Purpose
Return value
Syntax
=TANH(number)
- number - The input number.
Using the TANH function
The TANH function returns a number’s hyperbolic tangent. Given input -2, the function returns the number -0.96402758 as output.
=TANH(-2) // returns -0.96402758
Explanation
Just like the circular tangent, the hyperbolic tangent is defined in terms of the hyperbolic sine and hyperbolic cosine.
=SINH(a)/COSH(a) // definition of TANH(a)
Geometrically, the hyperbolic tangent of a number can be interpreted as the slope of the line from the origin to the point on the unit hyperbola corresponding to the number’s hyperbolic angle where the hyperbolic angle is half the area under the hyperbola between the origin and that point.
For example, given the input of -1 the function returns -0.761594156.
=TANH(-1) // returns the slope of -0.761594156
This value can be interpreted as the slope of the line from the origin to the point corresponding to the hyperbolic angle of -1.
Plot of TANH
The plot of the hyperbolic tangent is shown below and visualizes the range of possible output of the function.
Images courtesy of wumbo.net .
Purpose
Return value
Syntax
=AVEDEV(number1,[number2],...)
- number1 - First value or reference.
- number2 - [optional] Second value or reference.
Using the AVEDEV function
The Excel AVEDEV function calculates the average of absolute deviations from the mean in a given set of data.
Variance and standard deviation functions deal with negative deviations by squaring deviations before they are averaged. AVEDEV handles negative values by working only with absolute values. This average is called the average absolute deviation. It’s an easy way to show variability in a data set, but not as common as variance and standard deviation. One advantage of AVEDEV is that units remain unchanged. If values are centimeters, the absolute average deviation is in centimeters as well.
AVEDEV takes multiple arguments in the form number1 , number2 , number3 , etc. up to 255 total. Arguments can be a hardcoded constant, a cell reference, or a range . Empty cells, and cells that contain text or logical values are ignored.
Examples
In the example shown, the formula in G5 is:
=AVEDEV(B5:B10)
The formulas in C5 and D5 are, respectively:
=B5-$G$4 // deviation
=ABS(C5) // absolute deviation
The value in D12 (2) is simply the average of D5:D10, and agrees with the value returned by AVEDEV in G5.
Notes
- Arguments can be numbers, names, arrays, or references that contain numbers.
- Empty cells, and cells that contain text or logical values are ignored.
