160 175@ 165 175@ 170 175@ 175 175@ 180 175@

Example	You are measuring the height of students in a classroom to
	find the mean height. The first five students have the
	following measurements 160cm, 165cm, 170cm, 175cm,
	180cm.
	1. Open the Statistics aplet.
	>$3/( @ Select
	>$3/( @ Select
	Statistics675(6(7$5<(6

2.Enter the measurement data.

160 >(17(5@

165 >(17(5@

170 >(17(5@

175 >(17(5@

180 >(17(5@

3. Find the mean of the sample.

Ensure the 9$5_/ 9$5_ menu9$5key label reads

.Press 67$76_to see the statistics

calculated from the sample data in C1. Press the *e,key to scroll to further statistics.

Note that the title for the column of statistics is

H1. There are 5 data set definitions available for one-variable statistics:

H1–H5. If data is entered

in C1, H1 is automatically set to use C1 for data, and the frequency of each data point is set to 1. You can select other columns of data from the Statistics Symbolic setup view.

Statistics aplet

8-7

Page 99

Image 99

HP 40G manual 160 175@ 165 175@ 170 175@ 175 175@ 180 175@

Contents

USER’S Guide Page Contents Parametric aplet Importing Sample Statistics from the Statistics aplet Inference aplet Variables and memory management Programming Index +,7@CLEAR, 6+,7@MODES, 6+,7@ACOS, etc PrefaceManual conventions @, &26@, +20@, etc Preface On/off, cancel operations Getting startedHome To adjust the contrast To clear the display DisplayParts of the display Keyboard Menu keysAnnunciator Description Key Meaning Aplet control keys 75@ +,7@$/3+$@ 175@ +,7@$/3+$@ Shifted keystrokesHelpwith Key Description Math keys Program commands Inactive keys To cancel a menu MenusTo search a menu Input forms Mode settingsReset input form values Setting Options Setting Options Setting a mode Aplets E-lessonsPress+20@ to return to Home Aplet Use this aplet to explore Name N T Quad Explorer aplet *,*A, keys Trig Explorer aplet Aplets are stored in the Aplet library Symbolic view Plot view Numeric viewAplet library Aplet views Views menu contains the Plot-Table view To change views Aplet view configurationPlot Setup Numeric Setup Symbolic Configuration Example Mathematical calculationsEntering expressions Long results Negative numbers Scientific notation powers Explicit and implicit multiplication@4 6+,7@EEX @13@ @@6 6+,7@EEX 23@ j@ 3 6+,7@EEX 175@ +,7@√ @85 @9 @ Entering Calculates@ 45 @6+,7@π +,7@√ 85@9 Clearing numbers Using previous results 50175@ @25 175@175@ 175@ updates ANS from 50 to 75 to Accessing the display history $/3+$@ a 175@Key Function Clearing the display history Using fractionsSetting Fraction mode See Setting fraction precision below for more information Setting fraction precision Evaluate the calculation Fraction calculations Converting decimals to fractionsReturn to Home and enter the calculation @@@2@3 + iy Complex numbersConverting a number to a fraction Complex results To enter complex numbers Catalog/Editor Contents Catalogs and editorsStoring complex numbers Trig Explorer and Quadratic Explorer aplets Differences between the HP 38G and the HP 39G/40GMemory manager Plot Goto function Statistics Pred functionPage Aplet views About the Symbolic viewDefining an expression Symbolic view Aplets and their views Aplets and their views Evaluating expressions ApletsHome +,7@CLEAR Symb view keys$56@ $7+@ 175@ or Setting up the plot Plot view setupPlot view settings About the Plot view Reset plot settings Exploring the graph Plot view keys+,7@*A Zoom options Trace a graphZoom within a graph To jump directly to a value To turn trace on/ off Multiplies vertical scale only, using Divides horizontal scale only, usingMultiplies horizontal scale, using Divides vertical scale only, using =220Zoom Out 018Zoom=220Un-zoom Press *k, to move to the bottom of the Zoom list =220Y-Zoom Out =220X-Zoom=220X-Zoom Out =220Y-Zoom To box zoom To set zoom factors Options Other views for scaling and splitting the graph Menu key copies the right plot to the left Integer scaling Trigonometric scaling About the numeric viewOverlay plots Decimal scaling Setting up the table numeric view setup Numeric view settingsReset numeric settings Exploring the table of numbers NUM view menu keysZoom within a table 175@, the values for the dependent variables