- Inferential: methods using sample results to infer conclusions about a larger pop n.

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1 Chapter 6 Def : Statstcs: are commoly kow as umercal facts. s a feld of dscple or study. I ths class, statstcs s the scece of collectg, aalyzg, ad drawg coclusos from data. The methods help descrbe ad uderstad varablty. Types of statstcs: - Descrptve: methods to vew a gve dataset. - Iferetal: methods usg sample results to fer coclusos about a larger pop. Def : A varable s ay characterstc that s recorded for subjects a study. - Categorcal (qualtatve: caot assume a umercal value but classfable to or more o-umerc categores. - umercal (quattatve: measured umercally. - Dscrete: oly certa values wth o termedate values. - Cotuous: ay umercal value over a certa terval or tervals. Populato vs. Sample: Def : A populato cossts of all elemets whose characterstcs are beg studed. Ex6. A sample s a porto of the populato selected for study. Ex6. 6. Data Presetato Graphcal Summares for Categorcal Data Def : A bar chart s a graph of bars whose heghts represet the (relatve frequeces of respectve categores. Ex6.3 (created class Look for: frequetly ad frequetly occurrg categores. A Pareto chart arrages the categores order of decreasg frequecy Ex6.4 (created class Look for: frequetly ad frequetly occurrg categores. A pe chart s a crcle dvded to portos that represet (relatve frequecy belogg to dfferet categores. Ex6.5 (created class Look for: categores that form large ad small proportos of the data set. Graphcal Summares for umercal Data Def : A frequecy dstrbuto (for umercal data s a lstg of o-overlappg tervals, together wth the # of observatos for each terval (a.k.a. class or b. f Relatve frequecy (Cumulatve relatve frequecy also ests f The data dvde to tervals (ormally of equal wdth.

2 Worldwde Box Offce ( mllos 00 to to to to to to to 3000 umber of moves f Relatve Frequecy Cumulatve rel. freq. Def : A hstogram graphcally shows a frequecy dstrbuto for umercal data. Look for: - cetral or typcal value ad correspodg spread - gaps the data or outlers - presece of symmetry the dst - umber ad locato of peaks A outler s a obs that falls well above or below the overall bulk of the data. Ex6.6 (precedg table used for example class Hstogram trats: (correspodg curves draw class. Modes (umodal, bmodal, multmodal. Skewess (symmetrc, left-skewed & rght-skewed term refers to TAIL 3. Tal weght (ormal, heavy-taled, lght-taled 6.3 Sample Statstcs (ad more Def : A parameter s a summary measure calculated for pop data. A statstc s a summary measure calculated for sample data. Measures of Ceter: Def : If observatos a sample are deoted by x, x,, x, the sample mea s x + x x x Also, f there are obs s a etre populato, the the populato mea s µ The meda s the value of the mdpot of a data set that has bee raked order, creasg or decreasg. If dataset has a eve # of observatos, use the average of the mddle values. The mode s the most frequet value a data set. OTE: meda (ad mode resstat to outlers, mea uses all observatos.

3 Table 6X0 Estmated provcal populatos crca Jul. 0 ( mllos O PQ BC AB MB SK S B L PEI Ex6.7 Avg. pop of all provces: µ meda x mode o mode here Avg. pop from sample of 3 provces: x Outler effect? (remove Otaro & Quebec Comparg Mea, Meda & Mode Hstograms: (graphs draw class. Symmetrc curve & hstogram - all 3 detcal ad le at the ceter of the dstrbuto. Rght-skewed: Mode < Meda < Mea 3. Left-skewed: Mea < Meda < Mode Measures of Spread: Def : The sample rage s rage max(x m(x Ex6.8 (from Table 6X0 rage Devatos from the Mea: Ex6.9,, 4, 3 x x x ( x 0 ote that ( x µ ad ( x, aka devato of x from the mea, both equal zero. Varace ad Stadard Devato: The most commo measure of spread s stadard devato. Varace, however, must be calculated frst. The basc formulas for varace are: ( µ ( σ s where σ s the populato varace ad s the sample varace.

4 ( Sce(, the varace formulas become x ( x ( σ ad s Fdg the stadard devato oly requres takg the square root of the varace. Populato: σ σ Sample: s s Ex6.0,, 4, 3 x 0, x 30, σ If the data was a sample, ( x σ s, s Importat otes:. Stadard devato measures spread oly about the mea (.e. ot the meda.. Values of varace ad std. dev. are ever egatve. (Equals zero oly f o spread. 3. The measuremet uts of varace are always the square of the uts of the orgal data. 4. Stadard devato, lke the mea, s ot resstat to outlers. 5. Cosder the sample varace s to have degrees of freedom. There are observatos, ad devatos from the mea. Sce the total always sums to zero, of these quattes determes the remag oe. Thus, oly of the devatos, x x, are freely determed. (Degrees of freedom apply oly to samples. Boxplots: Def : The p th quatle s a value such that p percet of the observatos fall below or at that value. Three useful quatles are quartles. The lower (or frst quartle has p 5, the meda has p 50, ad the upper (or thrd quartle has p 75. The fve-umber summary cossts of the m, Q, meda, Q 3, ad the max. (vsual represetato of above draw class Def : The terquartle rage (IQR s the dfferece betwee the frst ad thrd quartles. IQR Q 3 Q (IQR s also a measure of spread Ex (examples regardg fdg quartles wth other # s of observatos dscussed class ote: For exams, ICLUDE the meda calculatg Q ad Q 3.

5 Def : A boxplot shows the ceter, spread, ad skewess of a data set. To costruct t: Step : Rak the data creasg order ad fd the meda, Q, Q 3, ad IQR. Use data from Ex6. to costruct a boxplot. Step : Fd the pots beyod the boudares:.5*iqr below Q ad.5*iqr above Q 3, kow as the lower & upper er feces, respectvely. These pots are outlers..5*iqr Lower.f. Upper.f. Step 3: Determe smallest & largest values wth the respectve er feces. small large Step 4: Draw lear scale cotag etre rage of data. Step 5: Draw perpedcular les to the scale to dcate Q ad Q 3. Coect eds of both les. Box wdth IQR Step 6: Draw aother le perpedcular to the scale to dcate the meda sde the box. Step 7: Draw two smaller les perpedcular to the scale for the values from Step 3. Jo ther ceters to the box to make whskers. (boxplot draw class What to do wth outlers? Cosder lower & upper outer feces at 3.0*IQR below Q ad 3.0*IQR above Q 3. Ex6. 3.0*IQR Lower o.f. Upper o.f. A mld outler s outsde a er fece but sde the outer fece. A extreme outler s outsde ether outer fece. Some textbooks represet mld outlers by shaded crcles, extreme outlers by ope crcles. Our textbook uses astersks, *, as well. Overall, classfyg outlers s mportat whereas drawg them a certa way s subjectve. Whskers exted o each ed to the most extreme obs s that are OT outlers. Ex6.3 Aalyzg ceter, spread, ad skewess: - What s the appromate value of the ceter? - What s the wdth of the IQR? - Are the data symmetrc or skewed? Boxplot vs. Hstogram: Each graph hghlghts dfferet features of a data set (layers of skewess ad skewess/modalty, respectvely, so t s always better to costruct both.

Inferential: methods using sample results to infer conclusions about a larger population.

Inferential: methods using sample results to infer conclusions about a larger population. Chapter 1 Def : Statstcs: 1) are commoly kow as umercal facts ) s a feld of dscple or study Here, statstcs s about varato. 3 ma aspects of statstcs: 1) Desg ( Thk ): Plag how to obta data to aswer questos.