Sharp EL-516, EL-W506, EL-W546 y = a + b ⋅ ln, Calculations Using Engineering PreÞxes, Modify Function, Simulation Calculation (ALGB), Solver Function, STATISTICAL CALCULATIONS, DRILL MODE

Calculations Using Engineering PreÞxes

Calculation can be executed in NORMAL mode (excluding N-base) using the following 9 types of preﬁ xes.

	Preﬁ x	Operation	Unit
k	(kilo)	N30	103
M	(Mega)	N31	106
G	(Giga)	N32	109
T	(Tera)	N33	1012
m	(milli)	N34	10–3
µ	(micro)	N35	10–6
n	(nano)	N36	10–9
p	(pico)	N37	10–12
f	(femto)	N38	10–15

Modify Function			18

Decimal calculation results are internally obtained in scientiﬁ c notation, with up to 14 digits in the mantissa. However, since calculation results are displayed in the form designated by the display notation and the number of decimal places indicated, the internal calculation result may differ from that shown in the display. By using the modify function (@n), the internal value is converted to match that of the display, so that the displayed value can be used without change in subsequent operations.

•When using the WriteView editor, if the calculation result is displayed using fractions or irrational numbers, press U to convert it to decimal form ﬁ rst.

•The modify function can be used in NORMAL, STAT, MATRIX, or LIST modes.

Simulation Calculation (ALGB)

If you have to ﬁnd values consecutively using the same expression, such as plotting a curve line for 2x2 + 1, or ﬁnding the variable values for 2x + 2y =14, once you enter the expression, all you have to do is to specify the value for the variable in the equation.

Usable variables: A–F, M, X and Y•Simulation calculations can only be executed in NORMAL mode.•Calculation ending instructions other than =cannot be used.Performing calculations1.Press b0.2.Input an expression with at least one variable.3.Press N1.

4.The variable entry screen will appear. Enter a value, then press eto conﬁ rm. The calculation result will be displayed after you have entered a value for each variable used in the equation.

•After completing the calculation, press N1to perform calculations using the same equation.

•Variables and numerical values stored in the memories will be displayed in the variable entry screen. If you do not want to change any values, simply press e.

•Performing simulation calculation will cause values in memory to be overwritten with new values.

Solver Function

The solver function ﬁ nds the value for x that reduces the entered expression to zero.

•This function uses Newton’s method to obtain an approximation. Depending on the function (e.g. periodic) or start value, an error may occur (ERROR 02) due to there being no convergence to the solution for the equation.

•The value obtained by this function may include a margin of error. If it is larger than acceptable, recalculate the solution after changing the “Start” and dx values.

•Change the “Start” value (e.g. to a negative value) or dx value (e.g. to a smaller value) if:

•no solution can be found (ERROR 02).•more than two solutions appear to be possible (e.g. a cubic equation).•to improve arithmetic precision.•The calculation result is automatically stored in the X memory.•Press jto exit the solver function.Performing solver function

1.Press b0.

2.Input an expression with an x variable.3.Press N2.4.Enter a “Start” value and press e. The default value is “0”.5.Enter a dx value (minute interval).6.Press e.

STATISTICAL CALCULATIONS

Statistical calculations can be performed in STAT mode.

There are eight sub-modes within STAT mode. Press b1, then press the number key that corresponds to your choice:

0(S#a# 0 [SD]): Single-variable statistics1(S#a# 1 [LINE]): Linear regression2(S#a# 2 [QUAD]): Quadratic regression3(S#a# 3 [E_EXP]): Euler exponential regression4(S#a# 4 [LOG]): Logarithmic regression5(S#a# 5 [POWER]): Power regression6(S#a# 6 [INV]): Inverse regression7(S#a# 7 [G_EXP]): General exponential regression

Statistical Calculations and Variables

The following statistics can be obtained for each statistical calculation (refer to the table below):

Single-variable statistical calculationStatistics of ① and the value of the normal probability function.Linear regression calculation

Statistics of ① and ②. In addition, the estimate of y for a given x (estimate y´) and the estimate of x for a given y (estimate x´).

Quadratic regression calculation

Statistics of ① and ②, and coefﬁcients a, b, c in the quadratic regression formula (y = a + bx + cx2). (For quadratic regression calculations, no correlation coefﬁcient (r) can be obtained.) When there are two x´ values, each value will be displayed with “1:” or “2:”, and stored separately in the X and Y memories.