are Building your own table of numbersArrow keys to place the cursor in the independent variable Column, then enter the value to jump to Clear data Build Your Own menu keys Example plotting a circle $3/7@ Select+,7@√@9 Open the Function aplet Function apletAbout the Function aplet Getting started with the Function aplet Plot the functions Define the expressionsPlot the functions @75@175@ Times Change the scale Trace a graphWith FCN functions Trace the linear function Find the greater of the two roots of the quadratic function SelectRootRoot value is displayed at the bottom of the screen @.2 2Select.SlopeMove the cursor to x = 1 by pressing the *A,or Choose the end value for Display the numeric view Display the numeric view Set up the tableDisplay the numeric setup To find the extremum of the quadratic Move to X = Match the table settings to the pixel columns in the graphExplore the table Display a table of numeric values Area Extremum Isect Root Slope Function aplet interactive analysis Function Description Access FCN variables FCN functions Symbolic view. Displays Cursor. You need to have at leastTwo selected expressions Plotting a piecewise defined function example = $3/ @ Select Page Open the Parametric aplet Define the expressions Parametric apletAbout the Parametric aplet Getting started with the Parametric aplet Set angle measure Set up the plot Plot the expression +,7@PLOT360 120 Overlay plot Display the numbersPlot a triangle graph over the existing circle graph +,7@ PlotPage +,7@CLEAR 46+,7@π 2.a Polar apletGetting started with the polar aplet Open the Polar aplet Explore the graph Display the numbers Getting started with the Sequence aplet Sequence aplet starts in the Symbolic viewSequence aplet About the Sequence aplet Keys to assist in the entry of equations Define the expression Select Cobweb Plot Setup, set the Seqplot option to CobwebPlot the sequence Display the table Plot the Fibonacci sequencePage About the Solve aplet Solve aplet Getting started with the Solve aplet Open the Solve apletDefine the equation Define known variables Solve the unknown variable Plot the equation Solve for the unknown variable a@ Select Auto ≈20 times Solve aplet’s NUM view keys Number format Use an initial guess Message Condition Interpreting results Root- Finder at work 180@ 30 175@ 2175@ *e,4175@ *e,*e, to highlight T Plotting to find guessesAt2 x = v0t + $/3+$@X To move cursor to the intersection Plot the graph 3175@*k,*k,*k Using variables in equationsHome variables Initial guess 1400 920 1100 2265 2890 2200 Statistics apletAbout the Statistics aplet Getting started with the Statistics aplet 1400 175@920 175@ 1100 175@2265 175@ 2890 175@2200 175@ Open the Statistics aplet Enter data175@1 175@ 175@5 175@ 175@4 175@ To move to the next column Choose fit and data columns Explore statistics Setup plot Select a fit in the Symbolic setup viewSelect2. Linear To move to the FIT1 +2field Display the equation for the best linear fit 6175@ Entering and editing statistical data$7+@ S to highlight To highlight +,7@ FXUVRU Statistics aplet’s NUM view keys 160 175@ 165 175@ 170 175@ 175 175@ 180 175@ $56@ Sets will need to be selected again Before re-useHeight cm Frequency Angle Setting Save dataDelete data Select the Sort Order option. You can choose either Defining a regression model 2VARInsert data Sort data values To choose the fit = ax3+bx2+cx+d. Needs at least Fit models To define your own fitFit model Meaning = m lnx + b Computed statistics One-variableStatistic Definition Columns for a linear fit only Two-variable Plotting To plot statistical dataYou can plot Histogram Box and Whisker Plot Scatter Plot Plot types Coefficient Relative ErrorFitting a curve to0182VAR data Correlation Plotting mark 2VAR Connected points 2VAR Setting up the plot Plot setup view Trouble-shooting a plot Statistics aplet’s Plot view keys Find predicted values Calculating predicted valuesPage Example data Default the input form contains example data. This exampleInference aplet About the Inference aplet Hypothesis Tests Confidence Intervals Getting started with the Inference apletOpen the Inference aplet Inference aplet’s Symb view keys ∝.a∝ Define the inferential method Field name Definition Open