Manual / Guide
A Curta calculating handbook that opens with a product description and goes on to business methods, statistics on grouped data, and five-place logarithm tables. The scan has a blank cover and no title page, so the title given here is descriptive. The text layer is OCR and carries errors.
A dwarf in size... A giant in calculating efficiency Curta is a complete pocket size calculating machine for all four arithmetical operations Like a chronometer or a miniature camera, the CURTA calculator is a precision machine of extremely small proportions. This amazing new construction, manufac- tured with up to date production-methods by CONTINA Ltd., is a masterpiece of matchless craftsmanship. CURTA is held in one hand while operated (see figure 2 , page 6 ) and is easily carried in a pocket or in a briefcase. Thus it fills a long felt gap in available calculating ma- chines and complies with the wishes of a great number of users demanding a small, yet complete and reliable individual instrument. The businessman on his trips, the profes- sional account at his client’s offices, the building contractor on the building site, the technician in the workshop, the draughtsman at his drawing board, professors and stu- dents, they all use and prefer CURTA for its handiness and accuracy. Wherever it is inconvenient to use noisy machines or to transport heavy and bulky instruments, all the outstanding advantages of the CURTA become fully evident. In the offices of private and public enterprises, in bureaus of the administration, in banks, in booking offices, in test-laboratories, to men- tion a few examples, CURTA is particularly appreciated for its quiet, convenient and fast operation: Unlike other machines, CURTA, held in one hand, is always in the operator's immediate angle of vision, right above his working place (see pages 5 and 6 ). Due to these remarkable features, CURTA, ever since its first appearance, has been en- thusiastically received both by experts and users and has been in rapidly growing de- mand all over the world. With the CURTA a miniature universal calcu- lating machine of an entirely new design has been created. Hand operated, with ‘‘safe- grip” setting knobs, visible setting dial and continuous tens transfer in the answering and the indicating dial. CURTA has the features and the perfection normally found only in more expensive modern calculating machines of far heavier weight and much larger size. 2 CURTA has the following features in common with heavy calculating machines: Performance It adds, subtracts, multiplies, divides, squares, cubes, extracts, square roots. CURTA is there- fore the ideal machine for invoicing, esti- mates, calculation of interest, currency con- versions, figuring out percentages, etc. Accuracy CURTA is fool-proof. Automatic devices pre- vent errors due to wrong handling. Special stops eliminate overspeeding of the axles in fast operation. Speed Exceptionally fast operation is possible thanks to the small size of all moving parts, the con- tinuous tens transfer in both dials and the one-way (clockwise) operation of the handle. Visibility The neatly engraved figures appear clearly on the non-glare surface of the machine. The set numbers appear automatically in the horizontal setting dial. Quality Only rigorously tested materials are selected for all parts of the CURTA. All parts are interchangeable and can easily be replaced. 3 Durability Practically no wear can be noticed even after years of use. Tests over a long period have shown that the whole mechanism of the CURTA will stand up to millions of rotations. Attractive appearance Fine finish, shock-proof container. Lower price Thanks to its modern design and the latest manufacturing methods CURTA is sold at a much lower price than any machine of com- parable performance. Resistance to corrosion CURTA is rust-proof and tropic-proof. Silent action On account of the small size of all moving parts and the use of automatic locking devices. Convenient and easy operation Thanks to the small weight, the easy action, the conveniently located ‘‘safe-grip’’ setting knobs, the clearly visible figures and the non- glare surface finish. For desk work the CURTA offers the special advantage that the operator remains in the same position for calculating as for his other work (compare the pictures on the two following pages). 