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28

7.

1

75

(Average for data X )

0.97357955

1

(Standard deviation for data X )

0.9

1

070028

(Standard deviation of the population for data X )

9.875

(Average for data Y)

3.4408263

1

3

(Standard deviation for data Y)

3.2

1

8598297

(Standard deviation of the population for data Y)

8

(Total count of data)

57.4

(Sum of data X )

4

1

8.48

(Data X  raised to the second power)

544.

1

(Sum of the product of data X  and data Y)

79

(Sum of data Y)

863

(Data Y raised to the second power)

<Let’s check the results based on the previous data.>

C alculates the sum of the product for sample data X  and sample data Y.

C alculates the sum of the data (sample data Y).

C alculates the sum of the data (sample data Y) raised to the second power.

C alculates the average value of the data (sample data Y).

C alculates the standard deviation of a data population (sample data Y).

C alculates the standard deviation for the data (sample data Y).

In addition to the 

1

-variable statistic keys, the following keys have been added for calcu-

lating 2-variable statistics.

N OT E :
The codes for basic statistical quantities of sample data X  and their meanings
are the same as those for single-variable statistical calculations.

“ A N S ”   K E Y S   F O R   2 -V A R I A B L E   S T AT I S T I C S

Summary of Contents for EL-531R

Page 1: ...SCIENTIFIC CALCULATOR OPERATIONGUIDE SCIENTIFIC CALCULATOR OPERATIONGUIDE V R Series ...

Page 2: ...e xth power of y square root cube root xth root of y 12 10 to the power of x common logarithm 13 e to the power of x natural logarithm 14 Factorials 15 Permutations combinations 16 Time calculation 17 Fractional calculations 18 Memory calculations 19 Last answer memory 20 Trigonometric functions 21 Arc trigonometric functions 22 Hyperbolic functions 23 Coordinate conversion 24 STATISTICS FUNCTION ...

Page 3: ...2 mode for performing2 variable statisti cal calculations If the calculator fails to operate normally press the reset switch on the back to reinitialise the unit The display format and calculation mode will return to their initial settings RESET 2 R E S E T S W I T C H Reset switch RESET 2nd function Normal mode STAT 1 mode STAT 2 mode N OT E Pressingthe reset switch will erase any data stored in ...

Page 4: ... point format FIX is displayed Displays the fractional part of the calculation result accordingto the specified number of decimal places Scientific notation SCI is displayed Frequently used in science to handle extremely small or large numbers Engineeringscientific notation ENG is displayed Convenient for convertingbetween different units Example specifies normal mode normal mode FIX modeTAB 3 Let...

Page 5: ...l of work and it s easy to make mistakes In such a case the numerical values are divided into mantissa and exponent portions displayed and calculated Example W hat is the number of electronics flowingin a conductor when the electrical charge across a given cross section is 0 32 cou lombs The charge on a single electron 1 6 x 10 19 coulombs 0 32 DEG normal mode SCI mode ENG mode SCI DEG X10 ENG DEG...

Page 6: ...radians equaling100 grads 3 14159 90 DEG RAD GRAD DEG Angular indicator Degrees DEG is shown at the top of the display A commonly used unit of measure for angles The angular measure of a circle is expressed as 360 Radians RA D is shown at the top of the display Radians are different than degrees and express angles based on the circumfer ence of a circle 180 is equivalent to radians Therefore the a...

Page 7: ...s all internal values includingcoefficients in 3 variable linear equations and statistics Values stored in memory in normal mode are not erased These arrow keys are useful for Multi Line playback which lets you scroll through calculation steps one by one refer to page 8 These keys are useful for editingequations The key moves the cursor to the left and the key moves the cursor to the right The key...

Page 8: ... Pressingπ automatically enters the value for π 3 14159 The constant π used frequently in function calculations is the ratio of the circumference of a circle to its diameter Example Numeric keys for entering data values Decimal point key Enters a decimal point Enters minus symbol or sign change key Changes positive numbers to negative and negative numbers to positive Pressingthis key switches to s...

Page 9: ...lace values between 0 000 and 0 999 Usingthis function enables the user to obtain unbiased samplingdata derived from random values generated by the calculator Example A PPLIC AT IO N S Building sample sets for statistics or research 0 a random number has been generated ...

Page 10: ...h appears on the display By usingthis function internal calculations will be performed using only the displayed value A PPLIC AT IO N S Frequently used in scientific and technical fields as well as business when performingchained calculations Example Rounded calculation MDF FIX mode TAB 1 normal calculation 5 0 0 6 0 6 5 4 5 9 9 5 9 9 Modify internally 0 5555 internally 0 6 internally 0 5555 ...

Page 11: ... can make addition and subtraction operations have precedence over multiplication and division by enclosingthem in parentheses The four basic operators Each is used in the same way as a standard calculator addition subtraction x multiplication and division Finds the result in the same way as a standard calculator ...

Page 12: ...ges Four methods of calculating percentages are presented as follows 1 125 increased by 10 137 5 2 125 reduced by 20 100 3 15 of 125 18 75 4 W hen 125 equals 5 of X X equals 2500 125 10 125 20 125 15 125 5 Percent DEG DEG DEG DEG ...

Page 13: ...h Root of y Example Calculates the inverse of the value on the display Squares the value on the display Calculates the square root of the value on the display The EL 506R 520R need to press 2ndF key first Calculates the xth root of y C alculates exponential values 2 4 4 16 DEG DEG DEG O peration Display 2 2 2 2 ...

