Statistical Calculations, Mean | HP 33s Scientific specs

Statistical Calculations

Once you have entered your data, you can use the functions in the statistics menus.

Statistics Menus

Menu			Key		Description

L.R.				The linear–regression menu: linear
				estimation { ˆ	} { ˆ } and curve–fitting {T} {P}
				º	¸
				{E}. See ''Linear Regression'' later in this
				chapter.
x ,	y			The mean menu: {			} {		} {		· }. See
x ,	y			The mean menu: {		º	} {	¸	} {	º	· }. See
				"Mean" below.
s,σ				The standard–deviation menu: {Uº} {U¸}
				{σº} {σ¸}. See "Sample Standard
				Deviation" and "Population Standard
				Deviation" later in this chapter.
SUMS				The summation menu: {Q} {;º} {;¸} {;º}
				{;¸} {;º¸}. See "Summation Statistics"
				later in this chapter.

Mean

Mean is the arithmetic average of a group of numbers.

Press { º } for the mean of the x–values.

Press { ¸ } for the mean of the y–values.

Press { º· } for the weighted mean of the x–values using the y–values as weights or frequencies. The weights can be integers or non–integers.

Example: Mean (One Variable).

Production supervisor May Kitt wants to determine the average time that a certain process takes. She randomly picks six people, observes each one as he or she carries out the process, and records the time required (in minutes):

11–4Statistical Operations

Image 148

HP 33s Scientific manual Statistical Calculations, Mean, Statistics Menus Key Description, 11-4Statistical Operations

