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HP 12C Financial 0012C-90001, 12C Financial 12C#ABA, 12C Financial F2231AA#ABA Standard Deviation, sample, x-value, y-value, x-value, y-value, x-value, y-value, Display, Display, Example:, 4,820.59, estimate, 4,463.00, 21,714.29

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Section 6: Statistics Functions

79

Standard Deviation

Pressing gv calculates the standard deviation of the x-values (sx) and of the y-values (sy). (The standard deviation of a set of data is a measure of the dispersion around the mean.) The standard deviation of the x-values appears in the display after vis pressed; to display the standard deviation of the y-values, press ~.

Example: To calculate the standard deviations of the x-values and of the y-values from the preceding example:

Keystrokes	Display
gv	4,820.59	Standard deviation of sales.
~	6.03	Standard deviation of hours worked.

The formulas used in the hp 12c for calculating sx, and sy give best estimates of the population standard deviation based on a sample of the population. Thus, current statistical convention calls them sample standard deviations. So we have assumed that the seven salespersons are a sample of the population of all salespersons, and our formulas derive best estimates of the population from the sample.

What if the seven salespersons constituted the whole population of salespersons. Then we wouldn’t need to estimate the population standard deviation. We can find the true population standard deviation (σ) when the data set equals the total population, using the following keystrokes.*

Keystrokes	Display
gÖ	21,714.29	Mean (dollars)
_	8.00	Number of entries + 1.
gv	4,463.00	σx
~	5.58	σy

To continue summing data pairs, press gÖg^before entering more data.

*It turns out that if you sum the mean of the population into the set itself and find the new s,

computed using the formulas on page 192, that s will be the population standard deviation, σ, of the original set.

File name: hp 12c_user's guide_English_HDPMBF12E44	Page: 79 of 209
Printered Date: 2005/7/29	Dimension: 14.8 cm x 21 cm