Page 14: ...wer of x Common Logarithm Example Calculates the value of 10 raised to the xth power Calculates logarithm the exponent of the power to which 10 must be raised to equal the given value 3 1000 O peration Display DEG DEG ...

Page 15: ...Natural Logarithm Calculates powers based on the constant e 2 718281828 Example Computes the value natural logarithm the exponent of the power to which e must be raised to equal the given value 5 10 O peration Display DEG DEG ...

Page 16: ...sser positive integers from 1 to n 1 is indicated by n and called the factorial of n A PPLIC AT IO N S Used in statistics and mathematics In statistics this function is used in calculations involvingcombinations and permutations Example c f n 1 x 2 x 3 x xn 7 O peration Display DEG ...

Page 17: ...ible orderings in selecting r objects from a set of n objects For example there are six different ways of ordering the letters ABC in groups of three letters ABC ACB BAC BC A C AB and C BA The calculation equation is 3 P3 3 x 2 x 1 6 ways This function finds the number of ways of selecting r objects from a set of n objects For example from the three letters ABC there are three ways we can extract ...

Page 18: ...imal notation Also converts a decimal value to sexagesimal notataion degrees minutes seconds Inputs values in sexagesimal notation degrees minutes seconds Example A PPLIC AT IO N S Used in calculations of angles and angular velocity in physics and latitude and longitude in geography 24 28 35 DEG DEG O peration Display Repeat last key operation to return to the previous display DEG Convert to decim...

Page 19: ...5 7 Convert to an improper fraction Press once to return to the previous display Convert to decimal notation Press once to return to the previous display A PPLIC AT IO N S There is a wide variety of applications for this function because fractions are such a basic part of mathematics This function is useful for calculations involving electrical circuit resistance DEG DEG DEG O peration Display DEG...

Page 20: ...memories A D X Y M Recalls values stored inA D X Y M Adds the displayed value to the value in the independent memory M Memory Calculations Example Enter 0 for M 25 27 7 3 Temporary memories 0 DEG M DEG M DEG M DEG O peration Display ...

Page 21: ...20 Solve for x first and then solve for y using x Last Answer Memory Example y 4 x and x 2 3 O peration Display M DEG M DEG 2 3 4 Automatically recalls the last answer calculated by pressing ...

Page 22: ...onomical observations civil engi neeringand in calculations involvingelectrical circuits as well as in calcula tions for physics such as parabolic motion and wave motion Trigonometric functions determine the ratio of three sides of a right triangle Combination of three sides are sin cos and tan Their relations are C alculates the sine of an angle C alculates the cosine of an angle C alculates the ...

Page 23: ...tions DEG mode arc sine Determines an angle based on the ratio b a of two sides of a right triangle arc cosine Determines an angle based on the ratio c a for two sides of a right triangle arc tangent Determines an angle based on the ratio a b for two sides of a right triangle Example At what angle should an airplane climb in order to climb 80 meters in 100 meters 80 100 O peration Display θ sin 1 ...

Page 24: ...ometric functions A PPLIC AT IO N S Hyperbolic and arc hyperbolic functions are very useful in electrical engineering and physics Arc hyperbolic functions are defined by usingnatural logarithms in trigono metric functions For the EL 506R select sinh sin 1 cosh cosh 1 tanh tanh 1 from the MATH key ...

Page 25: ...ta input Displays r θ and x y Cx y or r θ Example Determine the polar coordinates r θ when the rectangu lar coordinates of Point P are x 7 y 3 DEG mode A PPLIC AT IO N S Coordinate conversion is often used in mathematics and engineering espe cially for impedance calculations in electronics and electrical engineering 7 3 7 6 23 2 O peration Display DEG DEG DEG DEG Operation example usingthe EL 531V...

Page 26: ...0 70 80 90 100 N o of pupils 2 4 5 7 12 10 8 2 Data table 1 1 Select single variable statistics mode The statistics function is excellent for analyzingqualities of an event Though primarily used for engineeringand mathematics the function is also applied to nearly all other fields includingeconomics and medicine Statistics Function DEG STAT correct data input Score Number of pupils Data total up t...

Page 27: ...9583 standard deviation of the population 50 total count of data 3450 total A PPLIC AT IO N S Single variable statistical calculations are used in a broad range of fields includingengineering business and economics They are most often applied to analysis in atmospheric observations and physics experiments as well as for quality control in factories N OT E 1 Sample data refers to data selected rand...

Page 28: ... quantities for data X and dataY based on the data table Example 2 6 2 13 Data table 2 2 Select dual variable statistics mode Year 1983 1984 1985 1986 1987 1988 1989 1990 Average temperature 6 2 7 0 6 8 8 7 7 9 6 5 6 1 8 2 Date blossoms bloom 13 9 11 5 7 12 15 7 x y DEG STAT DEG STAT Temperature Date Data total up to this point 6 1 15 8 2 7 DEG STAT DEG STAT ...

Page 29: ...lculates the sum of the product for sample data X and sample dataY Calculates the sum of the data sample dataY Calculates the sum of the data sample dataY raised to the second power Calculates the average value of the data sample dataY Calculates the standard deviation of a data population sample dataY Calculates the standard deviation for the data sample dataY In addition to the 1 variable statis...

Page 30: ... SHARP CORP MAR 05 ...

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