Contents

Hp 33s scientific calculator Printing History Contents RPN The Automatic Memory Stack Clearing the X-Register Storing Data into Variables Fractions in Programs How You Can Use Equations Summary of Equation Operations Complex Stack Complex Operations Contents Solving an EquationFor More Information Accuracy of Integration Programming 12-4 Data Input and Output 12-4 Entering a Program 12-512-6 12-7 13-1 13-213-3 Branching GTO 13-4 Managing Calculator Memory Contents Part 3. Appendixes and ReferenceVector Operations 15-1 15-12 Resetting the Calculator Clearing Memory Round-Off Error ContentsDisabling Operations Neutral Operations About ALG How the Integral Is Evaluated UnderflowConditions That Prolong Calculation Time Page Part Basic OperationPage Adjusting Display Contrast Getting StartedImportant Preliminaries Turning the Calculator On and Off Shifted Keys Highlights of the Keyboard and Display2Getting Started Alpha Keys Cursor Keys Backspacing and Clearing Silver Paint Keys4Getting Started Keyboard-entry mode Are described in Using Menus on page 1-7. IfEquation-entry mode ¾ when number entry is complete 6Getting Started Using Menus HP 33s Menus Chapter NameProgramming Instructions Numeric Functions Other functions 8Getting StartedDescription To use a menu function Exiting Menus KeysDisplay RPN mode ALG mode To select RPN modeTo select ALG mode RPN and ALG Keys Display and Annunciators First Line Second Line HP 33s Annunciators Meaning Chapter 12Getting Started2 3 RAD or §,¨ Keying in Numbers Making Numbers NegativeExponents of Ten Keys Display Description Keying in Exponents of Ten Understanding Digit EntryOther Exponent Functions Doing Arithmetic Range of Numbers and OverflowKeys Display 16Getting Started One-Number Functions Two-Number Functions, \, , Qor T Key in the number. You dont need to press ‘ Controlling the Display Format Periods and Commas in Numbers‘3 z D, , \, ,Q Fixed-Decimal Format % Number of Decimal PlacesScientific Format SHOWing Full 12-Digit Precision 20Getting StartedEngineering Format ALL Format Entering Fractions FractionsKeysDisplayDescription 22Getting Started Displaying Fractions MessagesDisplayDescription Calculator Memory Checking Available MemoryClearing All of Memory 24Getting Started What the Stack Is RPN The Automatic Memory StackRPN The Automatic Memory Stack Clearing the X-Register X and Y-Registers are in the Display2RPN The Automatic Memory Stack ¶ Roll Down Reviewing the StackRµ Roll Up Exchanging the X- and Y-Registers in the Stack Arithmetic How the Stack Does It4RPN The Automatic Memory Stack How Enter Works Lost Using a Number Twice in a Row How Clear x Works6RPN The Automatic Memory Stack Filling the stack with a constant Last X Register Correcting Mistakes with Last , \, , Qor T8RPN The Automatic Memory Stack Wrong One-Number Function Reusing Numbers with Last ›Mistake 96.704 + 10RPN The Automatic Memory Stack Chain Calculations in RPN mode Work from the Parentheses Out 12RPN The Automatic Memory Stack Solution ExercisesOrder of Calculation 16.3805x5 = 181.0000 14RPN The Automatic Memory Stack More Exercises‘14 ‘ ⋅ 0.8 ⎟ 12.5 − 0.73 = Page Storing Data into Variables Storing Data into Variables Storing and Recalling Numbers 2Storing Data into VariablesTo recall a copy of a number from a variable to the display Example Storing Numbers Reviewing Variables in the VAR Catalog Viewing a Variable without Recalling ItTo review the values at any or all non-zero variables Clearing Variables Arithmetic with Stored VariablesStorage Arithmetic 4Storing Data into Variables Recall Arithmetic Result 3 That is, x LzE Exchanging x with Any Variable6Storing Data into Variables Variable Page Exponential and Logarithmic Functions Real-Number FunctionsReal-Number Functions Power Functions Quotient and Remainder of DivisionTo Calculate Press 2Real-Number Functions Entering π TrigonometryTo Calculate Press Result Setting the Angular Mode Trigonometric FunctionsOption Description Annunciator 4Real-Number Functions NzR Programming Note Hyperbolic Functions Percentage Functions6Real-Number Functions ‘x Q 16.12 ‘ 15.76 T . Const Menu Items Description Value Physics Constants8Real-Number Functions Items Description Value Conversion FunctionsTo insert a constant 10Real-Number Functions Coordinate ConversionsTo convert between rectangular and polar coordinates Example Polar to Rectangular Conversion Example Conversion with Vectors Time Conversions 12Real-Number FunctionsTo convert between decimal fractions and minutes-seconds Example Converting Time Formats Angle Conversions Unit ConversionsTo Convert Press Displayed Results To convert an angle between degrees and radians Probability Functions FactorialGamma Probability Example Combinations of People KeysDisplay Parts of Numbers 16Real-Number Functions Names of Functions Page Fractions Entering Fractions Display Rules Fractions in the Display2Fractions Accuracy Indicators Entered Value