4 Fig. 1 COMPARE the usual way... With a heavy calculating machine: concentration focused alternately on TWO points many movements additional strain Fig. 2 ...and the “CURTA’”’ way With the CURTA-Calculator e concentration focused on ONE point only e no unnecessary movements e less strain Short Description Operating handle Decimal '— Clearing lever marker Carriage ——: ————— Position indicator arrow Setting dial Setting knobs > setting knots Decimal marker Base of main —— {iaeaaateeeeees Sioeeewere ess Seevevewsy Severewnn ey Fig. 3 The machine consists of the main body which bears at its top the revolving carriage (see fig. 3) The main body contains the keyboard with the setting knobs protruding from slots, the adjustable white decimal markers at the base and the setting dial on top of the slots. The main axle, driven by the operating handle, passes through the center of the main body. The carriage contains the indicating dial (white) and the answering dial (black), the decimal markers set in a groove and the clearing lever (see fig. 4). The clearing lever can be folded over when the machine is stored in its container. Clearing lever The handling of the machine is similar to that of ordinary large machines, except that it is held in one hand, preferably in the left, with thumb and forefinger gripping the knurled edge of the carriage. The carriage, when lifted, can easily be rotated in either direction within the number of positions of the indicating dial; it is correctly fixed by stops, each of which is determined by the position indicator arrow being even with one of the numbers on the lower edge of the carriage. The setting of numbers (for example the terms of addition, one of the two multipli- cation factors, or the divisor) is done with the knobs projecting from the slots. Their zero position is at the top of the slots. To set a determined figure, the corresponding setting knob is moved down until the desired figure appears on the setting dial. The num- ber set can thus be readily checked. The operating handle is provided with a dis- tinctly felt stop which enables the operator to count each turn. With a gentle pull, re- spectively pressure, it can be brought into its upper or back into its lower positon, this latter serving for addition and multiplica- tion, whereas the upper is for subtraction and division. In both cases the handle is turned in the same clockwise direction. A safety de- vice prevents it from being turned backwards. 9 The indicating dial (white dial) counts the turns of the handle and indicates the num- ber of items of an addition, the multiplier of a multiplication, the quotient of a division and the root when extracting square-roots. The white dial will register the number of turns of the handle in the place correspond- ing to the number on the carriage edge in- dicated by the position indicator arrow. The answering dial (black dial) shows the re- sult of additions, subtractions ard multipli- cations and in division the dividend or re- mainder (according to the method of division selected). The tens transfer mechanism in both these dials saves considerable time for many oper- ations by reducing the number of turns of the handle (viz. in shortcut-multiplication). Among other advantages it permits the addi- tion of multipliers which is important in cubing and percentage calculations. The answering and the indicating dial are cleared with the clearing lever (see figs. 3 and 4.) It can be turned in both directions; two stops are provided between the black and the white dial. With one full turn in either direction both dials are cleared; however each dial can be cleared separately by mere- ly sliding the clearing lever over it from one stop to the other. 10 The reversing lever at the back of the ma- chine acts on the indicating dial. This latter will operate in opposite sense to the answer- ing dial when the reversing lever is brought into its lower position. Calculating example. The numbers visible in figs. 3 and 4 illustrate the multiplication: e——— Reversing lever Fig. 5 Back view of the machine 645432 X 63992. The multiplicand appears in the setting dial (see fig. 3), the multiplier in the white dial and the product in the black dial (see fig. 4). The total time required for this operation, in- cluding setting, is approx. 15 seconds when operating with 29 turns. In shortcut-multi- plication, which is made possible by the tens transfer mechanism, only 13 turns are neces- sary, which corresponds to a calculating time of approx. 10 seconds. In division, approximately 30 seconds in all, including setting, are required to ascertain a six digit quotient. All other operations are performed in the shortest time by the same methods as used currently with large universal calculat- ing machines. The dust and shock proof container of the CURTA. Fig. 6 Carriage with the counting mechanisms Main axle Pinions driving the counting mechanisms <<— Tens transfer mechanism Numeral Setting axles wheels of the seting dial Fig. 7 View of the stripped main assemble with the carriage above. 