Euler exponential regression, logarithmic regression, power regression, inverse regression, and general exponential regression calculations

Statistics of ① and ②. In addition, the estimate of y for a given x and the estimate of x for a given y. (Since the calculator converts each formula into a linear regression formula before actual calculation takes place, it obtains all statistics, except coefﬁcients a and b, from converted data rather than entered data.)

	–	Mean of samples (x data)
	x	Mean of samples (x data)
	sx	Sample standard deviation (x data)

①	σx	Population standard deviation (x data)

	n	Number of samples
	n	Number of samples

	Σx	Sum of samples (x data)

	Σx2	Sum of squares of samples (x data)
	–	Mean of samples (y data)
	y	Mean of samples (y data)
	sy	Sample standard deviation (y data)

	σy	Population standard deviation (y data)
	Σy	Sum of samples (y data)
②	Σy2	Sum of squares of samples (y data)
②	Σxy	Sum of products of samples (x, y)
	Σxy	Sum of products of samples (x, y)

	r	Correlation coefﬁ cient

	a	Coefﬁ cient of regression equation

	b	Coefﬁ cient of regression equation

	c	Coefﬁ cient of quadratic regression equation

•Use ;and tto perform a variable calculation in STAT mode.•Udoes not function in STAT mode.

Data Entry and Correction

Before entering new data, clear the memory contents (@Z).Data entrySingle-variable dataData _Data Hfrequency _(To enter multiples of the same data)Two-variable dataData x Hdata y _Data x Hdata y Hfrequency _(To enter multiples of the same data x and y)

Note: Up to 100 data items can be entered. With the single- variable data, a data item without frequency assignment is counted as one data item, while an item assigned with frequency is stored as a set of two data items. With the two-variable data, a set of data items without frequency assignment is counted as two data items, while a set of items assigned with frequency is stored as a set of three data items.

Data correctionCorrection before pressing _immediately after a data entry:Delete incorrect data with j, then enter the correct data.Correction after pressing _:Use uand dto display the previously entered data set.

Press dto display the data set in ascending (oldest ﬁrst) order. To reverse the display order to descending (latest ﬁrst), press the ukey. Press @uor @dto jump the cursor to the beginning or end of the data set.

Each data set is displayed with “X:”, “Y:”, or “F:”.

Data set number

Data x

Frequency

Data set number

Data x

Data y

Frequency

Display and move the cursor to the data item to be modiﬁ ed by using uand d, enter the correct value, then press _or e.

•To delete a data set, display and move the cursor to an item of the data set to delete by using uand d, then press @#. The data set will be deleted.

•To add a new data set, press jto exit the display of previously entered data and input the values, then press _.

Statistical Calculation Formulas		23

Type	Regression formula

Linear	y = a + bx
Quadratic	y = a + bx + cx2
Euler exponential	y = a ⋅ ebx
Logarithmic	y = a + b ⋅ ln x
Power	y = a ⋅ xb
	1
Inverse	⎯
Inverse	y = a + b x
General exponential	y = a ⋅ bx

An error will occur when:

•The absolute value of the intermediate result or calculation result is equal to or greater than 1 ⋅ 10100.

•The denominator is zero.

•An attempt is made to take the square root of a negative number.

•No solution exists in the quadratic regression calculation.

Normal Probability Calculations

In STAT mode, the three probability density functions can be accessed under the MATH menu, with a random number used as a normal distribution variable.

Notes:

•P(t), Q(t), and R(t) will always take positive values, even when t < 0, because these functions follow the same principle used when solving for an area.

•Values for P(t), Q(t), and R(t) are given to six decimal places.•The standardization conversion formula is as follows:x − xt = —σx

DRILL MODE

Math Drill: b20

Math operation questions with positive integers and 0 are displayed randomly. It is possible to select the number of questions and operator type.

Multiplication Table (⋅ Table): b21

Questions from each row of the multiplication table (1 to 12) are displayed serially or randomly.

To exit DRILL mode, press band select another mode.

Using Math Drill and ×Table

1.Press b20for Math Drill or b21for ⋅ Table.2.Math Drill: Use uand dto select the number ofquestions (25, 50, or 100).× Table: Use uand dto select a row in the multiplication table (1 to 12).

3.Math Drill: Use land rto select the operator type for questions (+, −, ⋅, ⎟, or + −⋅⎟).

× Table: Use land rto select the order type (“Serial” or “Random”).4.Press eto start.

When using Math Drill or ⋅ Table (random order only), questions are randomly selected and will not repeat except by chance.