Internal Value Displayed Fraction Longer Fractions Changing the Fraction Display4Fractions Setting the Maximum Denominator Choosing a Fraction Format Examples of Fraction Displays To Get This Fraction Format Change These FlagsFraction How 2.77 Is Displayed Format 6Fractions Fraction Number Entered and Fraction Displayed Format ¼ Rounding FractionsDenominator Fixed Fractions in Equations 8Fractions Fractions in Programs Page Entering and Evaluating Equations How You Can Use EquationsEntering and Evaluating Equations Example Calculating with an Equation ZLL ZNz2Entering and Evaluating Equations Summary of Equation Operations Enters and leaves Equation modeKey Operation Entering Equations into the Equation List Variables in Equations4Entering and Evaluating Equations To enter an equation Numbers in Equations Functions in Equations Displaying and Selecting Equations Parentheses in EquationsLR d ZLC z Editing and Clearing Equations ———To view a long equation To select an equation 8Entering and Evaluating Equations Types of Equations Evaluating Equations Type of Equation Result for ‘ 10Entering and Evaluating EquationsFx ¼ To evaluate an equation Using Enter for Evaluation Example Evaluating an Equation with Enter Using XEQ for Evaluation Responding to Equation Prompts12Entering and Evaluating Equations Example Evaluating an Equation with XEQ Syntax of Equations Operator Precedence‘5 g „ To display digits hidden by the prompt, press Equations Meaning Order Operation Example14Entering and Evaluating Equations Equation Functions Σxy Operation Equation function 16Entering and Evaluating EquationsExample Perimeter of a Trapezoid Perimeter = a + b + h HLA ’.25 zLN zLD 2 zR NqLN `qONqLN `‘ Cos π / nExample Area of a Polygon Area = Syntax Errors Verifying Equations18Entering and Evaluating Equations Example Checksum and Length of an Equation Solving Equations Solving an EquationSolving Equations Markup ⋅ Cost = Price LD dLV ZLT ›2Solving Equations Example Solving the Equation of Linear Motion Value HL P z ZL T4Solving Equations Example Solving the Ideal Gas Law Equation LV q Understanding and Controlling Solve Verifying the Result 6Solving Equations Interrupting a Solve Calculation Choosing Initial Guesses for Solve Example Using Guesses to Find a Root 8Solving Equations H 40 ZL H 10Solving Equations For More Information Page Integrating Equations Integrating Equations J0 x = π1 ≥0π cos x sin t dt Integrating Equations ≥ FN2Integrating Equations ≥ 0π f t Value Example Sine Integral 4Integrating Equations= ≥ t Accuracy of Integration Specifying Accuracy Interpreting Accuracy6Integrating Equations Example Specifying Accuracy Example Changing the Accuracy 8Integrating Equations Its uncertainty indicates Operations with Complex Numbers Complex Stack+ iy To enter a complex number 2Operations with Complex Numbers Complex OperationsTo do an operation with one complex number Functions for One Complex Number, z To Calculate Press To do an arithmetic operation with two complex numbers 2 5 ‘ ‘2 ‘ ‘4 4Operations with Complex Numbers Using Complex Numbers in Polar Notation 2 3 ‘‘2 6Operations with Complex Numbers Example Vector Addition Operations with Complex Numbers Page Base Conversions and Arithmetic Base MenuMenu label Description Base Conversions and Arithmetic Arithmetic in Bases 2, 8, 10-2Base Conversions and Arithmetic Keys Display Representation of Numbers Negative Numbers˜˜ 10-4Base Conversions and Arithmetic Range of Numbers 7FFFFFFFF Windows for Long Binary Numbers 10-6Base Conversions and Arithmetic Entering Statistical Data Statistical OperationsStatistical Operations Correcting Errors in Data Entry Entering One-Variable DataEntering Two-Variable Data 11-2Statistical Operations 400 Initial x, y Corrected x, y‘20 Statistical Calculations MeanStatistics Menus Key Description 11-4Statistical Operations Example Weighted Mean Two Variables · Price per Part Number of Parts y Sample Standard Deviation Population Standard DeviationUº 11-6Statistical Operations Linear Regression σºKeys DisplayDescription Linear Regression Menu 11-8Statistical Operations Example Curve FittingNitrogen Applied Grain Yield Limitations on Precision of Data 70, y Summation Values and the Statistics Registers Summation Statistics11-10Statistical Operations Normalizing Close, Large Numbers Access to the Statistics Registers Statistics Registers in Calculator MemoryExample Viewing the Statistics Registers # ™ ´º¸/ ™ ´¸/ ™ ´º/ ™ ´¸/ ™ ´º/ ‡ 11-12Statistical Operations Programming Page RPN mode 5 !Nz ALG mode 5 !zN‘ Simple ProgrammingSimple Programming Example a Simple Program RPN mode ALG mode RPN modeDisplay Description 12-2Simple Programming Selecting a Mode Designing a ProgramProgram Boundaries LBL and RTN Program Labels Using RPN, ALG and Equations in Programs Data Input and OutputStrengths of RPN Operations ALG Operations Entering a Program To enter a program into memory 12-6Simple Programming Keys That ClearTo