13 Numeral wheel Pinion Arresting disc axle Tens transfer pinion Gearing for Numeral wheel of the setting dial Setting knob Setting wheel Setting axle Diagram showing the transmission of figures in the Curta Fig. 8 The above illustration shows that by means of the setting knobs the setting wheels on the setting axles are brought within range of the toothed segment of the step drum whose number of teeth corresponds to the figure set. When rotating, the single central step drum acts successively on each setting wheel. The rotation of the setting wheels is transmitted through the pinions directly to the numeral wheels of the counting mechanisms. For clarity’s sake the above illustration is confined to one single digit. In the Curta, subtraction is converted to mere addition, the step drum acting automatically with its comple- mentary teething when it is placed in its upper position. These simple construction principles result in a considerable economy of parts and are responsible for the robust design to which the Curta owes its high dependability. 14 CURTA COMES IN TWO MODELS Both machines operate on the same principle, however Model # 2 is slightly larger to give you greater capacity. Speci fications MODEL # 1 MODEL # 2 8X6X 141 11 X 8 X 15 Keyboard 8 columns 11 columns Result Dial 14 columns 15 columns Counting Dial 6 columns 8g columns Add or Multiply to 11 places 15 places Divide to 6 places 8 places 1 . 9 . : 2/16 ine 27/16 Ine Diameter (53. mm) (65 mm) . 3.43 ins 3 °%8 in. Height (85 mm) (90 mm) . 8 OZS. 124 ozs. HENGE (230 g) (360 g) Our machines give the accuracy of a desk calculator plus the portability of a slide rule. 15 SERVICE Curta is made entirely of high quality metals, with the same manufacturing precision as a fine watch, therefore service required is kept at a minimum. we recommend, however, that once every two years, machines be sent in for cleaning and lubrication. When machine does require service, you may return it to the dealer from which it was purchased. If you are some dis— tance away, you may send it via ordi- nary parcel post, in its metal shock- proof container. Place the entire machine in its container into a small carton or wrap with several layers of newspaper or corrugated paper. Prices for servicing our machine are com- parable to that of a watch rather thar of a desk calculating machine. WHERE AND HOW TO BUY CURTA You may purchase our machines from the dealer or distributor whose name ap- pears on the back of this book. Our guarantee, our terms of sale, are the same regardless of which dealer your machine is purchased from; i.e. pur- chase may be made on a money back guarantee. Check with your dealer re- garding local taxes, cash discount, open account, time payments, if desired, etc. 16 ACCESSORY For those who wish to use Curta in the field, we have a leather shoulder strap carrying case. Leather case for Small Machine: No. 1 (holds calculator without metal case) Leather case for Large Machine; No. 2 (holds calculator without metal case) Leather case for Large Machine Only: No. S 2 (holds calculator in metal case) Also has belt loop Every CURTA-machine is supplied with detailed operating instructions giving the elementary rules for addition, sub— traction, multiplication and division. In addition, a booklet containing the following computing examples for the CURTA calculating machines is included: General Division by breaking down (subtractive method) Division by multiplying by a reciprocal The rule of three The rule of three in a single calcula-— tion (only CURTA Model # 2) axbXc dxexf Extended rule of three Calculation of roots Continued multiplication axbxcxd..,etc. Cubes without intermediate notes Commerce and Industry Checking of invoices and goods Percentage calculations A) Percentage increase B) Percentage decrease (Continued on next page) 17 (Continued from preceding page) C) Profit margin D) Compound percentages E) Profit and loss F) Capital and interest Costing Costing with simultaneous control (only CURTA Model # 2) Calculations with nines transfer Exchange calculations Calculations with English currency STATISTICS . Simultaneous accumulation of asum and a sum of squares (only CURTA Model # 2) Computation of arithmetic mean and standard deviation Technical and Survey Calculations Division into a negative number (com- plementary number) Calculation of co-ordinates Determination of the amount of silver in an alloy (only CURTA Model # 2) Determination of the angles in an acute-angled triangle, given three sides (only CURTA Model # 2) Determination of a side of an obtuse—- angled triangle (given the two other sides and their included angle) Calculation of area from co-ordinates Calculation of the distance between two points, given their co — ordinates (using Pythagoras’ theorem) Calculation of distance and azimuth (only CURTA Model # 2) Linear interpolation 18 ARI THMETICAL COMPUTATION FRACTIONS To Reduce Common Fractions: Divide the numerator and denominator by common divisors'until further reduction is impossible; 63,5) = 2727. 