List of probability and statistics math functions. Many functions include links to more in-depth descriptions and examples.

__Statistics and regression functions are only available in templates. Probability functions are available in both the calculator and templates.__

Algebraic: ++fact(value)++

RPN: ++value [fact]++

Returns the factorial of 'value'.

** Details**

- 'value' must be greater than 0 and less than or equal to 170, and must be a whole number

- 'value' outside this range will return a "Parameter out of range" calculation error

- 'value' can either be a whole number or a table of whole numbers, where the same is returned

++fact(value)++

Returns the factorial of 'value'.

**Details**

- 'value' can either be a number or table where the same is returned

- 'value' must be greater than 0 and less than or equal to 170, and must be a whole number

- 'value' outside this range will return a "Parameter out of range" calculation error

- 'value' can either be a whole number or a table of whole numbers, where the same is returned

**Example**

[https://.../t/79d233ecb8b5acfb9549|Probabilities]

Algebraic: ++perm(n; r)++

RPN: ++n [ENT] r [perm]++

Returns the number of permutations of 'n' taken 'r' at a time. Permutations are used when several choices are made from the same set and the order they are chosen matters.

** Details**

- 'n' and 'r' must be whole numbers where 'n' is greater than or equal to 'r' and both are greater than 0

- 'n' or 'r' less than 0 or 'n' less than 'r' will return a "Parameter out of range" calculation error

- 'n' and 'r' can either be a table or a number where the same is returned

- If both 'n' and 'r' are tables then they both must be the same length or 'Invalid dimensions' is returned

++perm(n; r)++

Returns the number of permutations of 'n' taken 'r' at a time. Permutations are used when several choices are made from the same set and the order they are chosen matters.

**Details**

- 'n' and 'r' must be whole numbers where 'n' is greater than or equal to 'r' and both are greater than 0

- 'n' or 'r' less than 0 or 'n' less than 'r' will return a "Parameter out of range" calculation error

- 'n' and 'r' can either be a table or a number where the same is returned

- If both 'n' and 'r' are tables then they both must be the same length or 'Invalid dimensions' is returned

**Example**

[https://.../t/79d233ecb8b5acfb9549|Probabilities]

Algebraic: ++ comb(n; r)++

RPN: ++n [ENT] r [comb]++

Returns the number of combinations of 'n' taken 'r' at a time. Combinations are used when several choices are made from the same set and the order they are chosen does not matter.

** Details**

- 'n' and 'r' must be whole numbers where 'n' is greater than or equal to 'r' and both are greater than 0

- 'n' or 'r' less than 0 or 'n' less than 'r' will return a "Parameter out of range" calculation error

- 'n' and 'r' can either be a table or a number where the same is returned

- If both 'n' and 'r' are tables then they both must be the same length or 'Invalid dimensions' is returned

++ comb(n; r)++

Returns the number of combinations of 'n' taken 'r' at a time. Combinations are used when several choices are made from the same set and the order they are chosen does not matter.

**Details**

- 'n' and 'r' can either be a table or a number where the same is returned

**Example**

[https://.../t/79d233ecb8b5acfb9549|Probabilities]

Algebraic: ++rand()++

RPN: ++[rand]++

Returns a random real number between 0 and 1 inclusive.

++rand()++ : returns a random real number between 0 and 1 inclusive

++rand(length)++ : returns a table of 'length' count filled with random real numbers between 0 and 1 inclusive

++rand(lower; upper)++ : returns a random whole number between 'lower' and 'upper' inclusive

++rand(lower; upper; length)++ : returns a table of 'length' count filled with random whole numbers between 'lower' and 'upper' inclusive

Returns a random number or table.

**Details**

- 'lower', 'upper' and 'length' must be whole numbers or they will be truncated

- 'lower' greater than 'upper' will be reversed internally

- 'lower', 'upper' or 'length' less than or equal to 0 will return a 'Invalid array dimensions' calculator error

++count(table)++

Returns the number of rows in 'table' where the first column is the values and the second column is the number of occurrences for each row. If there is no second column (the table is a list) then count(table; 1) is returned.

++count(table; column)++

Returns the number of rows in 'column' of 'table'. No occurrences are considered. Returns the same result as length(table).

__This function is only available in templates.__

** Details**

- The first column is index 1

- 'column' less than 1 or greater than the number of columns will return a 'Invalid array dimensions' error

**Example**

[https://.../t/978bb40758d638ba7847|One-Variable Statistics]

[https://.../t/3f45c711c20b46b0c0be|Two-Variable Statistics]

++sum(table)++

Returns the sum of rows in 'table' where the first column is the values and the second column is the number of occurrences for each row. If there is no second column (the table is a list) then sum(table; 1) is returned.

++ sum(table; column)++

Returns the sum of rows in 'column' of 'table'. No occurrences are considered.