enter an equation in a program line Function Names in Programs RPN modeExample Entering a Labeled Program HN ZLR12-8Simple Programming Example Entering a Program with an Equation Testing a Program Running a ProgramExecuting a Program XEQ NzX Example Testing a Program 12-10Simple Programming Entering and Displaying Data Using Input for Entering Data@ 12-12Simple Programming To use the Input function in a program Using View for Displaying Data To respond to a prompt 12-14Simple Programming Using Equations to Display MessagesExample INPUT, VIEW, and Messages in a Program NzLR LR z › LH ›p = 2π R2 + 2π RH = 2π R R + H Displaying Information without Stopping 12-16Simple Programming Error Stops Stopping or Interrupting a ProgramProgramming a Stop or Pause STOP, PSE Interrupting a Running Program Editing a Program 12-18Simple ProgrammingTo delete a program line To insert a program line Program Memory Viewing Program Memory Memory Usage Catalog of Programs MEMClearing One or More Programs 12-20Simple Programming Checksum To clear all programs from memory Selecting a Base Mode in a Program Nonprogrammable FunctionsProgramming with Base V Decimal mode set Hexadecimal mode set Polynomial Expressions and Horners MethodNumbers Entered in Program Lines Ax4 + Bx3 + Cx2 + Dx + E ‰X Keys Display ALG mode12-24Simple Programming Checksum and length E41A Page Routines in Programs Programming TechniquesProgramming Techniques Calling Subroutines XEQ, RTN 13-2Programming Techniques Nested Subroutines Example a Nested Subroutine 13-4Programming Techniques Branching GTOA2 + B2 Using GTO from the Keyboard Programmed GTO Instruction Conditional Instructions 13-6Programming Techniques Tests of Comparison x?y, x?0 Test Menus Program Lines Description RPN mode Flags13-8Programming Techniques !- % ! ! ! º¸@ ! Fraction-Control Flags Status Clear FlagSet 13-10Programming Techniques Flags Menu Menu Key Description Using FlagsAnnunciators for Set Flags Example Using Flags 13-12Programming Techniques Program Lines Description RPN mode$ @ $ $ @ $ 13-14Programming Techniques Example Controlling the Fraction Display Program Lines Description Loops 13-16Programming Techniques ! ! Conditional Loops GTO . ! º6¸@ ! #$ ! 13-18Programming Techniques Loops with Counters DSE, ISGLoop-Control Number $ ! $ $ $ Variable Indirectly Addressing Variables and Labels13-20Programming Techniques Indirect Address If i contains Then i will address Program Control with 13-22Programming TechniquesExample Choosing Subroutines With ! L If i holds Then XEQi calls Program lines- L & %1L2 Example Loop Control With Equations with 13-24Programming Techniques L 1L2 Page Solving and Integrating Programs Solving a ProgramSolving and Integrating Programs To solve a programmed function 14-2Solving and Integrating Programs Example Program Using ALGV= N x R x T Pressure ⋅ volume. Pressure ⋅ volume LP z LV ’ LN z LR z LT ‘ Example Program Using Equation14-4Solving and Integrating Programs @ @ ‘10 !@ # / Using Solve in a Program 14-6Solving and Integrating Programs/ label #variable Example Solve in a Program Integrating a Program Program Lines In RPN modeTo integrate a programmed function 14-8Solving and Integrating Programs To write a program for ≥ FN Sin Using Integration in a Program/ label ≥ G variable 14-10Solving and Integrating ProgramsExample ≥ FN in a Program Restrictions on Solving and Integrating Page Mathematics Programs Vector OperationsMathematics Programs = R cosP = arctan = XU + YV + ZW 15-2Mathematics ProgramsV1 = X i + Y j + Z k V2=U i + V j + W k X2 + Y2 + Z2 and P Program Listing Program Lines Description ALG mode 15-4Mathematics Programs Goes to the vector-addition routine 15-6Mathematics Programs Remarks Flags UsedProgram Instructions 15-8Mathematics Programs Variables Used XR 15-10Mathematics Programs @ 07 g !@ 125 g @ 15-12Mathematics Programs Solutions of Simultaneous EquationsAX + DY + GZ = J BX + EY + HZ = K CX + FY + IZ = L % 15-14Mathematics Programs Mathematics Programs 15-16Mathematics Programs Flags Used 15-18Mathematics Programs Scratch @ Polynomial Root Finder 15-20Mathematics Programs@ @ @ Where J = a3/2 = y0 /2 X2 + J + Lx + K + M =X2 + J Lx + K M = ⋅ the sign of JK a1/2 15-22Mathematics Programs Polynomial 15-24Mathematics Programs ! Checksum and length C7A6 B0 =a04a0 a32 a12B2= -a2 B1 = a3a1 4a0 15-26Mathematics Programs JK. a1 + L + M 15-28Mathematics Programs Terms and Coefficients Order 15-30Mathematics Programs %/ Coordinate Transformations 15-32Mathematics Programs Old coordinate System 15-34Mathematics Programs Checksum and length 8C82 15-36Mathematics Programs Remark Ÿ @ 15-38Mathematics Programs Curve Fitting Statistics ProgramsStatistics Programs = B + MIn 16-2Statistics Programs Description 16-4Statistics Programs #$ #$ 16-6Statistics Programs 16-8Statistics Programs XS%@ 40.5 g &@ value 104.5 g %@ 38.6 g &@ %@ 37.9 g &@ / 16-10Statistics Programs/ / %@ Logarithmic Exponential Power Normal