779 To Reduce Improper Fractions: Divide the numerator by the denominator, the quotient being a whole number and the remainder the new numerator: 43/6 = 439 +6 =7'/6. To Express a Fraction as a Decimal: Divide the numer- ator by the denominator: %= 3.00 +4 =0.75. To Reduce Complex Fractions: First express both num- erator and. denominator as simple fractions then multiply the upper numerator by the lower denominator for the new numerator and the lower numerator by the upper denominator 1% _ 7/4_ 42 27/20 = 2'/ 10. for the new denominator: = He 76 20 To Reduce Fractions to a Common Denominator: Multiply the numerator of each fraction by the product of all of the denominators except its own for the new numerators and multiply all denominators together for the new common de- nominator: 7/3, ‘sa, 9/5 = 4°/e0, 'S/e0. 3% /eo. To Add Fractions: Reduce to a common denominator and add the numerators: °/4 + 2/3 = %/12 + ®/i25!7/12= 15/12. To Subtract Fractions: Reduce to a common denominator and subtract numerators: % - 2/3 = %/12-- 8/42 = "Vie. To Multiply Fractions: Multiply the numerators for a new numerator and the denominators for a new denominator: 374 X Se = '8/52. To Divide Fractions: Invert the divisor and multiply: 874776 = aX 8/7 = 24728 = 8/7. 19 DECIMALS To Express a Decimal as a Fraction: Ignore the de- cimal point and write the figures as the numerator of the fraction. For the denominator write a figure 1 with as many ciphers after it as there were figures following the 125 10000 decimal point in the original decimal; .0125 = To Add or Subtract Decimals: Set down the figures so that the decimal points are one above the other and pro- ceed as in simple addition or subtraction. To Multiply Decimals: proceed as in simple multipli- cation pointing off as many decimal places in the result as there are in the multiplier and multiplicand together. To Divide Decimals: Proceed as in simple division pointing off as many decimal ploces in the quotient as there are decimal places in the dividend in excess of the divisor. RATIO AND PROPORTION Ratio: The relation of one figure to another is termed the ratio and is sometimes expressed as a fraction with the first quantity as the numerator: the ratio of lto2= 1:25 &. Proportion: Wnen ratios are equal to each other they are said to be in proportion. The ratio of 3 to 6 = 3:6 = y%, therefore it is equal to and inproportion to the ratio of 1 to 2 and the proportion would be written 3:6 = 1:2 and read *3 is to G as ] is to 2.° The first and last terms in a statement of proportion are called the extremes and the middle terms the means, A rule of proportion is that ‘the product of the extr is equal to the product of the means’. Thus, in the example given above: 3X 2= 6 and 6 X 1 = 6. Mean Proportional: When the middle terms are identi- cal this quantity is called the mean proportional of the first and last terms. In 1:2 = 2:4, 2 is the mean propor- tional between ] and 4, To find the mean proportional of any two terms multiply them and extract the square root of their product; Thus the an proportional of 2 and § is ¥ 2X 50 = VY 100 = 10 andtherefore 2:10 = 10:50. Formulas Based on Proportion: If proportion is ex- pressed algebraically as a:b=c:d, then ad = be F= 5 a= 'ep= Sd ¢ = $8, anda = 28 : thus having givenany three terms the fourth can be determined, 20 BUSINESS FORMULA DISCOUNT To find the amount of a discount, multiply the list price, or base, by the rate of discount. Formula: P = B x R, indicating the first type of percentage problem. To find the net price, subtract the amount of the discount from the origi- nal or list price. Formula: Difference = Base - Percentage D= B-P COMMISSION OR BROKERAGE To find the commission, multiply the principal amount, or the base, by the rate of commission. Formula: Commission (P) = Base (B) x Rate (R), or P =BXR INTEREST Interest problems employ the rules of percentage problems but include the additional factor of time. The interest (1) is the amount of money paid for the use of money. The principal (P) is the base, or the money for the use of which interest is paid. The rate (R) is the percent charged on the basis of one year's use of the money. 21 The time (T) is the number of years, months and days over which the money is used. Note especially that 30 days are considered a mcnth and 360 days are considered a year. The amount (A) is the sum of the principal and the interest. To find the interest for any given period of time, multiply the principal by the rate by the time. Formula: | = Px R XT To find the amount, add the interest (1) to the principal (P). Formulas A= P+ | To find the rate when the principal, interest and time are given, divide the total interest by the time to get the amount of the interest for one year; then divide this quotient by the principal. To find the time when the principal, interest and rate percent are given, multiply the principal by the rate to obtain the amount of interest for