__This function is only available in templates.__

** Details**

- The first column is index 1

- 'column' less than 1 or greater than the number of columns will return a 'Invalid array dimensions' error

**Example**

[https://.../t/978bb40758d638ba7847|One-Variable Statistics]

[https://.../t/3f45c711c20b46b0c0be|Two-Variable Statistics]

++avg(table)++

Returns the average of rows in 'table' where the first column is the values and the second column is the number of occurrences for each row. If there is no second column (the table is a list) then avg(table; 1) is returned.

++ avg(table; column)++

Returns the average of rows in 'column' of 'table'. No occurrences are considered.

__This function is only available in templates.__

** Details**

- The first column is index 1

- 'column' less than 1 or greater than the number of columns will return a 'Invalid array dimensions' error

- mean(), average() and avg() return the same results

**Example**

[https://.../t/978bb40758d638ba7847|One-Variable Statistics]

[https://.../t/3f45c711c20b46b0c0be|Two-Variable Statistics]

++ min(table)++ : returns the minimum value in the first column of 'table'. This is the same as min(table; 1)

++ min(table; column)++ : returns the minimum value in 'column' of 'table'

++ min(valueA; valueB; ...)++ : returns the minimum value from a series of numbers. If valueA, valueB, etc. are equal length, single-column tables then this function returns the smallest value of each table row as a new table.

__This function is only available in templates.__

** Details**

- The first column is index 1

- minimum() and min() returns the same results

**Example**

[https://.../t/978bb40758d638ba7847|One-Variable Statistics]

++ max(table)++ : returns the maximum value in the first column of 'table'. This is the same as max(table; 1)

++ max(table; column)++ : returns the maximum value in 'column' of 'table'

++ max(valueA; valueB; ...)++ : returns the maximum value from a series of numbers. If valueA, valueB, etc. are equal length, single-column tables then this function returns the largest value of each table row as a new table.

__This function is only available in templates.__

** Details**

- The first column is index 1

- maximum() and max() returns the same results

**Example**

[https://.../t/978bb40758d638ba7847|One-Variable Statistics]

++ range(table)++

Returns the difference between the maximum and minimum value in the first column of 'table'. This is the same as range(table; 1).

++ range(table; column)++

Returns the difference between the maximum and minimum value in 'column' of 'table'.

__This function is only available in templates.__

** Details**

- The first column is index 1

**Example**

[https://.../t/978bb40758d638ba7847|One-Variable Statistics]

++product(list)++

Returns the product of values in 'list'. 'list' is a single column from a table, which can be extracted from a full table using the [https://.../t/help_functions_tables | column()] function. The product means all elements in the list are multiplied together.

__This function is only available in templates.__

++ median(table)++

Returns the median of rows in 'table' where the first column is the values and the second column is the number of occurrences for each row. If there is no second column (the table is a list) then median(table; 1) is returned.

++ median(table; column)++

Returns the median of rows in 'column' of 'table'. No occurrences are considered.

__This function is only available in templates.__

** Details**

- The first column is index 1

**Example**

[https://.../t/978bb40758d638ba7847|One-Variable Statistics]

++ quartile1(table)++

Returns the first quartile (median between min() and median()) of rows in 'table' where the first column is the values and the second column is the number of occurrences for each row. If there is no second column (the table is a list) then quartile1(table; 1) is returned.

++ quartile1(table; column)++

Returns the first quartile of rows in 'column' of 'table'. No occurrences are considered.

__This function is only available in templates.__

** Details**

- The first column is index 1

**Example**

[https://.../t/978bb40758d638ba7847|One-Variable Statistics]

++ quartile3(table)++

Returns the third quartile (median between median() and max()) of rows in 'table' where the first column is the values and the second column is the number of occurrences for each row. If there is no second column (the table is a list) then quartile3(table; 1) is returned.

++ quartile3(table; column)++

Returns the third quartile of rows in 'column' of 'table'. No occurrences are considered.

__This function is only available in templates.__

** Details**

- The first column is index 1

**Example**

[https://.../t/978bb40758d638ba7847|One-Variable Statistics]

++stddev(table)++

Returns the __sample__ standard deviation of rows in 'table' where the first column is the values and the second column is the number of occurrences for each row. If there is no second column (the table is a list) then stddev(table; 1) is returned.

++stddev(table; column)++

Returns the __sample__ standard deviation of rows in 'column' of 'table'. No occurrences are considered.

++stddevp(table)++

Returns the __population__ standard deviation of rows in 'table' where the first column is the values and the second column is the number of occurrences for each row. If there is no second column (the table is a list) then stddevp(table; 1) is returned.

++stddevp(table; column)++

Returns the __population__ standard deviation of rows in 'column' of 'table'. No occurrences are considered.

__This function is only available in templates.__

** Details**

- The first column is index 1

**Example**

[https://.../t/3f45c711c20b46b0c0be|Two-Variable Statistics]

++variance(table)++

Returns the __sample__ variance of rows in 'table' where the first column is the values and the second column is the number of occurrences for each row. If there is no second column (the table is a list) then variance(table; 1) is returned.

