy (QL) UNISA Durba Learig Cetre, Dr Piley Ka Seme St

3 Cr! r!( r)! 9! 9C 6 6!(9 6)! 9 ( 6 ( 9 6 ) ) = 84 Both sets of brackets NB! Why? 9 df 4 ( 6 df 4 ( 9 6 ) df 4 ) = 84 Both sets of Brackets NB! Why? Coutig r objects i differet ways (repeats/repetitio) 6 5 r 5 6 ) = y 6 = 565 See diagram for determiig the differeces betwee PERMUTATIONS & COMBINATIONS. Epoets i a bracket (Appedi A attached at the ed of this QL worksheet) (9 6) 0.75 (9 6) 0.75 Powers with base e e 3 e ) = 0.4 The calculator already opes with a bracket, it just eeds to be closed. Why ad whe? You get the aswer without closig the bracket, BUT what would happe if you multiplied the epressio by? ) = Now closig the bracket is importat. Why? l 3 ) =.396 Alteratively, 0.75 y ( 9 6 ) = 0.4 Multiply the epressio by before pressig the equal sig, 0.75 y ( 9 6 ) =0.844 Brackets NB! Why? df l b a c 3 =.396 Alteratively, Quatitative Literacy (QL) UNISA Durba Learig Cetre, Dr Piley Ka Seme St 3

4 l 3 ) =.396 df l ( 3 ) =.396 e 3 l ( ) 3 ) = 0.05 df l 3 = 0.05 The calculator automatically puts brackets aroud the first term. Why is there o eed to put brackets i this situatio? 3 e l 3 ) = 0.05 Alteratively, df l ( 3 ) = 0.05 Alteratively, 4e 3 l 3 ) = 0.05 Note: e 3 e But: e e.. Why? ( ) 4 l ( ) 3 ) = Alteratively replace with. b a c df l ( 3 ) = 0.05 Note: 3 e e But: e e.. Why? 4 df l ( 3 ) = Alteratively replace a b. c with Discrete probabilty distributios make use of the uiversal costat e. Try a worksheet or QL workshop o DISCRETE PROBABILITY DISTRIBUTION FUNCTIONS Square root Whe to use brackets 6 6 ) =.45 The calculator automatically ( 6 ) =.45 Brackets are ot required Quatitative Literacy (QL) UNISA Durba Learig Cetre, Dr Piley Ka Seme St 4

5 puts brackets aroud the first term. 6 =.45 Whe there is oe term brackets are ot ecessary. Why? whe there is oe term. Why? 6 =.45 Two terms uder the square root sig ) = 6.63 Leavig out the closig brackets gives the same aswer. Why the emphasis o brackets????? ( ) = 6.63 Ca you see why brackets are importat i this situatio? ) = 3.3 The bracket must be closed. Why? Alteratively replace. with ( ) = 3.3 The brackets tell the square root sig what eeds to be beeath the square root. Square root as a deomiator 6 Square root as a fractio i the deomiator, where is i the umerator 6 ) = 0.4 Similar to 6 above. Brackets for Deomiator ( 6 ) ) = 0.8 The calculator automatically ( 6 ) = 0.4 Similar to 6 above. Brackets for Deomiator ( ( 6 ) ) = 0.8 The outer red bolded set of brackets (arrows above) is Quatitative Literacy (QL) UNISA Durba Learig Cetre, Dr Piley Ka Seme St 5

6 of the fractio 6 Square root as a fractio i the deomiator, where is i the deomiator of the fractio Deomiator havig a square root with two 6 terms 4 Brackets required above ad below opes the square root sig with a bracket. Now the bracket must be closed. Why? The deomiator also requires brackets. Why? ( ) ) = Alteratively, ) = Usig the fuctio meas that there is o eed for the fractio to go ito brackets. 6 ( 4 ) =.73 Alteratively replace. Brackets for Deomiator with The calculator always opes the square root sig. I this situatio it is ot essetial to close bracket but it creates a habit. ( ) ( ) ) = Get ito the habit of puttig brackets at the top of a divisio lie ad at the bottom. Why? ecessary. (a must!) The ier is ot (see 6 above). Why? ( 3. 5 ( 0 ) ) = Alteratively, 3. 5 b a c 0 = Usig the fuctio a b c meas that there is o eed for the fractio to go ito brackets. Yes you ca use a b for both but lower c oe requires brackets. Why? 6 ( 4 ) =.73 Alteratively replace a b. c Brackets for Deomiator with It is essetial to ope with a bracket uder the square root sig. I this situatio it is ot essetial to close bracket but it creates a habit. ( ) ( ) = Get ito the habit of puttig brackets at the top of a divisio lie ad at the bottom. Why? Quatitative Literacy (QL) UNISA Durba Learig Cetre, Dr Piley Ka Seme St 6