one year; then divide the total interest by the interest for one year. To find the principal when the inter- est, the rate percent and the time are given, divide the interest by the time to get the interest for one year, then divide this by the rate. To find the principal when the amount, rate percent and time are given, divide the given amount by the amount of $1 for the given time at the given rate. 22 COMPOUND INTEREST Compound interest is interest which for each successive interest period is figured on a base that represents the original principal plus all the inter-— est that has accrued in previous interest periods. To compute compound interest, add the interest for each period to the principal before figuring the interest for the next period. PROFIT AND LOSS PROFIT AND LOSS BASED ON COST To find the percent gain or loss, divide the amount gained or lost by the cost. To find the gain and the selling price when the cost and the percent gain are given, multiply the cost by the percent gain and add the result to the cost. To find the loss and the selling price when the cost and the percent loss are given, multiply the cost by the percent loss and subtract the product from the cost. To find the cost when the profit and the percent profit are given or to find the cost when the loss and the percent loss are given, divide the pro- fit or loss by the percent profit or loss. To find the cost when the selling price and the percent profit are given, divide the selling price by 1 plus the percent profit. 23 To find the cost when the selling price and the percent loss are given, divide the selling price by 1 minus the percent loss. PROFIT AND LOSS BASED ON SELLING PRICE To find the percent profit or loss, divide the amount gained or lost by the selling price. To find the profit and the cost when the selling price and the percent profit are given, multiply the selling price by the percent profit and sub—- tract the result from the selling price. To find the loss and the cost when the selling price and the percent loss are given, multiply the selling price by the percent loss and add the result to the selling price. To find the selling price when the profit and the percent profit are given, or to find the selling price when the loss and the percent loss are given, divide the profit or loss by the percent profit or. loss. To find the selling price when the cost and the percent profit are given, subtract the percent profit from 100% and divide the cost by the remainder. To reduce percent profit on selling price to percent mark-up (percent profit on cost), divide profit on selling price by 100% minus percent profit on selling price. To find the selling price when the cost and the percent loss are given, add the percent loss to 100% and divide the cost by this sum. 24 To reduce percent mark-up (percent profit on cost) to percent profit on selling price, divide percent mark-up by 100% plus percent mark-up. To reduce percent loss on selling price to percent loss on cost, divide percent loss on selling price by 100% plus percent loss on selling price. To reduce percent loss on cost to percent loss on selling price, divide percent loss on cost by 100% minus percent loss on cost. MULTIPLICATION OF DECIMALS To multiply decimals, proceed as in multiplication of whole numbers. But in the product, beginning at the right, point off as many places as there are in the multiplier and in the multipli- cand. To multiply a decimal by any multiple of ten, move the decimal point as many places to the right as there are zeros in the multiplier. DIVISION OF DECIMALS Law of division: A quotient is not changed when the dividend and divisor are both multiplied by the same number. To divide a decimal by a whole num- ber, proceed as with whole numbers, but place the decimal point in the quotient directly above the decimal point in the dividend. To divide a decimal by a decimal, move the decimal point of the divisor to the right until it becomes a whole number (i.e. multiply it by ten or a multiple of ten). Next move the decimal point of the dividend the same number of places to the right, adding zeros if necessary. 25 COMPOUND INTEREST - Showing the amount of $1.00 at various rates Yr. 2% 24% 3% 34% 4% 4% 5% 54% 6% 7% 1 {1.02000 | 1.02500 | 1.03000 | 1.03500 | 1.04000 | 1.04500 | 1.05000 | 1.05500 } 1.06000 | 1.07000 2 |1.04040 | 1.05063 | 1.06090 | 1.07123 | 1.08160 | 1.09203 | 1.10250 | 1.11303 | 1.12360 | 1.14490 3 j1.06121 | 1.07689 | 1.09273 | 1.10872 | 1.12486 | 1.14117 | 1.15763 | 1.17424 | 1.19102 | 1.22504 4 |1.08243 | 1.10381 | 1.12551 | 1.14752 | 1.16986 | 1.19252 | 1.21551 | 1.23882 | 1.26248 | 1.31080 5S {1.10408 | 1.13141 | 1.15927 | 1.18769 | 1.21665 | 1.24618 | 1.27628 | 1.30696 | 1.33823 | 1.40255 6 |1.12616 | 1.15969 | 1.19405 | 1.22926 | 1.26532] 1.30226 | 1.34010 | 1.37884 | 1.41852 | 1.50073 7 |1.14869 | 1.18869 | 1.22987 | 1.27228 | 1.31593 | 1.36086 | 1.40710 | 1.45468 | 1.50363 | 1.60578 8 |1.17166 | 1.21840 | 1.26677 | 1.31681 | 1.36857 | 1.42210 | 1.47746 | 1.53469 | 1.59385 | 1.71819 9 {1.19509 | 1.24886 | 1.30477 | 1.36290 | 1.42331 | 1.48610 | 1.55133 | 1.61909 | 1.68948 | 1.83846 10 {1.21899 | 1.28009 | 1.34392 | 1.41060 | 1.48024 | 1.55297 | 1.62889 | 1.70814 | 1.79085 | 1.96715 1 |1. 