++variance(table; column)++

Returns the __sample__ variance of rows in 'column' of 'table'. No occurrences are considered.

++variancep(table)++

Returns the __population__ variance of rows in 'table' where the first column is the values and the second column is the number of occurrences for each row. If there is no second column (the table is a list) then variancep(table; 1) is returned.

++variancep(table; column)++

Returns the __population__ variance of rows in 'column' of 'table'. No occurrences are considered.

__This function is only available in templates.__

** Details**

- The first column is index 1

**Example**

[https://.../t/3f45c711c20b46b0c0be|Two-Variable Statistics]

++sum2(table)++

Returns the sum of all squared rows in 'table' where the first column is the values and the second column is the number of occurrences for each row. If there is no second column (the table is a list) then median(table; 1) is returned.

++sum2(table; column)++

Returns the sum of all squared rows in 'column' of 'table'. No occurrences are considered.

__This function is only available in templates.__

** Details**

- The first column is index 1

**Example**

[https://.../t/3f45c711c20b46b0c0be|Two-Variable Statistics]

++sumXY(table; x-column; y-column)++

Returns the sum of rows in 'x-column' of 'table' multiplied by its corresponding 'y-column' in 'table'.

__This function is only available in templates.__

** Details**

- The first column is index 1

**Example**

[https://.../t/3f45c711c20b46b0c0be|Two-Variable Statistics]

++regression(type; table; x-column; y-column)++

Returns a table of regression values where 'table' contains x and y data points, 'x-column' is the column number containing x data, 'y-column' is the column number containing y data, and 'type' is the regression method.

The table returned by the regression() function contains the following results: row 1 contains the coefficient of determination (r²), row 2 contains the correlation coefficient (r), row 3 contains the regression coefficient A, and row 4 contains the regression coefficient B. To extract individual results use the table function [https://.../t/help_functions_tables|item()].

__This function is only available in templates.__

** Details**

- The first column of 'table' is index 1

- 'type' should be 1 for linear regression, 2 for natural log regression, 3 for logarithmic regression, 4 for exponential regression, and 5 for power regression methods

- 'x-column' or 'y-column' less than 1 or greater than the number of columns will return a 'Invalid array dimensions' error

- 'type' less than 1 or greater than 5 will return a 'Parameter out of range' error

**Regression Equations**

The following formulas are used for regression calculations:

- Linear: y = A*x + B

- Natural Log: y = A + B * ln(x), for x > 0

- Logarithmic: y = A + B * log(x), for x > 0

- Exponential: y = A*Bᕽ

- Power: y = A*x^B

**Example**

[https://.../t/3f45c711c20b46b0c0be|Two-Variable Statistics]

++forecast(type; value; table; x-column; y-column)++

Returns the predicted value of the y data set where 'table' contains x and y data points, 'x-column' is the column number containing x data, 'y-column' is the column number containing y data, and 'type' is the regression method. To forecast, an x 'value' is used to predict a y value or vice-a-versa. This form of the function assumes an x-value predicts a y-value.

++forecast(type; value; table; x-column; y-column; forecastXColumn)++

Same as previous except can control whether an x-value is used to predict a y-value (set 'forecastXColumn' equal to 0) or whether a y-value is used to predict an x-value (set 'forecastXColumn' equal to 1).

__This function is only available in templates.__

** Details**

- The first column of 'table' is index 1

- 'type' should be 1 for linear regression, 2 for natural log regression, 3 for logarithmic regression, 4 for exponential regression, and 5 for power regression methods

- 'x-column' or 'y-column' less than 1 or greater than the number of columns will return a 'Invalid array dimensions' error

- 'type' less than 1 or greater than 5 will return a 'Parameter out of range' error

**Regression Equations**

The following formulas are used for forecast calculations:

- Linear: y = A*x + B

- Natural Log: y = A + B * ln(x), for x > 0

- Logarithmic: y = A + B * log(x), for x > 0

- Exponential: y = A*Bᕽ

- Power: y = A*x^B

**Example**

[https://.../t/3f45c711c20b46b0c0be|Two-Variable Statistics]

-------------

Stats

Probabilities

Probability

Factorial

fact()

Permutations

perm()

Combinations

comb()

Random

rand()

Statistics

Count

count()

Sum

sum()

Average

avg()

average()

Mean

mean()

Minimum

min()

minimum()

Maximum

max()

maximum()

Range

range()

Median

median()

First Quartile

Third Quartile

quartile1()

quartile3()

Standard Deviation

Sample Standard Deviation

Population Standard Deviation

stddev()

stddevp()

Variance

Sample Variance

Population Variance

variance()

variancep()

Sum Squared

sum2()

Sum XY

Sum X times Y

Sum X * Y

sumxy()

regression()

forecast()

Regression

Forecast

Product

product()