7 The calculator opeed the bracket beeath the square root sig, hece the double closed bracket before the equal sig. The bottom brackets ca be removed ONLY if the fractio fuctio is used to replace the secod divisio sig. Try this! brackets are ot required beeath the square root sig because there is oly oe term. The bottom brackets ca be removed ONLY if the fractio fuctio b a c to replace the secod divisio sig. Try this! Havig difficulty aswerig all or some of the why? above.. try a worksheet or QL workshop o percetage sig % ORDER OF OPERATION (BODMAS) covertig from 67% to a probability 6 7 ( = df = ERROR Begi by doig 6 7 = 67 ow df = 0.67 Why does this work? The calculator requires a ANS the the df = 0.67 Havig difficulty doig the above without a calculator, the try a worksheet or QL workshop o PERCENTAGES The et sectios deal with usig the MODE fuctio o a scietific calculator. ONE variable of data ENTER Data for : MODE Choose optio 3:STAT by pushig the keypad for 3 Choose optio : -VAR by MODE Choose optio STAT by pushig the keypad for Quatitative Literacy (QL) UNISA Durba Learig Cetre, Dr Piley Ka Seme St 7

8 6; 5; 4; 7; 9; ; 34 pushig the keypad for Eter the data as follows: 6 = 5= 4= 7= 9= = 34= usig the toggle butto REPLAY move the cursor up to the last value, i.e. 34 o the scree the push AC Choose optio SD by 0 pushig the keypad for 0 Notice the followig o the scree Stat 0 Eter the data as follows: 6 M+ 5 M+ 4 M+ 7 M+ 9 M+ M+ 34 M+ Notice the scree says DATA SET 7 There are 7 values i the dataset. Use either the teal butto or the RCL butto to recall the iformatio SUM of 6 3 STAT 3: SUM : 6 3 STAT 3: SUM : The or the RCL butto egages the teal colour stats fuctios i the right had corer of each umerical pad butto. Combiig sum ad variable fuctios fuctios 8 3 STAT 3: SUM : 4 STAT 4: VAR : 8 0 Quatitative Literacy (QL) UNISA Durba Learig Cetre, Dr Piley Ka Seme St 8

9 Before begiig such a problem, isert the brackets Before begiig such a problem, isert the brackets Brackets iserted: udereath the square root sig; at the top (umerator) ad the bottom (deomiator) of a fractio. Brackets iserted: udereath the square root sig; at the top (umerator) ad the bottom (deomiator) of a fractio calculator opes this oe 3 STAT 3: SUM : 4 4: VAR : 3 STAT 3: SUM : 4 STAT 4: VAR : = 9.74 STAT See the importace of brackets? Brackets create steps. 0 = See the importace of brackets? Brackets create steps. SIZE sample Sample MEAN STAT 4: VAR : 4 STAT 4: VAR : Quatitative Literacy (QL) UNISA Durba Learig Cetre, Dr Piley Ka Seme St 9

10 Sample STD DEVIATION s Sample VARIANCE s STAT 4: VAR 4: s Optio 3: is for the POPULATION stadard deviatio. What is the differece betwee a sample ad populatio stadard deviatio? 4 4 STAT 4: VAR 4: s 86 Notice that whe usig the calculator, the sample stadard deviaito is obtaied first, squarig the value gives the sample variace. s is for the POPULATION stadard deviatio. What is the differece betwee a sample ad populatio stadard deviatio? s 5 86 Notice that whe usig the calculator, the sample stadard deviaito is obtaied first, squarig the value gives the sample variace. stadard deviatio variace stadard deviatio variace It is oe thig to lear to use a calculator, but a soud uderstadig of Descriptive Statistics is eeded. Try do worksheets or QL workshops o the followig: DESCRIPTIVE STATISTICS ONE variable of data usig FREQUENCY optio Eample: pdf of a discrete radom variable 0 3 P ( ) MODE toggle dow usig 4 4: STAT MODE 3 3: STAT REPLAY Frequecy? : VAR : ON Eter the data as follows: MODE Choose optio STAT by pushig the keypad for Choose optio SD by 0 pushig the keypad for 0 Notice the followig o the scree Stat 0 Eter the data as follows: 0 = = = 3= Quatitative Literacy (QL) UNISA Durba Learig Cetre, Dr Piley Ka Seme St 0

