Lecture Notes for Introductory Statistics, 9th Edition

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Chapter1IntroductionUse of TechnologyStatistics is a field that deals withsets ofdata.After the data is collected,it needs to be organizedand interpreted.There is a limit to how much of thework can be doneeffectively without thehelp ofsome type of technology.The use oftechnology, such as a calculator with enhancedstatistical functions,cantake care of most of the details of our work so that wecan spend moretime focusing on what we are doing and how to interprettheresults.Technology can help us not only to store and manipulate data, but also tovisualize what the datais trying to tell us.As we work withacalculator, we will be able to:Enter, revise, and store data.Perform statistical computations on stored dataor entered statistics.Draw graphs (often called plots)based on the data,to help us to understand what usefulinformation can beinferred from thatdata.Advantages of Using a CalculatorThere are many good statistical software packages available, such as MINITAB,SAS, and SPSS.Excel also contains many built-instatisticalfunctions,as wellas supporting plugins for statisticalwork.Still, for the student starting to learn statistics, it’s hard to beat the advantagesof using apowerful hand-held calculator.It is portable and easy to use in many different work environments.It has battery power that lasts far longer than that of a laptop computer.It is less expensive than a computer.It is less expensive than a statistical softwarepackage.

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2Advantages to Using theTI-84 PlusThiscalculator manualwill focus on how to get the most out of using theTI-84 Pluscalculatorby Texas Instruments. The TI-83 was first released in 1996,improving upon its predecessors(theTI-81 and TI-82)with the addition of manyadvanced statistical and financial functions. The TI-83 Plusand the TI-84 Plushaveessentially thesame features as the TI-83, but with increasedmemory capacityand a few extra statistical features.They arepowerfulcalculators withadvanced functions, but at the same timeeasy to use.Most complicated statistical computations are handled through menuswhich promptyoufor the necessary input.Data entry and revision is handled through aStatistical List Editorthat issimilar to aspreadsheet in how it is used.Statistical graphs are handled through menusandimportant parts of thegraph can bereadby tracing along with the arrow keys.Thecalculators are built sturdilyandcanwithstandmany falls off of student desks.Entering and Revising DataThischapterfocusesongettingnumbersintoyourcalculatorandstoringthemfortheorganization, interpretation, and analysis part of statistics.When you are not given the necessarystatistics to perform calculations, you will need to enter data into the calculator to generate thestatistics.We will learn how to do statistical calculations with the calculator in future chapters.Using theDataEditorThedata editorin theTI-84 Plus calculator providesa convenient waytoenternumbers andreview them.Numbersfrom adata setcan bestored inalist in thecalculator so that we can keepnumbers that are related to each other together.Example:Calories ConsumedAn individual is modifying eating habits and has kept track of calories consumed for the last 10days, as follows:1474,1633,1686,1748,1326,1112,1245,1539,1220,1561If we want to do any sort of analysis onthese numbers, we will need toentertheminto thecalculator and keep them together as a group.

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3Accessing theDataEditorPress thekey to reveal the STATmenu.To input data or to make changes to an existing set of datavalues use thedata editor, which isnumber 1undertheEDITmenu.Pressorkey if1:is highlighted.Resetting theDataEditorIf thedata editordoes not showthe columns labeledasL1, L2, and L3,you canreset theeditortoits default settingsbyusing theSetUpEditorfunction:Press.Pressto paste theSetUpEditorfunctiononthe home screen.Press.Once the Editor isset up,return to theEdit function.

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4Entering Data in theDataEditorTypeinthe tencaloriecountsunderthe column labeled L1.Pressthewhen youare done withone number and ready to moveon to the next number.Type in 1474and press.Type in 1633and press.Type in 1686and press.Continuethis processuntil all data values have been entered.Use the up and down arrow keys tomoveback and forth between thedata values.Try changingthe value of one of the entries by typing in a newcalorie count.Clearing a List of Data ValuesAfter a list of data values is no longer needed,you can delete the values by using one of thefollowing methods:You can highlight each data value andpress.This method is slow and clears the listone data value at atime.You can highlight the list name, for example L1at the top of the column,press,andthen press.You can go to the EDIT menu and pressto clearthelistas follows:Press.Pressto paste theClrListfunction on the home screen.Pressand then presstopasteL1immediately after theClrListfunction.Press.The calculator will displayDoneto confirm that thelist has been cleared.

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5Entering Lists Directly to the Statistical Editor ListThe home screen is where you do most of your calculator work that doesn’tinvolve menus.From any menu in your calculator, you can alwaysreturnto the home screen by pressingandthen().From the home screen, you can enter data into a list by typing it betweenasetofbraces,{}, and separating the numbers by commas:{1474,1633,1686,1748,1326,1112,1245,1539,1220,1561}Once you’ve typed the numbers into your calculator, you willwant to save themfor future use.Pressfollowed by L1,L2orany other list. (L1throughL6canbe accessed by pressingand then,or, or, etc.)Note:When you presskey, the screen will display anarrowpointingto the right.Now, press.Once you’vestore thelistas L1, you can see the list bytyping its name. For example, if youstored thecaloriesinL1, typing L1()onthe home screen will display the list’s contents.(You will need to useandto see all of the list’s contents.)Entering Lists Directly to a NameYou can also store data to a named listthat you create.From the home screen,type the datavalues within braces as described above. However, instead of storing thelist as L1, follow thesesteps to create a named list:Press.Press() to enable the alpha lock. Now, whenever youpress a key, the alphabetical letter will display on your screen.Press([C]).Press([A]).Press([L]).Press.