24337 | 1.31209 | 1.38423 | 1.45997 | 1.53945 | 1.62285 | 1.71034 | 1.80209 | 1.89820 | 2.10485 12 |1.26824 | 1.34489 | 1.42576 | 1.51107 | 1.60103 | 1.69588 | 1.79586 | 1.90121 | 2.01220 | 2.25219 23 }1. 29361 | 1.37851 | 1.46853 | 1.56396 | 1.66507 | 1.77220 | 1.88565 | 2.00577 | 2.13293 | 2. 40985 14 |1.31948 | 1.41297 | 1.51259 | 1.61870 | 1.73168 | 1.85194 | 1.97993 | 2.11609 | 2.26090 | 2.57853 15 |1.34587 | 1.44830 | 1.55797 | 1.67535 | 1.80094 | 1.93528 | 2.07893 | 2.23248 | 2.39656 | 2.75903 16 |1.37279 | 1.48451 | 1.60471 | 1.73399 | 1.87298 | 2.02237 | 2.18287 | 2.35526 | 2.54035 | 2.95216 17 {1.40024 | 1.52162 | 1.65285 | 1.79468 | 1.94790 | 2.11338 | 2.29202 | 2.48480 | 2.69277 | 3.15882 18 |1.42825 | 1.55966 | 1.70243 | 1.85749 | 2.02582 | 2.20848 | 2.40662 | 2.62147 | 2.85434 | 3.37993 19 /1.45681 | 1.59865 | 1.75351 | 1.92250 | 2.10685} 2.30786 | 2.52695 | 2.76565 | 3.02560 | 3.61653 20 {1.48595 | 1.63862 | 1.80611 | 1.98979 | 2.19112] 2.41171 | 2.65330 | 2.91776 | 3.20714 | 3.86968 26 000°09 | o00°ss | oo0°0S | DOO’Sr | DOO-OF | DOO'’sE | DOO°OE | 000°SZ apak JT oo00'oe | oos’zz | ooo’sz | oos*zz | oo0'o% | OOS*zT | ODO'ST | OOS "ZT syjuom 9 ooo'st | oSz'eT | Oos*zt | osz*TT | O00°OT | OSz's 90S °L 0sz°9 sy}uom ¢ oo0*OT | L9T’6 eee 's 00S°L 499°9 eee's 000°S LOT? syjuom Z% 000°S €8S°P LOT Y OSL eee 116° 00S °Z €80°Z yuo T 000°T LT6°0 ee8°0 0SZ°0 499°0 €8s ‘0 00S°0 LTv ‘0 skpp 9 ceo 79L°0 769°0 ¢z9°0 9S¢°0 98h 0 LTP 0 Lye 0 kop § 499°0 TT9°0 9s¢°0 00S *0 vrr 0 68e "0 eee "0 812 °0 sivp > 00S°0 Bsr 0 LT¥°0 gle°0 eee "0 7620 0sz°0 80z “0 spp € eee 0 goe “0 8LZ°0 0sz “0 ZZZ 0 v6T ‘0 L9T “0 6eT “0 skvp Z L9T ‘0 est‘o 6eT “0 STO TIT ‘0 460°0 €80°0 690°0 kp T %9 KAS %S SAV %Y SAE %E GG aut, isoq}pd1 snoTipa 3D OOO’T$ wo Ysor9szUT eur Hutaoys *ipek App-09€ D pup yzuoMm App-0E D UO pesDg LSAYSLINI FIdWIS 27 TABLE OF CUMULATIVE DISCOUNTS AND NET PRICE FACTORS To find the net price, multiply the base price by the number that is shown under the principal discount and opposite the desired additional discounts. To compute the net price on a $10.50 article with discounts of 40-20-5: under 40 and opposite 20-5 we find the number .456. The product of .456 and $10.50 is $4.79 net. To determine the conversion factor on any chain of cumulative discounts not shown in the table, multiply their complementary numbers. Example: What is the conversion factor of 40-10-2? Solution: .60 X .90 X .98 = .5920. Additional PRINCIPAL DISCOUNT (%) Discounts | 10 20 25 30 35 40 42% 45 47%, 2% .8775 | .78 73125 | .6825 | .63375 |.585 |.56063 | .53625 | .51188 a 855 | .76 7125 | .665 | .6175 | .57 54625 | .5225 | 149875 3° % 18336 |.741 | 169469 | .64838 | :60206 | .55575 | -53259 | 50944 | . 48628 —e 18123 |.722 | 167688 | .63175| .58663 |.5415 |.51894 | .49638 | .47381 A 79199 | .7035 | .65995 | .61596 | .57196 | .52796 |.50596 | .48397 | . 46197 % -81169 | .74 .69375 | .6475 | .60125 | .555 .53188 | .50875 | .48563 a" oh .7914 |.7215 | .67641 | .63131 | .58622 | 54113 | .51858 | .49603 | .47348 ae 77111 | .703_ | .65906 | .61513| .57119 | .52725 |.50528 | .48331 | .46134 Ta" 5-24 1.67933 | 68542! 164259 | 159975 | 155961 | 51407 1.49265 | 47123 | 44981 28 €428e° ) S600%° , 8TETHF VLEV* | S8ELF~ €OTS* , SL9PS~ sees”, Tg9o9* OT-OT-0T B Serge ° LT8€* | SOGEE° vOTv* | 6OTSF* 8S8h" |] 6YOZS" | BTSSS* | CEST91%Z-G-%AL-OT-OT 69ELE* | GYTGE” | 8Z60F" | LOLZH" | 99Z9H° | SZ86H"| FEEES* | EyE9S* | TITE9" 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c9zev° | 9S¥0S*| s9zS* |] BeoZs* | szPT9"| eTBS9° ZOL° 684" Wz -OT SZLP° s6v° | SZTS° vS° ges° 69° $29° ZL" 18" OT ALY SP ag OF sé Oo 4 02 OT s}unoosTq (%) LNNODSId TydIDNIYd TeuoTy FPPY Kddsi onal PRINCIPAL DISCOUNT (%) Discounts lo 20 25 30 35 40 42y 45 A7¥, l0-10-10-2%4 {6397 |.56862 |.53308 |.49854| .462 | .42647 | .4087 | .39093 | .37316 10-10-10-5 6233 |.55403 | .51941 |.48479 | .45016 | .41553 | .39822] .3809 | .36359 10-10-10-5-24160771 | .54018 | .49344 |.47257 | .4389 | .40514 | .38807 | .37138 | 13545 10-10-10-10 }5905 |.5248 |.4921 |.4593 | .4265 | .3937 | .37725| .3609 | .34445 10-10-10-10-5[ 561 .4986 | .4675 |.4363 | 140518 | .374 | .35839| 134286 | .32723 15 765 | .68 .6375 |.595 | .5525 |.51 .48875| .4675 | .44625 15-24% 17459 |.663 | .62156 |.5801 | .53869 | .4973 | .47653| 14558 | . 