16.10 Average Multiple CurvesMathAveCurve
Overview
The Average Multiple Curves tool can average or concatenate input curves, and output the result as XY Range. If the Method is set to Concatenate, the input curves will be concatenated to create a new curve. If the Method is set to Average, the input curves will be averaged to create a new curve. Other additional outputs such as standard deviations, standard errors, and number of points can be also outputted when the Method is set to Average.
To Use Average Multiple Curves Tool
 Create a new worksheet with input data.
 Activate the worksheet.
 Select Analysis: Mathematics: Average Multiple Curves from the Origin menu to open the avecurves dialog box.
 Choose options and click OK. The XFunction avecurves is called to perform the computation.
Dialog Options
Recalculate

Controls recalculation of analysis results
For more information, see: Recalculating Analysis Results

Input

Specifies multiple curves to be averaged or concatenated.
For help with range controls, see: Specifying Your Input Data

Method

Specifies the average method.
 Average
 Average the input curves.
 Concatenate
 Concatenates the input curves.

Averaged X

Available only when Method = Average. Determines how X values will be computed for the averaged curve.
 Same as Source X
 For each unique X in all datasets, all Y datasets that have values at that X are averaged. X values within Tolerance for Common X Values limit (see below) will be treated as the same point and averaged.
 Common X Range
 Create a set of “Number of Points” of equally spaced X values from the largest minimum X to the smallest maximum X and calculate an average of all interpolated Y. Use the Interpolate list (see below) to control interpolation method.
 Full X Range
 Create a set of “Number of Points” of equally spaced X values from the smallest minimum X to the largest maximum X and calculate an average of all interpolated Y. Use the Interpolate list (see below) to control interpolation method.
 Custom
 Create a set of “Number of Points” of equally spaced X values where you define the minimum and maximum X and calculate an average of all interpolated Y. Use the Interpolate list (see below) to control interpolation method.
 Follow Curve Trace
 Create a set of “Number of Points” of trace interpolated X values and calculate an average of all interpolated Y. Use the Interpolate list to control interpolation method. This method is used with cyclic or periodic data.

Tolerance for Common X Values

Available only when Same as Source X is selected for Averaged X. Values of X within the tolerance, will be averaged.

Number of Points

It is available when Averaged X is not set to Same as Source X. It specifies the number of points of the interpolated curves. It computes a number automatically if the nearby Auto checkbox is enabled. You can also disable the Auto checkbox and specify the values by yourself.

X Minimun

Editable only when Custom is selected for Averaged X (readonly for Common X Range, Full X Range). Specifies the minimum X value of the averaged curve. Computes a number automatically if the Auto check box is selected. Alternately, clear the Auto check box and enter a value.

X Maximum

Editable only when Custom is selected for Averaged X (readonly for Common X Range, Full X Range). Specifies the maximum X value of the averaged curve. Computes a number automatically if the Auto check box is selected. Alternately, clear the Auto check box and enter a value.

Interpolate

Available only when Averaged X is not set to Same as Source X. Determines how to interpolate the X values before the averaging the input curves.
 Linear
 Perform linear interpolation on the X values.
 Spline
 Perform spline interpolation on the X values.
 BSpline
 Perform BSpline interpolation on the X values.

No Extrapolation

Available only when Averaged X is not set to Full X Range, Custom, and Follow Curve Trace. Determines whether to extrapolate the curves when the input curves have different X ranges.

Sort X

Available only when Method = Concatenate. Determines how to sort the X values of the averaged curve. Y values will be reordered accordingly.
 None
 Do not sort the X values.
 Ascending
 Sort the X values from smallest to largest.
 Descending
 Sort the X values from largest to smallest.

Additional Output

These options are only available when Method = Average.
 Std Dev
 Compute the standard deviation of the averaged curve.
 Std Err
 Compute the standard error of the averaged curve.
 N
 Compute the counts of input data points that correspond to each averaged X value.
 Minimum
 Output the minimum value.
 Maximum
 Output the maximum value.
 SD times 2
 Compute the standard deviation times 2.
 SD times 3
 Compute the standard deviation times 3.

Output

Determine where to output results.
For help with the range controls, see: Output Results

Algorithm
When the Method variable is set to Concatenate, all the input ranges are simply joined together and the data points from every input curve are concatenated one by one.
When the Method variable is set to Average, the X and Y values of the averaged curve are computed. This XFunction supports five methods to compute the X values of the averaged curve.
Same as Source X: The simplest way to compute X values is to specify a tolerance and then treat two X values, X1 and X2, as the same and averaging them if . The corresponding Y values will not be averaged. The resulting X are sorted in ascending order.
Common X Range, Full X Range and Custom: These three methods compute the X values of the averaged curve by performing linear, spline or Bspline interpolation on X range input. The first step is to determine what range of X values should be interpolated. Origin interpolates the input curves individually to establish a common set of X values. The corresponding Y values are then obtained by averaging Y values at each X.
Follow Curve Trace: This method uses trace interpolation to compute the XY values. This method is useful for interpolating periodic or cyclic data and can create a new curve whose shape is similar to that of the input curves.