11 The epected value of The stadard deviatio of The variace of The toggle to the top where is 0 the move to the freq colum usig the right arrow o the replay butto. 0.5 = 0.4 = 0. =0.5 =usig the toggle butto move the cursor up to the last lie where =3 ad freq=0.5 o the scree the push AC i this situatio is the variables ad freq is the probability of, i.e. P..5 4 STAT 4: VAR : Notice that 4 3 STAT 4: VAR 3: 4 4 STAT 4: VAR 4: s I this situatio the POPULATION stadard deviatio is used. Why? REPLAY 4 3 STAT 4: VAR 3: stadard deviatio variace ERROR Remove frequecy from the scree: 0 STO 0.5 M+ STO 0.4 M+ STO 0. M+ 3 STO 0.5 M+ Notice the scree says DATA SET 4 There are 4 values i the dataset. i this situatio is the variables ad y is the probability of, i.e. P Notice that s 5 ERROR. I this situatio the POPULATION stadard deviatio is used. Why? stadard deviatio variace The or the RCL butto egages the teal colour stats fuctios i the right had corer of each umerical pad butto. Quatitative Literacy (QL) UNISA Durba Learig Cetre, Dr Piley Ka Seme St

12 MODE toggle dow usig REPLAY 4 4: STAT Frequecy? : OFF It is ot sufficiet to lear oly the calculator versio. Do a worksheet or QL workshop o DISCRETE PROBABILITY DISTRIBUTION FUNCTIONS TWO variables of data y ; For eample: y MODE 3 3: STAT : A BX Eter the data as follows:.6 =.6= 3.= 3.0=.4= 3.7= 3.7= The toggle to the top REPLAY to the very first equal to.6 the move to the freq colum. 5.6 = 5. = 5.4 = 5.0= 4.0 = 5.0= 5.= usig the toggle butto move the cursor up to the last lie where =3.7 ad y=5. o the scree the push AC Make sure that the variable is etered udereath the colum ad the y variable udereath the y colum. MODE Choose optio STAT by pushig the keypad for Choose optio LINE by pushig the keypad for Notice the followig o the scree Stat Eter the data as follows: Always the variable first, the the y variable. NB!!.6 STO 5.6 M+.6 STO 5. M+ 3. STO 5.4 M+ 3.0 STO 5.0 M+.4 STO 4.0 M+ 3.7 STO 5.0 M+ 3.7 STO 5. M+ Quatitative Literacy (QL) UNISA Durba Learig Cetre, Dr Piley Ka Seme St

13 SIZE sample Sample MEAN Notice that a b is the mathematical equatio for a straight lie STAT 4: VAR : 4 STAT 4: VAR : Notice the scree says DATA SET 7 There are 7 paired values i the dataset y Sample STD DEVIATION s sy STAT 4: VAR 5: y 4 4 STAT 4: VAR 4: s 4 7 STAT 4: VAR 7: sy y s sy The or the RCL butto egages the teal colour stats fuctios i the right had corer of each umerical pad butto. SUM of 3. STAT 3: SUM : Use either the teal butto or the RCL butto to recall the iformatio. Quatitative Literacy (QL) UNISA Durba Learig Cetre, Dr Piley Ka Seme St 3

14 y STAT 3: SUM 4: y y STAT 3: SUM : y y 3 3 STAT 3: SUM 3: y STAT 3: SUM 5: y y y The or the RCL butto egages the teal colour stats fuctios i the right had corer of each umerical pad butto. Regressio coefficiets Itercept: b0 a Itercept: b0 a ŷ b 0 b itercept slope Subscript icreases 0 to O calculator ŷ a b itercept slope Alphabet icreases from a to b. Hece, Itercept b0 a Slope: b STAT b 5:Re g : A 5 STAT 5:Re g : B Correlatio coefficiet: r STAT 5:Re g 3: r Slope: b a ( b b ) 0.34 Correlatio coefficiet: r r 0.37 Quatitative Literacy (QL) UNISA Durba Learig Cetre, Dr Piley Ka Seme St 4

15 Slope b b Coefficiet of Determiatio: r Coefficiet of Determiatio: r 5 3 STAT 5:Re g 3: r 0.07 r 0.07 Estimated value of y i.e. ŷ whe 3. : 5 5:Re g :Re g : B =5.065 STAT Alteratively, STAT :Re g 5: yˆ STAT : A Estimated value of y i.e. ŷ whe 3. : a ( b ) Alteratively, y ' 3. df ) The above sectio requires a soud uderstadig of correlatio ad simple regressio. Try a worksheet or a QL workshop o CORRELATION AND SIMPLE REGRESSION. Cotact acalit@uisa.ac.za or a Quatitative Literacy Facilitator i your regio Quatitative Literacy (QL) UNISA Durba Learig Cetre, Dr Piley Ka Seme St 5

16 Appedi A: Repetitio (repeats) Yes No r ORDER importat Yes Permutatio ( Pr ) No Combiatio ( Cr ) Note that Cr combiatio Pr. Why?! r!( r)! combiatio permutatio! permutatio r!( r)! r! r! combiatio So there will be r! permutatios for every possible combiatio. Diagram : Coutig: Permutatios ad Combiatios Quatitative Literacy (QL) UNISA Durba Learig Cetre, Dr Piley Ka Seme St 6