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6Viewingthe Named ListintheDataEditorThe data is storedas the named listCAL,but itcannot be seenin the data editor. To view the data in the data editor:Press.Pressto enter the data editor.Pressto highlight the name at thetop ofone of the columns.Press() to create a blank column.Type thename of your new list–CAL.Note:isautomatically enabled.Press.Thenumbers that you stored in CALshould now appear in thedata editor.Create a Named List Within theDataEditorThe lists L1through L6are good places to work with data if youdo notneedto savethe dataforlater use. Ifyouwillneed thedata laterand donot want to accidentally overwrite it, you canstorethe dataas anamed list.Alist can be named with 1–5 characters. The first character mustbe a letterA-Zor the angle symbolθ(“theta”).The othercharacters can be a letter,θ, or anumber0-9.To get letters from the keyboard, pressbefore each letter. The lettersappear above and to theright of most of the keys. If you are typing severalletters in a row, press(), type theletters, andthen presstheALPHAkeyagain to release the lock.To create anewlistnamedBURNwithin thedata editor:Press.Pressto enter the data editor.Pressto highlight the nameL1at thetop of one of thecolumns.Press() to create a blank columnbetween CAL and L1.Type thename of your new list–BURN.Note:is automatically enabled.Press.BURNshould now appearat the top of thecolumn.

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7The individual also kept track of the number of calories burnedby exercisingfor each of the last10 days. Enterthe followingdata into the newly named list, BURN.{128, 37, 440, 128, 258, 486, 325, 171, 0, 529}Getting the Names of ListsSome of thecalculatorcommands requirethatyou type inthename of a list.Ifthe name of the listisone ofL1throughL6, then you can typeit quicklypressingand the corresponding number keythrough.If the listis a named list,you cannot just type the name of a listfrom thekeyboard using. List names on theTI-84 Pluscalculatoraredistinguished from thenames of other variables by a small L tothe left of thename.Press()anduse the arrowkeys tochoose one of the list names. Thenpress.DisplayingListsin the DataEditorYou can create custom views in the data editor to display thelists you wish to see.Begin by setting the data editor back to itsdefault settings:Pressto paste theSetUpEditorfunction on the homescreen.Press.Pressto enter the data editor. You will see L1, L2, and L3displayed in the data editor.Now suppose you wish to view the CAL and BURN listsat some future time. You must changewhich lists are displayed in the data editor.Pressto paste theSetUpEditorfunction on the homescreen.Press() to enter the list menu.Select CAL from the NAMES menu by highlighting it andpressing.Type(comma).Select BURN from the NAMES menu by highlighting it andpressing.Press. The calculator will displayDone, confirming thatthese lists can now be viewed in the data editor.Pressto enter the data editor. You will see the CAL andBURN lists displayed in the data editor.

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8Removea Named List Within the Statistical List EditorIn thedata, use the arrow keys,,, andto move to the name of the list to beremoved.PresstheDELkeyfordelete. The list disappears, butthe contentsof thelisthave not beendeleted.To erase the contents of a list, highlight thename of the list and pressandthen.This will leave the listnamein the editorandclear its entries.Deleting Liststo Free Up MemoryIf you store many lists, programs, etc. on your calculator, you may run out of memory.To deletelists from the calculator’s memory:Press().Select2:Mem Mgmt/Del…Select4: List…to see all of the current lists.Move the cursorto the list that you want to delete andpress.

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2Now that we have told the calculator how to organize the data into classes (bins), we are ready toset up the frequency histogram.Pressto view the STAT PLOTS menu.Press.HighlightOnand pressto turn the plot on.Pressto highlight the histogram picture ().Press() and select the IPODS list.LeaveFreqat 1, since each data value in the IPODS list represents only one point.Now you are ready to draw the frequency histogram.Pressto view the histogram.Pressto trace the histogram.Pressandto move from one bar to the next. You will seethe frequency in each class (n = 8) and the range of values ineach class (min = 15; max < 20) displayed at the bottom of thescreen.The histogram provides us with the following information.ClassFrequency5 - 9310 - 14615 - 19820 - 24825 - 295Summary of How to Create a Histogram.1.Enter the data into a list.2.Determine the range of values for your data, as well as your desired class width.3.Pressand setXmin,Xmax,Xsclto the range of data values and class width. SetYminto 0 andYmaxto a value large enough for the tallest box in the histogram. (Youmay need to revise this after seeing the histogram.)4.Pressand thento see theSTAT PLOTmenu. Highlight4: PlotsOffand press. This will turn off all of the plots.