Contents

Edition HP Part Number 0012C-90001 Notice REGISTER YOUR PRODUCT AT: www.register.hp.com Printing History Introduction 4 Introduction Financial Calculations in the United Kingdom For More Solutions to Financial Problems Contents 6Contents Section 4: Additional Financial Functions Section 5: Additional Operating Features Section 6: Statistics Functions Section 7: Mathematics and Number-AlterationFunctions Section 8: Programming Basics Section 11: Multiple Programs Section 12: Real Estate and Lending Section 13: Investment Analysis Section 14: Leasing Section 15: Savings Appendix A: The Automatic Memory Stack Getting Numbers Into the Stack: The Key One-NumberFunctions and the Stack Two-NumberFunctions and the Stack Appendix E: Battery, Warranty, and Service Information Appendix F: United Kingdom Calculations Function Key Index Programming Key Index Subject Index Example 1: zn: the number of compounding periods zi: the interest rate per compounding period zPV: the present value of a compounded amount zPMT: the periodic payment amount 12Making Financial Calculations Easy Note: running Keystrokes fCLEARHf2 CLEAR Example 3: Keystrokes Display fCLEARG 10,470.85 14gA –41.65 Page Problem Solving Getting Started Section 1: Getting Started Keying in Numbers Digit Separators Negative Numbers 18 Section 1: Getting Started Keying in Large Numbers The CLEAR Keys Key(s)Clears: Simple Arithmetic Calculations 20 Section 1: Getting Started Chain Calculations Example: Solution: 1,064.54 22 Section 1: Getting Started Your hp 12c calculates the answer in just the same way: 3\4§ Step 1: Multiply the numbers in the first parentheses Storage Registers Storing and Recalling Numbers 3,250.00 2,500.00 24 Section 1: Getting Started 19,500.00 22,000.00 Clearing Storage Registers Storage Register Arithmetic 1,053.00 Percentage and Calendar Functions Section 2: Percentage and Calendar Functions Net Amount 13,250.00 1,060.00 12,190.00 28 Section 2: Percentage and Calendar Functions Percent of Total Calendar Functions Date Format Month-Day-Year 30 Section 2: Percentage and Calendar Functions 11,09,2004 Number of Days Between Dates Basic Financial Functions Section 3: Basic Financial Functions Clearing the Financial Registers Simple Interest Calculations 1.Key in or calculate the number of days, then press n 2.Key in the annual interest rate, then press ¼ 3.Key in the principal amount, then press Þ$ 4.Press fÏ to calculate and display the interest accrued on a 360-daybasis Financial Calculations and the Cash Flow Diagram Page 36 Section 3: Basic Financial Functions The Cash Flow Sign Convention The Cash Flow Sign Convention: The Payment Mode BEGIN Generalized Cash Flow Diagrams 38 Section 3: Basic Financial Functions Compound Interest Calculations Specifying the Number of Compounding Periods and the Periodic Interest Rate Calculating the Number of Payments or Compounding Periods 40 Section 3: Basic Financial Functions total n equal fCLEARG 10.5gC 35000$ 12z Twenty-sevenyears and four months full 328n Stores total number of payments 42 Section 3: Basic Financial Functions –775.00 –50.00 4,000.00 4,027.27 Calculates FV – which equals the balance in the account if 58 full deposits were made 3,977.27 Recalls amount of deposits 44 Section 3: Basic Financial Functions 8\4§w –6,000.00 10,000.00 Calculating the Present Value –150.00 5,389.72 6,889.72 46 Section 3: Basic Financial Functions 17,500.00 540,000.00 –369,494.09 Calculating the Payment Amount 29gA 43400$ 43,400.00 gÂ 43,400.00 P –523.99 –3200.00 48 Section 3: Basic Financial Functions Calculating the Future Value 5gA 43,400.00 –523.99 2gA 1,281.34 50 Section 3: Basic Financial Functions noninteger n Page: 51 of 52 Section 3: Basic Financial Functions 4,500.00 –157.03 3,950.00 –120.00 54 Section 3: Basic Financial Functions Amortization To obtain an amortization schedule: 3.Enter the amount of the loan (the principal), using $ Key in the periodic payment, then press 5.Press g× or (for most direct reduction loans) gÂ to set the payment mode –573.35 –6,608.89 –271.31 49,728.69 –6,570.72 56 Section 3: Basic Financial Functions 1f! –552.08 ~ –21.27 1f! –551.85 ~ –21.50 Additional Financial Page Page Page Page Page Page Page Page Page Page Page Page Additional Operating Features Section 5: Additional Operating Features The Display Status Indicators Number Display Formats Standard Display Format 72 Section 5: Additional Operating Features Scientific Notation Display Format Mantissa Display Format fCLEARX f214.87 Special Displays Running 74 Section 5: Additional Operating Features Errors Arithmetic Calculations With Constants 1,095.00 Recovering From Errors in Digit Entry 429,000.00 9,987 Statistics Functions Section 6: Statistics Functions Register Statistic Correcting Accumulated Statistics gFg^ Mean 78 Section 6: Statistics Functions Salesperson Hours/Week 21,714.29 Standard Deviation 4,820.59 Standard deviation of sales Standard deviation of hours worked best estimates Linear Estimation 28,818.93 gR~d 0gR 1 gR~d Weighted Mean 82 Section 6: Statistics Functions Mathematics and Number-AlterationFunctions 84 Section 7: Mathematics and Number-AlterationFunctions Fractional Section 7: Mathematics and Number-AlterationFunctions The Power Function To Calculate 2Þ\3q –8.00 2\3yq Page Programming Programming Basics Section 8: Programming Basics Running a Program 90 Section 8: Programming Basics Program Memory Identifying Instructions in Program Lines Instruction Keycode nn ?=1 92 Section 8: Programming Basics Displaying Program Lines 08- 43, 33 The 00 Instruction and Program Line 94 Section 8: Programming Basics Expanding Program Memory Setting the Calculator to a Particular Program Line gi 96 Section 8: Programming Basics gi.00 Executing a Program One Line at a Time Interrupting Program Execution Pausing During Program Execution 98 Section 8: Programming Basics ?