the Statistics aplet Open Statistics aplet. Note Reset current settingsImporting Sample Statistics from the Statistics aplet Plot test results @529 175@ @295 175@ @952 175@ @259 175@ @925 175@ @592 175@ Calculate statistics Open Inference aplet Choose inference method and type Import the data2one.a Display the confidence interval in the Plot view Display Numeric view Display Plot viewSpecify a 90% confidence interval in the C field E, to move to Field Inputs Hypothesis testsOne-Sample Z-Test Menu name Two-Sample Z-Test ResultsResult Description One-Proportion Z-Test Two-Proportion Z-Test Successes in the two populations is equalH0 π1 = π2 Hypothesis is that the sample mean has some assumed value One-Sample T-TestTest 1 ∝ Selected hypothesis against the null hypothesis. The null Two-Sample T-Test Sample 2 standard deviation Sample 1 standard deviation Confidence level Confidence intervalsConfidence interval calculations that the HP 39G/40G can Perform are based on the Normal Z-distribution or Student’s Deviations, σ1 and σ2, are known Two populations, ∝1 ∝2, when the population standardTwo-Sample Z-Interval Confidence interval for the difference between the means Sample success count One-Proportion Z-Interval Sample 2 success count Two-Proportion Z-IntervalSuccesses in two populations Sample 1 success count One-Sample T-Interval Two-Sample T-Interval Page Using mathematical functions Math functionsMath menu To select a function Function categoriesCalculus Loop Stat-Two Complex Matrices Math functions by category SyntaxFunctions common to keyboard and menus Keyboard functions +,7@√ +,7@ASIN+,7@ACOS +,7@ATAN +,7@ n Valuepower+,7@ABS ABSvalue Lower,upper,expression,variable Calculus functionsTaylor Variableexpression Complex number functions ARGConj Hyperbolic trigonometry Constants EXPM1 List functionsAlog EXP Recurse Loop functionsMatrix functions Iterate Polyform Polynomial functionsPolycoef Polyeval Random Probability functionsComb Perm Utpt UtpcUtpf Utpn Real-number functions Mant HMS→→HMS INT RAD→DEG MODChange Total Xpon Statistics-TwoSign Truncate Quad Symbolic functionsIsolate LINEAR? Quote Trigonometry functions Home Symbolic calculationsSymbolic calculations in the Function aplet Using formal variables Evaluate the function Finding derivativesTo find derivatives GG@$/3+$@S1 GG@@$/3+$@ To find derivatives in the Function aplet’s Symbolic view Thus, substituting X for S1, it can be seen that To find the indefinite integral using formal variables+,7@GG@0 @ $/3+$@ S1 @ 3 @ Show the result format 10-26 Introduction Variables and memory management Storing and recalling variables Numeric PrecisionTo store a value To store the results of a calculation 65 @$/3+$@A 175@ Vars menuTo use variables Calculations +,7@LIST Names or values of variables into programs List names directly from the keyboard 2contents,.a is copied to the command line$56@ *e,*e,*e,*A $/3+$@L3175@ Category Available names To access an aplet variable Aplet variablesTo copy the value of the variable into the edit line +,7@MEMORY Memory ManagerStart the Memory Manager. a list of variable categories Is displayedPage Matrix Variables MatricesVectors Matrices +,7@*e, or Creating and storing matricesMatrix Catalog keys + 7@CLEAR Select the type of matrix to create To create a matrix in the matrix catalog +,7@*k, *e Working with matricesTo transmit a matrix Clears all elements from the matrix 728 672? 175@ 8 175@ Matrix arithmeticTo multiply and divide by a scalar 175@ 2175@*e 175@ 4175@ $/3+$@M1 j@$/3+$@M2 175@ $/3+$@M1@ $/3+$@M2 175@ +,7@MATRIX Solving systems of linear equations+,7@MATRIX1 175@ 175@7 175@ About functions Matrix functions and commands Argument conventions Inverse EigenvalEigenvv Idenmat Schur RankRownorm Rref Identity Matrix Transposing a Matrix ExamplesTrace TRN Reduced-Row Echelon Form Open the List catalog ListsCreating lists Create a list in the List Catalog List catalog keys List edit keys Create a list @ /@ Displaying and editing listsTo display a list To display one element To edit a list To insert an element in a list To store one element 16a*e To delete all lists Deleting listsTransmitting lists To delete a list List functions $/3+$@A @ $/3+$@L 5175@ $7+@L *A$/3+$@L5175@ $7+@L *A,Select