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35.Return to theSTAT PLOTmenuand select a plot. Turn the plot on by pressing the.Then select the picture of the histogram picture (). Enter the name of yourdata list inXlist, and leaveFreqas 1.6.Press. Pressto display the information needed to create the frequencydistribution table.Enter the Frequency Distribution Table into the Data EditorSince the class intervals cannot be entered into a List, the midpoint of each class is used. Such afrequency distribution for the example of the number of Ipods sold would look as follows:ClassMidpointFrequency5 - 97310 - 1412615 - 1917820 - 2422825 - 29275Create two new lists, MIDPT and FREQ. Enter the midpointsand frequencies from the table above into two new lists, MIDPTand FREQ, as shown in the screenshot to the right.Create a Frequency PolygonThe steps to create a frequency polygon are similar to those needed to create a histogram. Usethe data stored in the lists MIDPT and FREQ.Press()to get to the STATPLOT menu.Press.SelectOn.Select the xyline picture ().Press() and select the MIDPT list as theXlist.Press() and select the FREQ list as theYlist.Select the square as theMark.

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4ThesameWINDOWthatwasusedforthehistogramisapplicable to the Polygon. Another option is to let the calculatordetermine the correct window by using the ZOOM menu, asfollows:Press.Pressthenumber9keytoselectZoomStat.Press.Pressto trace points in the frequency polygon.Create a Relative Frequency ColumnA relative frequency column can be generated from the frequency column.Create a new list in the data editor and name it RELFR. Withthe cursor still highlighting the name RELFR,Press() and select the FREQ list.Press.Press(), and presstwice to view the MATHmenu.Select5:sum(and press.Press() and select the FREQ list.Pressand press.The above sequence of commands calculates each value in theRELFR column by dividing the corresponding value in theFREQ column by the sum of all of the values in the FREQcolumn.Create a Percentage ColumnApercentagecolumncanbegeneratedfromtherelativefrequency column.CreateanewlistnamedPERC.Withthecursorstillhighlighting the name PERC,

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5Press() and select RELFR list.Press.Type 100 and press.The above sequence of commands calculates each value in thePERC column by multiplying the corresponding value in theRELFR column by 100.Create a Cumulative Frequency ColumnA cumulative frequency column can be generated from the frequency column.Create a new list named CUMFR. With the cursor still highlighting the name CUMFR,Press() and pressonce to view the OPSmenu.Select6:cumSum(and press.Press() and select the FREQ list.Pressand press.The above sequence of commands calculates each value in the CUMFR column by adding thecorresponding value in the FREQ column to the sum of the previous values in the FREQ column.The table at the right was displayed by using the SetUpEditor todisplay just these 3 Lists.Create an Ogive For The Cumulative FrequencyThe steps to create an ogive are very similar to those needed to create a frequency polygon. Wewill begin by using the data stored under the labels MIDPT, FREQ, and CUMFR.The ogive uses the first lower and all of the upper boundaries rather than the midpoint. Thus itdoes require an additional data value at the beginning of the list.

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6Insert a new row of data:Move the cursor to the top value in the MIDPT list (the ‘7’).Press().A ‘0’ will appearand the rest of the data will shift down.Repeat the above steps for the FREQ and CUMFR columns.Overwrite the values in the MIDPT column with the first lowerand all of the upper boundaries, as shown to the left.Press()to get to the STATPLOT menu.Press.SelectOn.Select the xyline picture ().Press() and select the MIDPT list as theXlist.Press() and select the CUMFR list as theYlist.Select the square as theMark.Some modifications to the window settings will be needed toincorporate the lower boundary and the increased y-values.Press.Pressto trace the points in the ogive.

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1Chapter3Numerical DescriptiveMeasuresAfterdata iscollected andorganized,thenextstepis togeneratedescriptivestatistics.Descriptive statistics help you describe the contents of the data set.The two most commonmeasures are measures of central tendency and measures of dispersion.These measures tell youwherethe datais centered andhow spread out it is, respectively. The center of the data can bedescribedbysuch statistics as themeanand themedian, while the spread of the data can bedescribed by thestandard deviation, therange,and theinterquartile range.You may also want todescribe where one number iswith respect to all the other numbersin alarge set of numericaldata.Youcan usepercentilesto say what percent of the data lies below agiven number.After learning about percentiles, another visual display can be created called thebox-and-whisker plot.Measures of Central TendencyFor Ungrouped DataExample: 2015Earnings Before Taxes.Example 3-15gives the 2015earnings (in thousands of dollars)before taxes for all six employees of a small company. Enterthe 2015earnings in to alistnamed EARN.Calculate The MeanTo calculate the mean, or the average, of the 2015earningsstored in EARN, go to the home screen-press().Press()and select.Select5: sum(and press.Press()and choose thelistnamed EARN.Press,,, and.Calculate the Median

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