and Inverse-Normal Distributions 16-12Statistics Programs Function 16-14Statistics Programs ª º ª -+. H % ! Inverse program Variable used temporarily to pass the value S ⋅ 2 π toXS@ 16-16Statistics Programs Grouped Standard Deviation 2f − 16-18Statistics Programs Updates ƒxi 2fi in register Increments or decrements N 16-20Statistics Programs Group /%@ @ XU/ %@ 13 g @ / 16-22Statistics Programs %@ %@ %@ Time Value of Money Miscellaneous Programs and EquationsMiscellaneous Programs and Equations …LN ` QLI ›LF z›LI 17-2Miscellaneous Programs and Equations Solve instructions šas Keys Display Description RPN mode17-4Miscellaneous Programs and Equations Retains 5750 in B calculates monthly interest rate Prime Number Generator 17-6Miscellaneous Programs and Equations LBL Y 17-8Miscellaneous Programs and Equations #$ No test is made to ensure that the input is greater than 17-10Miscellaneous Programs and Equations Appendixes and Reference Page Support, Batteries Service Support, Batteries, and Service A-1Calculator Support Answers to Common Questions Environmental Limits 2Support, Batteries, and ServiceChanging the Batteries Support, Batteries, and Service A-3 To install batteries Testing Calculator Operation 4Support, Batteries, and ServiceDo not mutilate, puncture, or dispose of batteries Fire. The batteries can burst or explode Self-Test Support, Batteries, and Service A-5™Ÿ˜—š Warranty 6Support, Batteries, and Service Support, Batteries, and Service A-7 ServiceEurope Country Telephone numbers Asia Pacific Country Telephone numbers 8Support, Batteries, and ServiceAmerica Country Telephone numbers Regulatory Information Support, Batteries, and Service A-9Canada 10Support, Batteries, and Service Japan Managing Calculator Memory User Memory and the StackUser Memory and the Stack Resetting the Calculator 2User Memory and the Stack Clearing Memory DefaultCategory Status of Stack Lift Disabling OperationsNeutral Operations 4User Memory and the Stack Vlabel nnnn EQN FDISP 6User Memory and the Stack Status of the Last X Register€ θ ,r About ALG ALG SummaryALG Summary C-1 Power Functions Doing Two-number Arithmetic in ALGSimple Arithmetic 2ALG Summary ‘27 Q… Percentage CalculationsALG Summary C-3 Permutations and Combinations Quotient and Remainder Of Division16.12 T 4ALG Summary Keys Display Description ALG Summary C-5 Reviewing the Stack 6ALG Summary Coordinate Conversions ALG Summary C-7 Q3 z Integrating an Equation8ALG Summary Operations with Complex Numbers ALG Summary C-9To view the result of complex operations Complex Operations ` Q2 › 2 ›3 `10ALG Summary Ë5 ¹cº  ºy3 ÃË  ºy4 ÃË2ALG Summary C-11 Initial x, y Corrected x, y 12ALG Summary 20 ALG Summary C-13Page How Solve Finds a Root More about SolvingMore about Solving D-1 2More about Solving Function Whose Roots Can Be Found More about Solving D-3 Interpreting ResultsExample An Equation With One Root 4More about Solving Example An Equation with Two Roots More about Solving D-5 / / -%. LX `’1.56More about Solving Example Discontinuous Function − 1= More about Solving D-7 When Solve Cannot Find a Root 8More about Solving More about Solving D-9 Example a Relative Minimum 10More about Solving Example An Asymptote ⎟ x + 0.3 − 0.5 = #LX q LX ›3 ``…More about Solving D-11 Example Find the root of the equation !1%ª1%-22 12More about SolvingExample a Local Flat Region Round-Off Error More about Solving D-13 Underflow 14More about Solving How the Integral Is Evaluated More about IntegrationMore about Integration Conditions That Could Cause Incorrect Results 2More about Integration ≥0∞ xe −x dx LX z LX ` ‡ 4More about Integration More about Integration 6More about Integration Conditions That Prolong Calculation Time 8More about Integration . More about Integration Page Messages Messages F-1 2Messages Or program. This might take a while Messages F-3 # variable 4Messages Self-Test Messages Name Keys and Description Operation IndexOperation Index G-1 ˜or — jh 2Operation Index Operation Index G-3 Polar to rectangular coordinates P 4Operation Index M Operation Index G-5 6Operation Index GComplex Change sign›Complex …Complex Subtraction Operation Index G-7 8Operation Index RHyperbolicVRadians to degrees DSE variable Mvariable Operation Index G-9 Natural exponentialWlabel ?Fractional part 10Operation Index GTO label Vlabellabel Nnnn ”I” Operation Index G-11Input variable ‰variable Integer part ISG variable Lvariable 12Operation Index LBL label •labelNatural logarithm Common logarithm Operation Index G-13 Permutations of n itemsFPause WDegrees to radians 14Operation Index Operation Index G-15 16Operation Index Operation Index G-17 18Operation Index Operation Index G-19 ≠0? 13-7If x=0, skips the next program Line ≤0? 13-7 11-10 Given an x-value Power Returns y raised to the xth power 20Operation Index Index Index-1 Index-2 Index-3 Index-4 Index-5 Index-6 Index-7 Index-8 Index-9 Index-10 Index-11 Index-12 RPN Index-13 Index-14 View Index-15