43509 15-5 [7268 | .646 60563 |.5653 | .52488 | .4845 | .46431| 144413 | .42384 15-10 16885 |.612 |.57375 |.5355 | .49725|.459 | .43988| .42075 | .40163 20 72 64 .6 .56 52 .48 46 44 42 20-5 L684 | .608 .57 .532 | .494 | .456 .437 .418 399 20-10 L648 .576 54 .504 | .468 |.432 |.414 | 2396 | .378 20- 10-5 .6156 | .5472 |.513 |.4788 | .4446 | 14104 | 73933 | :3762 | 3591 25 L675 | .6 .5625 |.525 | .4875 | .45 -43125] .4128 | .39375 25-5 16413 | .57 .53438 |.4987 | .36313 | .4275 |.4097 | .39198 | .37406 25-10 .6075 | .54 50625 |.4725 | .43875 | .405 | .38813| .37125 | 135438 25-10-5 .5771 |.513 ' 48094 '.4488 | 141681 '.3848 | .36872' .3527 | .33666 jo} 3 TSerz’ | 8E9Z° | 60F8Z* , BEFOE’ | B9"ZE* | LOPE” , 9zS9E* , SSSBE*y PESO" %z -%L-O0T S$L6PZ° | 9S0LZ° | 8ETEZ* | 6TZTE* eee’ | Teese’ | e9rze° | prS6E*| SZ9TP % OT 600SZ° | €602Z° | LLT6Z* | T97TE* | SvEeE’ | 62HSEe° | eTSLe* | LeS6Ee*| T89TF" Wy =S-OT s9sz° | 88zlz° | Ste6z* | €90zE° zpe’| seese’ | S4pse* | ET90R°}] SLzr° SOT sze9z" | 6TS8Z° | ETLOE* | 906zE° Tse" | pezle* | s8r6e° | T8gTh’ | SzsEer° ¥z-Ol LZ° | SZ6Z° ste’ | szee* ge°| szse° sor’ | Sar Sy OT €0LSZ° | Sv8Lz" | LeeEz’ | 6zTZE* | Tuzve* | eTH9e" | SSSse* | L690K"| GEsZr” 4 -G-%KL egc9z* | essez° | 9Sz40e° | eseze* | STSEe* | Leeze* | pHSGE’ | THLTH" | BE6Er" SH-KL 9S04Z° | Tte6z° | 99STE* | zZeee* | SLO9E"| eCEse’ | PESOr* | GEeszr’| PEOSH" 4 KL SL4lZ* | €900€° | SzezEe* | B8grE" Le’ | ete6e’ | SZ9Tr’ | se6er*| SzgoP° KL geegz° | 86s8z° | 8640€° | 866ze° | BETSE*| LeEde* | LeS6e* | LELTH* | LEEEr" AZ -S-S Slozz° | Tee6z* | 88sTe* | prsee” T9e° | gsese’ | eT90r° | Bgezr’| SzTSF’ g-s 88LLZ° | cOTOe’ | 6THZE* | PELVE’ | SOLe* | 99E6E° | TSSTH’ | LeEeh" | ETE9r- ¥%-S sez | SZ80e* | szee* | szgse" ge*| SLeov’ | Szzv° | SzTsr’ Sly" S $z6z° | ssgte* | Sztve* | egsge" 6€° | 8erTy’ | SL8Eh" | ETESP*| SLBF° id OL ALY $9 A 9 09 ALS Ss ACS 0s sz unoos 1q (%) LNNODSId TYdIONIYd TDUOTI TPPY Additional PRINCIPAL DISCOUNT (%) Discounts 50 52% 55 57% 60 62% 65 67% 70 10-7%-5 39544 | .37567 | .35589 | .33612 | .31635 | .29658 | .27681] .25703 | . 23726 10-74-5- 2% 38555 |. 36627 | .347 .32772 | .30844 | .28916 | . 26989 | .25061 | . 23133 10-10 .405 .38475 | .3645 | .34425 | .324 .30375 | .2835 | .26325 | .243 10-10-2% 39488 | .37513 | .35539 | .33564].3159 | .29616 | .27641]| . 25667 | . 23693 10-10-5 .38475 | .36551 | .34628 | .32704] .3078 | .28856 | .26933] .25099 | .23085 10-10-5-2% .37513 | .35637 | .33762] .31886 | .30011 | .28135 | .26259 | .24384 | .22508 10-10-74 .37463 | .35589 | .33716 | .31843 | .2997 | . 28097 | .27224] .24351 | .22478 10-10-7%-2% 36526 | .347 .32873 | .31047 | .29221 | .27394 | .25568 | .23742] .21916 10-10°7%-5 .35589 |.3381 | .3203 | .30251] .28472 | .26692 | .24913| .23133 | .21354 10-10-7%-5-2%|.347 .32965 | .3123 | .29495] .2776 | .26025]| .2429 | .22555]| .2082 10-10-10 -3645 | .34628 | .32805 | .30983 | .2916 | .27338 | .25515| .23693 | .2187 10-10-10-24 |.35539 | .33762 | .31985 | .30208 | .28431 | .26654 | . 24877] .231 . 21323 10-10-10-5 .34628 | .32897 | .31165 | .29434 | .27702 | .25971 | .24239 | .22508 | . 20777 10-10-10-5-241.33762 _.32074 | .30386 ! .28698 ! .27009 ' .25321! .23633' .21945 ' .20257 N oO B6zel | 92IIs | VHYeS’ | LvOVe , S9SZ° | Bree’, 9680%°, ShOE* | 690CE™ §-0T-Sz 2 szoz° | sezzz° | szgez* | etesz’ 12° | 8848z°| Szeoe*| eg0ze* | szee* OT-SZ gletz*| gstez’ | seevz’ | etz9z° | $ez°| tezoe’| egoze*| vrsee’ | egsz° $-Sz gzz° | s4erz° | sz9z° | sztez° e* | szuste’| szee’| szase- | suse- 4 zsoz’| sezz’| veez* | sosz°| gezz°| soez’| szoe*| eyze*| zve- $-0T-02 giz°| vez’ | zsz° La" gez°| g90e°| vze°| zre- 9e° OT-02 ezz° | Lbe" g9z° | sez’ | voe’] eze*| zrer| taser 8e° $-0% 92° 92° 8z" ° zee re" 96° 8e° 7 02 s6zz*| e9srz° | Szz9z° | 8998z° | zg0e’| etsze*| szrre*| seege’ | szec- OT-ST szzvz° | vyzoz’ | z9zez° | tezoe’ | eze’| zere’| sezge*| gsese*| seor- $-ST egerz’ | veegz’ | 9006z° | s4zote’ | stee’| zzzse| vezze*| g9e6e° | PPT” 4G-ST ssz°| szgzz° | szez* | Szete’ ve'| sztge*| szse°| szeor’ | oszr- ST eeget’| uszoz-| stetz* | paeez’ | eerz’| 679%°| pyosz’| 9096%° | 9TTE*|S-OT-OT-OT-OT eeget’| ezetz: | r9ezz°| posrz’ | vz9z°| veszz*| zS6z°| poTTe’| TS8Ze‘| OT-OT-OT-OT OL ALY $9 9 09 ALS ss AS os sj] unoostq (%) LNNODSIG T¥dIONIUd poeta TPPs Addi tional PRINCIPAL DISCOUNT (%) Discounts 7%, 75 17% 80 82% 85 874 90 % . 26813 | .24375 | .21938 | .195 .17063 | .14625 | .12188 | .0975 5 .26125 | .2375 | .21375 | .19 -16625 | .1425 | .11875] .095 5- 2% .25472 | .23156 | .20841 | .18525]| .16209 | .13894 | .11578 | .09263 5-5 .24819 | .22563 | .20306 |.1805 | .15794 | .13538 | .11281 |] .09205 5-5-2% .24198 | .21998 | .19799 | .17599 | .15399 | .13199 | .10999 | .08799 7% -25438 | .23125 | .20813 | .185 .16188 | .13875 | .11563 | .0925 TA 2, -24802 | .22547 | .20292 | .18038 | .15783 | .13528 | .11273 | .09019 74-5 . .24166 | .21969 | .19772 | .17575] .15378 | .13181 | .10984 | .08788 7%" 5- 2% -23561 | .2142 | .19278 | .17136 | .14994 | .12852 | .1071 | .08568 10 .2475 | .225 .2025 | .18 .1575 | .135 .1125 | .09 10- 2% . 