+1 :0 b ?+2 ?+3 100 Section 8: Programming Basics gu ?+2 1,312.20 1,400.77 2,040.00 Stopping Program Execution Keystrokes fs fCLEARÎ ?+1 :0 b t ?+2 ?+3 fs fCLEAR² 13\68.5 102 Section 8: Programming Basics Branching and Looping 104 Section 9: Branching and Looping Looping f! gu gi02 Section 9: Branching and Looping –543.35 106 Section 9: Branching and Looping Ê 03- –531.25 –531.25 –12.10 –531.12 Conditional Branching 108 Section 9: Branching and Looping Keystrokes fs Î : 110 Section 9: Branching and Looping Keystrokes gi07 gi08 :1 b fs 06- 43, 33 08- 25 –12.36 Display 15,000.00 3,000.00 20,000 25,000 112 Section 9: Branching and Looping 25,000.00 Ê06- 43, 33 08 Line 06: gi08 6,250.00 Program Editing Page Section 10: Program Editing Adding Instructions Within a Program Adding Instructions by Replacement 116 Section 10: Program Editing gi.08 12,000.00 Adding Instructions by Branching ~gogi gi12 01- 43 gi.10 11- 43 118 Section 10: Program Editing go gi00 :0 7,500.00 6,500.00 Page Multiple Programs Section 11: Multiple Programs Keystrokes fs gi.17 t gi19 fs 122 Section 11: Multiple Programs gi.27 Running Another Program gi19 Solutions Real Estate and Lending Section 12: Real Estate and Lending –594.17 :$2b-$ 58,800.00 :$150-$ Price of a Mortgage Traded at a Discount or Premium gÂ fCLEARG 72n 9gC 137.17P*137.17 2000M$ –8,777.61 Yield of a Mortgage Traded at a Discount or Premium 9gC –100,000.00 89,849.34 Þ$¼ 130 Section 12: Real Estate and Lending NCPR :.0 Page: 130 of KEYSTROKES DISPLAY KEYSTROKES DISPLAY 132 Section 12: Real Estate and Lending REGISTERS n: Period i: Apprec PV: Price 16.Press tto compute the yield on your investment in the house 17.Press tto compute the value of a savings account or other investment 7000?1 7,000.00 30?2 Deferred Annuities 0gJ 0gK 8ga 15,218.35 5ga 6ga 12,831.75 Investment Analysis Section 13: Investment Analysis gi30 41-43,33 n: Life i: Unused 138Section 13: Investment Analysis ~:$:3 +~- gi00 125,000.00 Book value 1,666.67 3,333.33 6,730.00 Declining-BalanceDepreciation gi31 21-43,33 140 Section 13: Investment Analysis ?+0 gi22 30-43,33 37-43,33 8,000.00 11,458.33 Sum-of-the-Years-DigitsDepreciation 142 Section 13: Investment Analysis ~-:M 9.For a new case press gi00 and return to step 12000$ 11t Fourth year: Full- and Partial-YearDepreciation with Crossover gi53 51-43,33 gi65 52-43,33 Section 13: Investment Analysis ?-2 ?-1 gi39 32-43,33 146 Section 13: Investment Analysis 94-43,33 gi58 95-43,33 R1: Dep fCLEARH 11000$ 500M 8n 11,000.00 Book value 500.00Salvage value 8.00Life 200.00Declining-balancefactor Excess Depreciation 10,500.00 1,312.50 8,531.25 Modified Internal Rate of Return Group # of Months Cash Flow ($) 0gK5ga 0gK9ga 150 Section 13: Investment Analysis 10gCfl Þ$ 6gCfl 657,152.37 775,797.83 Leasing 152 Section 14: Leasing Section 14: Leasing ?2t 154 Section 14: Leasing Solving for Yield :P§+$ ?0-n -23,200.00 :gC 17-45,43 156 Section 14: Leasing Advance Payments With Residual Solving for Payment Page 158 Section 14: Leasing ?1t Solving For Yield §=gJ –4,710.00 1,500.00 fL12§ Savings Section 15: Savings 162 Section 15: Savings Nominal Rate Converted to Continuous Effective Rate g>à Bonds 164 Section 16: Bonds Section 16: Bonds 166 Section 16: Bonds Annual Coupon Bonds –4.58 –94.75 Page Appendixes The Automatic Memory Stack Appendix A: The Automatic Memory Stack 172 Appendix A: The Automatic Memory Stack Termination of Digit Entry replaces Stack Lift Rearranging Numbers in the Stack The key Pressing ~ exchanges the numbers in the X- and Y-registers The Key One-NumberFunctions and the Stack Two-NumberFunctions and the Stack Mathematics Functions 174 Appendix A: The Automatic Memory Stack Percentage Functions Calendar and Financial Functions n, ¼, $ Register P, M, l INT365 The LAST X Register and the Key LAST Arithmetic Calculations with Constants 2 178 Appendix A: The Automatic Memory Stack 84,000 Enters base amount into displayed X-register 168,000.00 More About L 180 Appendix B: More About L Error Conditions 182 Appendix C: Error Conditions Error 1: Storage Register Overflow Error 2: Statistics Error 3: IRR Error 4: Memory Appendix C: Error Conditions Error 5: Compound Interest Error 6: Storage Registers K a l 184 Appendix C: Error Conditions Error 7: IRR Error 8: Calendar Error 9: Service Refer to Appendix E Pr Error Formulas Used Base(y) ⋅ Rate(x) Base(y) Total(y) ⎠ I360 = 360n ⋅ PV ⋅ 0 PV (1 iS) PMT ⎢⎥ FV (1 i) ∑ INT = ∑ INTj = INT1 + INT2 + ... + INTn ∑ PRN = ∑ PRNj = PRN1 + PRN2 + ... + PRNn PVn = PV0 + ∑ PRN NPV = CF0 0 = ∑CF 100(RDV + CPN DSM DPNJ SBV − SAL SOYDk = (W + 1)(W + 2F) DPNJ = (L − j + 1) ⋅ (SBV − SAL) SOYDL DPN1 DPNj ⎝ SOYD ⎠ ⎛ LADJ − j + ⋅ (SBV − D − SAL) NOM ⎞C EFF = ⎜1+ EFF = (eNOM − 1) yˆ = A + Bx xˆ = y − A B ⎢∑ xy − Battery, Warranty, and Service Information p sitive p l rity facing ou ward slide ; Appendix E: Battery, Warranty, and Service Information Page: 195 of 196 Appendix E: Battery, Warranty, and Service Information Warranty Service Europe Country : Telephone numbers 198 Appendix E: Battery, Warranty, and Service Information Asia Pacific L.America N.America Regulatory Information USA Canada Japan Temperature Specifications Disposal of Waste Equipment by Users in Private Household in the European Union United Kingdom Calculations 202 Appendix F: United Kingdom Calculations Annual Percentage Rate (APR) Calculations Function Key Index 204 Function Key Index Financial CLEAR GClears contents of financial registers (page 33) (page 37) Sets payment mode to End for compound interest calculations involving payments Function Key Index (page 81) (page 79) (page 80) Mathematics Programming Key Index Programming Key Index Go to. Followed by a decimal point and a (page 95) (page 92) Pressed from Subject Index with Constants, arithmetic calculations with 37, 70, 72, 93 , 29–31 , 68 210 Subject Index