Sorts elements in ascending order Calculates the product of all elements in listPOSlist, element Calculates the number of elements in a list Finding statistical values for list elements 89@65@ 0@89$/3+$@ L1 175@ Go to the Numeric view To display calculated statistics 180@67$76aPage Your work is automatically saved. Press any view key Aplet note viewTo write a note in Note view +,7@letter +,7@ Cmds +,7@%.63$= Aplet sketch view Sketch keysTo draw a line Draw keys Where you want any corner of the box to beYou can adjust the size of the box by moving the cursor To draw a box Keys Press 2.again to affix the labelHighlight2. the variable name you want to use and press Name of the note is ‘MYNOTE’ To import a graphics variableTo create a note +,7@NOTEPAD Another HP 39G/40G or PC Opens the selected note forBegins a new note, and asks for Transmits the selected note to 14-8 Programming Contents of a Program Structured Programming Open Program catalog Program catalog +,7@*k, or *e Program catalog keys Create a new program Creating and editing programs To enter functions more to come Enter commands Edit a program+,7@CMDS A,*e Editing keys Using programs Debug a program Stop a programRun a program From HOME, type RUN programname. or Transmit a program Delete a program Working with programsCopy a Program Programs Delete the contents of a programAbout customizing an aplet Delete all Aplet naming convention Customizing an aplet example$3/7@Select Configuring the Setviews menu option programs Setviews ’’’’’’’’18 Programming 15-13 Select Programming commandsAplet commands Check Syntax for the command is as follows Command syntax Auto-run programs If test-clause Branch commandsUncheck IF...THEN...END END Iferr trap-clause Then error-clause ENDIF... then ELSE... END CASE...END Iferr Then Drawing commands Graphic commands Grobxor →GROBGrobnot Grobor Loop commands Matrix commands Scaleadd RandmatRedim Scale Prompt commands Print commands Editmat matrixname DispDisptime Disp linenumbertextitem Input nametitle,labelhelpdefault GetkeyInput Wait seconds MsgboxPrompt Wait Stat-One and Stat-Two commands Stat-One commandsStat-Two commands Axes Storing and retrieving variables in programsPlot-view variables Area Grid CoordExtremum FastRes Isect HwidthIndep InvCross S1mark-S5mark Nmin / NmaxRecenter Root Umin/Umax SimultSlope StatPlot Xcross Tmin / TmaxTracing Tstep Ymin / Ymax XtickYtick Xmin / Xmax Angle Symbolic-view variablesXzoom Yzoom E1...E9, E0 X1, Y1...X9,Y9 X0,Y0R1...R9, R0 U1...U9, U0 Numeric-view variables C1...C9, C0Digits NumIndep FormatNumCol NumFont NumType NumRowNumStart NumStep PageNum Creating new aplets based on existing aplets Extending aplets Aplet Keys $/3+$@ H 175@ $1@ $/3+$@ θ @$/3+$@ C @ 175@ 180@ 35 175@ $3/ @Select Length of the ladder is approximately 8.72 metres Resetting an apletDownloading e-lessons from the web Solve for the missing To transmit an aplet Sending and receiving aplets Sorting items in the aplet library menu list To sort the aplet listTo delete an aplet Reference information Regulatory informationCanada Warranty LED safety Reference information To reset using the keyboard Resetting the HP 39G/40G To erase all memory and reset defaults If the calculator does not turn on21@ key Cross matrix1,matrix2 Glossary Operating temperature 0 to 45C 32 to 113F Operating detailsBatteries Menu maps of the Vars menu Home variables areCategory Available name Function aplet variables are Function aplet variablesUser-named Modes Parametric aplet variables Plot-FCNParametric aplet variables are Polar aplet variables are Polar aplet variables Sequence aplet variables are Sequence aplet variables Solve aplet variables are Solve aplet variables Statistics aplet variables Statistics aplet variables areStat-One Calculus Menu maps of the Math menuMath functions Math functions are = = Polynom Program constants Category Command Program commands Selected status messages Message Meaning+,7@ Memory Function value, root, extremum Or intersection is not visibleCurrent screen Index Index Index Index Index Index Index Index Index Index Index Index Index

Example

>$3/( @ Select

Statistics675(6(7$5￿<(6

160 >(17(5@

165 >(17(5@

170 >(17(5@

175 >(17(5@

180 >(17(5@

Statistics675(6(7$5<(6