Statistical Functions

Data Entry

DATA : Adds the current value(s) to the statistical memory.

[:] 'colon' : Separator between the value and its frequency, or in regression mode, between x and y inputs. If the separator [:] is omitted, in SD mode the frequency is assumed to be 1, and in regression modes y defaults to zero.

CLD : Clears all statistical memory, including the cash-flow list.

<-DATA : Deletes the last row in the statistical list memory.

S-SUM Functions

In Standard Deviation (SD) Mode

S:x : Sum of the values in SD statistical memory.

S:x² : Sum of the squares of the values in SD memory.

N : Number of values in the list. In SD mode, this may not be the same as the number of row elements in the list due to the fact that N takes account of frequency values.

In Regression Modes

S:x : Sum of the x-values, calculated for the respective mode of regression.

S:x² : Sum of the squares of the x-values, calculated for the respective mode of regression.

N : Number of values in the list. In regression modes, this will be the same as the number of row elements in the list.

S:y : Sum of the y-values, calculated for the respective mode of regression.

S:y² : Sum of the squares of the y-values, calculated for the respective mode of regression.

S:xy : Sum of the x-y products, calculated for the respective mode of regression.

S-VAR Functions

In Standard Deviation (SD) Mode

mean : Mean of the values in SD memory.

std(N) : Population standard deviation.

std(N-1) : Sample standard deviation.

stderr : Standard error.

In Regression Modes

x mean : Mean of the x-values, calculated for the respective mode of regression.

x std(N) : Population standard deviation for x-values, calculated for the respective mode of regression.

y mean : Mean of the y-values, calculated for the respective mode of regression.

y std(N) : Population standard deviation for y-values, calculated for the respective mode of regression.

x std(N-1) : Sample standard deviation for x-values, calculated for the respective mode of regression.

x stderr : Standard error for x-values, calculated for the respective mode of regression.

y std(N-1) : Sample standard deviation for y-values, calculated for the respective mode of regression.

covariance : Covariance between x and y values, calculated for the respective mode of regression.

Regression Calculation Functions

Note that these functions are not menu driven, but can be found directly on the keypad.

R-A : Calculates the coefficient A of the data in the regression memory, for the respective mode of regression. Returns syntax error if the calculator is not in a regression mode.

R-B : Calculates the coefficient B of the data in the regression memory, for the respective mode of regression. Returns syntax error if the calculator is not in a regression mode.

R-r : Calculates the correlation coefficient of the data in the regression memory, for the respective mode of regression. Returns syntax error if the calculator is not in a regression mode.

R-f(x) : Calculates y, as a function of x, based on regression coefficients calculated for the data in the regression memory and the respective mode of regression. Returns syntax error if the calculator is not in a regression mode.

R-f(y) : Calculates x, as a function of y, based on regression coefficients calculated for the data in the regression memory and the respective mode of regression. Returns syntax error if the calculator is not in a regression mode.

DISTR Functions

In Standard Deviation (SD) Mode

P(t), Q(t) and R(t) : Calculates Gaussian probability distributions for areas shown below.

Gaussian Probability Distributions

For example: {0.89} [DISTR] -> P(t) = 0.813267

The calculator employs a numerical integration technique to calculate the selected area under the Gaussian curve for an input value t. Input values of t outside the range -4.89 ~< t ~< +4.89 are considered to approximate to infinity with respect to the Gaussian curve.

Z(a) : Calculates the Z value given alpha. Note that this function is intentionally symmetric around 0.5, therefore, the following equalities apply:

Z(0.90) = Z(0.10) = 1.2816
Z(0.95) = Z(0.05) = 1.6449
Z(0.99) = Z(0.01) = 2.3264

The calculator employs a numerical integration technique to calculate the point Z on the Gaussian x-axis, determined such that the area shown by Q(t), above, is equal to the input value alpha. This function returns range error if the input value is outside the range, 0.0 < alpha < +1.0.

t(x) : Calculates the normalized variant t for the input value, using the data in the SD statistical memory. The result is calculated for the respective mode of regression.

conf(a) : Calculates the confidence interval for the data in the SD statistical memory and an input value alpha.

In Regression Modes

P(t), Q(t), R(t) and Z(a) : The same as in standard deviation (SD) mode, as these functions are independent to the content and type of data in the statistical memory.

t(x) : Calculates the normalized variant t for the input value, using the x-value data in the regression statistical memory. The result is calculated for the respective mode of regression.

confx(a) : Calculates the confidence interval for the x-value data in the regression statistical memory and an input value alpha. The result is calculated for the respective mode of regression.

t(y) : Calculates the normalized variant t for the input value, using the y-value data in the regression statistical memory. The result is calculated for the respective mode of regression.

confy(a) : Calculates the confidence interval for the y-value data in the regression statistical memory and an input value alpha. The result is calculated for the respective mode of regression.