24131 | .21938 | .19774 | .1755 | .15356 | .13163 | .10969 | .08755 10-5 , . 23513 | .21375 | .19238 | .171 .14963 | .12825 | .10688 | .0855 10-5-2% .22925 | .20841 | .18757 | .16673]| .14588 | .12504 | .1042 | .08336 10-7% : -22894 | .20813] .18731 | .1665 | .14569 | .12488 | .10406 | .08325 10-7%-2% «22321 .20292 | .18263 | .16234° .14205 |! .12175 | .10146 ' .08117 34 Z2$490°| Tv780° |) 6ZTOT’ , ATSTT* | SOSET* } EGTST* | T889T° | S9S8T° YZ -S-OT-OT-OT 9%690°| L£S980° | 88e0T° | ZTZT° | TSseT’ | Z8SST° | PIEZT*’ | SPOGT’ S-0T-OT-OT 80T 40° | $8880° | Z990T° | 6EPZT* | 9TZHT* | ZESST° | B9LLT* | 9FSET° 4% -OT-OT-OT 6Z40°| €TT60° | SEGOT’ | BSLZT° | BSPT* | COST’ | SZZzBT° | 8PO0z" -oT- OT-OT-OT v690° | $4980° | TROT’ | SPTZT° | SBeT° | ST9ST° | SEZLT* | S806T° AG ~S -AL-OT = OT 8TTL0° | L6880° | LL90T* | 9SHZT° | 9EZHT” | STOST* | SBLLT* | PLSET $-%L- OT -OT $0€L0°| TET6G* | 8S60T* | P8LzT° | T9HT° | LevOT° | E9Z8T° | 6800z° Az -AL- OT - OF €67L0°| 99€60° | GBEZTT’ | ZTTET’ | S86HPT* | BS89T° | TEL8T* | ¥O90Z" %L~ OT -OT €0SZ0°| 8ze60° | PSZTT’ | EeTeT* | SOOST* | T889T° | ZGZ8T* | ZE90z° AZ-S-OT-OT G6940°| 61960° | EPSTT’ | 99VET* | GEST’ | PTELT* | BEZET* | TOTTZ° S-0T-0T 868L0°| ZL860° | 9P8TT* | TZ8ET° | SGLST* | B99AT* | PHLET* | STLTZ° AZ -OT-OT T80°| SzTOT’ | STZT° | SZTHT* Z9T* | Stzet* | szoz° | S4zzz" OT-OT ITLL0°} 6€960° | LOSTT’ | PEPET* | ZZPST* | SELT* | BL4ZET* | SOZTZ* YE -S-AL- OT 60640°| 98860° | €98TT* | wP8ET° | 8TBST* | SELLT* | ZLLET* | 6HLTZ~ S-AL-OT 06 ALB $8 YB 08 ALL SL AGL syunoostq (%) LNNODSIG TYdIDNIYd [pUOCT} Tppy 35 AAiStened PRINCIPAL DISCOUNT (%) Discounts 72%, 75 17%, 80 82, 85 87% 90 10- 10-10-10 18043 | .16403 | .14762 | .13122] .11482]| .09842| .08201] .06561 10-10-10-10-5 |.17141] .15582| .14024] .12466| .10908| .09349| .07791] .06233 1s .23205 | .2125 | .19125 | .17 .14875| .1275 | .10625] .0765 15-24% .22625 | .20719 | .18647 | .1658 | .14503] .12431| .10359] .07459 15-5 .22045 | .20188 | .18169 | .1615 | .13731] .12112| .10094] .07268 15-10 . 20885| .19125| .17213] .153 | .13388| .11475| .09563] .06541 20 22 2 .18 .16 14 12 1 .08 20-5 -209 | .19 -171 | .152 | .133 | .114 | .095 | .076 20-10 -l98 | .18 -l62 | .144 | .126 -lo8 | .o9 072 20-10-5 -1881 | .171 | .1539 | .1368 | .1197 | .1026 | .o85s | .o684 25 .20625 | .1875 | .16875] .15 .13125] .1125 | .09375]| .075 25-5 .19594 | .17813 | .16031] .1425 | .12469] .10688 | .08906 | .07125 25-10 -18563 | .16875 | .15188] .135 | .11813| .10125] .08438| .0675 25-10-5 -17635 | .16031 | .14429| .1283 | .11222! .09629! .os0i6! .06413 36 STATISTICAL FORMULA MEASURES OF CENTRAL TENDENCY Arithmetic Mean = X when X refers to the values of the individual items, 2 (sigma) means that these values are to be sunmed, and n refers to the number of items, UNGROUPED DATA x - 28 n GROUPED DATA The mean of a frequency distribution with equal class intervals; Where xX, = the mid point of any class n = total frequencies i = class width For any class; F = class frequency d = unit deviation of class mid point from Xp SRd n Pd | i = X, + 37 MEDIAN (SHORT METHOD) GROUPED DATA N “3 ~ ~2FP ei sum of the frequencies prior frequencies in median class absolute difference between class frequency prior to it. absolute difference kLetween MED =L+ |“{——— FMed L = lower limit of median class No L ‘ ie 2 number of frequencies * 2 2F_= to the median class Fawd = i = width of the class MODE - GROUPED DATA d MODE = Ly +3 ty }3 1 2 Ly = lower limit of modal class ay = modal class frequency and dy = 38 modal class frequency and frequency subsequent to it. STANDARD DEVIATION Short Form Group Data (Small Sample) 2 N- 1 Large Sample Group Data nf BE GR’ Ungrouped Small Sample 5 = oxt _ (oxi? x N-1 N(-1) Ss. = standard deviation > = sum d = deviations F = frequency N = number of items i = class width X = value of item SAMPLING For Infinite Populations —= x ox = a For Finite Populations ox = ie <n? N- 1 39 ox = standard deviation of the population being sampled N = finite population size n = sample size = finite correction factor SAMPLING Standard Deviation of the Sample Mean Infinite Populations s = x sx = Ja Finite Populations sss Ni = no. 8X sx=f/ N= 1 Sa s, = sample deviation Confidence Interval for Population Mean Simple Large Random Somple x + 2% Sx z = normal deviate Small Sample Table of t-Values Corresponding to Various Areas in Both Tails of t-Distribution -t MEAN +t Regregs of 90 95 .98 .99 «a0 05 02 O01 Bearess ise Total Area in Both Tails 1 6.314 12.706 31.821 63.657 2 2.920 4.303 6.965 9.925 3 2.353 3.182 4.541 §.841 4 2.132 2.776 3.747 4.604 5 2.015 2.571 3.365 4.032 6 1.943 2.447 3.143 3.707 7 1.895 2.365 2.998 3.499 8 1.860 2.306 2.896 3.355 9 1.833 2.262 2.821 3.250 10 1.812 2.228 2.764 3.169 ll 1.796 2.201 2.718 3.106 12 1.782 2.179 2.681 3.055 13 1.77.1 2.160 2.650 3.012 14 1.761 2.145 2.624 2.977 15 1.753 2.1