Measures of variation or measures of spread: is a descriptive measure that describes how much variation or spread there is in a data set.

Transcription

1 Secto.6 Meaure o Dpero Meaure o varato or meaure o pread: a decrptve meaure that decrbe how much varato or pread there a data et. Wh th mportat? Whch Catheter IV mauacturer would ou preer to ue or purchag our 4 G catheter? Drawg wll be o the board cla. Rage o a Data Set The rage o a data et gve b the ormula. Rage Max M, Where Max ad M deote the maxmum ad mmum obervato, repectvel Note that th rage ot the ame a the Iterquartle Rage. Th rage repreet all o the data wherea the Iterquartle Rage ol repreet the mddle 50%. Sample Stadard Devato For a varable, the tadard devato o the obervato or a ample called a ample tadard devato. It deoted b or, whe o couo wll are, mpl. We have 1

2 Procedure or dg the Stadard Devato 1. Calculate the ample mea,. Cotruct a table to obta the um o quared devato, 3. Appl the deto to determe the ample tadard devato Roudg Rule Do ot perorm a roudg (ve decmal place to the rght o the decmal pot e) utl the computato complete; otherwe, ubtatal roud o error ca reult. Example 1 Determe the rage ad ample tadard devato or each o the data et. For the ample tadard devato, roud each awer to oe more decmal place tha that ued or the obervato Th data or ATP (Adeoe trphophate) whch a hgh eerg molecule that tore eerg that eeded to do everthg that a huma or plat would eed to do. The ATP cotet or a group o brch eedlg wa meaured. All o the eedlg were grow a greehoue ad were hadled detcall. (ATP meaured mol/mg tue)

3 Varace o a ample the varace o a ample the ample tadard devato quared. Coecet o varato: the tadard devato expreed a a percetage o the mea: Coece t o Varato 100% Example Brch Seedlg Fd the coecet o varato o the brch eedlg. Notce that the ut cacel ad the awer expreed a a percetage. Wh th mportat? Varato ad the Stadard Devato The more varato that there a data et, the larger t tadard devato. Computg Formula or a Sample Stadard Devato A ample tadard devato ca be computed ug the computg ormula. where the ample ze. 1

4 Example 3 Ue the computg ormula to d the tadard devato or the brch eedlg Emprcal Rule For a data et havg roughl a bell-haped dtrbuto. Approxmatel 68% o the obervato le wth oe tadard devato to ether de o the mea. Approxmatel 95% o the obervato le wth two tadard devato to ether de o the mea. Approxmatel 99.7% o the obervato le wth three tadard devato to ether de o the mea. Example 4 The MAO (Mooame oxdae) level chzophrec were meaured the ordered data

5 The mea ad tadard devato or th data et ad Fd the oe tadard devato lmt rom the mea, the two tadard devato lmt rom the mea, ad the three tadard devato lmt rom the mea.. Doe the data meet the approprate percetage accordg to the Emprcal Rule? Outler: Are extreme data pot that do ot appear to be part o a dtrbuto. Obervato that all well outde o the overall patter o the data. Thee data pot are mportat ad hould ot be gored. Comparo o Meaure o Dpero The rage a oretat meaure o ceter a t deped ol o the extreme tal o the dtrbuto. The terquartle rage a more retat meaure o ceter a t meaure the ceter porto o the dtrbuto. The tadard devato clude all o the obervato the data et o t ca be lueced b extreme value the tal. Th mea that the tadard devato alo a oretat meaure o ceter.

6 Grouped-Data Formula Whe data are grouped a requec dtrbuto, we ca ue the ollowg ormula to obta the ample mea ad ample tadard devato Where the cla requec, the ample ze ( ) ad a product o how ma tme the value o each -value occur. The deg ormula or the ample tadard devato 1 The computg ormula or the ample tadard devato 1

7 Example 5 Mle ru per week over a ear perod (b Beth Joe) Mle ru Number o per week week Ue the group data ormula or the ample tadard devato.