17.1.2.1 The Statistics on Rows Dialog Box

Specify the data range to be performed:

Data Range

The input data range. Support for multiple sheets as input (e.g. [Book1](1:2)!A[2]:B[8]).

For help with range controls, see: Specifying Your Input Data

Group

Multiple column label rows contains grouping information can be inserted into the Group box. Different grouping values indicate the data in the corresponding cells are from different groups. You can add, remove, order grouping rows via controlling buttons: Move Up button , Move Down button , Remove button , Select All button , Select button in toolbar .

\(\bar{x}=\frac 1n\sum_{i=1}^n x_i\).

where \(d=n-1 \,\)

Note: In OriginPro, \(d\) has another option, defined in the Variance Divisor of Moment branch.

\[\frac S{\sqrt{n}}\]

\[\bar{x}-t_{(1-\alpha/2)}\frac{s}{\sqrt{n}}\]

where \(t_{(1-\alpha/2)}\) is the \(1-\alpha/2\) critical value of the Student's t-statistic with n-1 degrees of freedom

\[\bar{x}+t_{(1-\alpha/2)}\frac{s}{\sqrt{n}}\]

where \(t_{(1-\alpha/2)}\) is the \(1-\alpha/2\) critical value of the Student's t-statistic with n-1 degrees of freedom

Skewness measures the degree of asymmetry of a distribution. It is defined as

\[\gamma_1=\frac n{(n-1)(n-2)}\sum_{i=1}^n (\frac{x_i-\bar{x}}s)^3 ,\mbox{for DF}\]

\[\gamma_1=\frac 1n\sum_{i=1}^n (\frac{x_i-\bar{x}}s)^3,\mbox{for N}\]

\[\gamma_1=\frac 1n\sum_{i=1}^n (\frac{x_i-\bar{x}}s)^3,\mbox{for WVR}\]

Kurtosis depicts the degree of peakedness of a distribution.

\[\gamma_2=\frac{n(n+1)}{(n-1)(n-2)(n-3)}\sum_{i=1}^n (\frac{x_i-\bar{x}}s)^4-\frac{3(n-1)^2}{(n-2)(n-3)},\mbox{for DF}\]

\[\gamma_2=\frac 1n\sum_{i=1}^n (\frac{x_i-\bar{x}}s)^4 -3,\mbox{for N}\]

\[\gamma_2=\frac 1n\sum_{i=1}^n (\frac{x_i-\bar{x}}s)^4 -3,\mbox{for WVR}\]

\[\sum_{i=1}^n x_i^2\]

\[\sum_{i=1}^n (x_i-\bar{x})^2\]

\[\frac s{\bar{x}}\]

\[\frac{\sum_{i=1}^n |x_i-\bar{x}|}n\]

Standard deviation times 2.

\[2s \,\]

Standard deviation times 3.

\[3s \,\]

\[\bar{x}_g=\left( \prod_{i=1}^n x_i\right) ^{\frac 1n}\]

The geometric standard deviation \(e^{std(\log x_i)}\) Where std is the unweighted sample standard deviation.

Note: Weights are ignored for the geometric standard deviation.

The mode is the element that appears most often in the data range. If multiple modes are found, the smallest will be chosen.

harmonic mean (sometimes called the subcontrary mean)

without weight: \(\frac n{\frac 1{x_1} + \frac 1{x_2} + ... + \frac 1{x_n}}=\left(\frac {\sum_{i=1}^n (x_i)^{-1}}n\right)^{-1}\)

with weight: \(\frac {\sum_{i=1}^n w_i}{\sum_{i=1}^n \frac {w_i}{x_i}}=\left(\frac {\sum_{i=1}^n w_i x_i^{-1}}{\sum_{i=1}^n w_i}\right)^{-1}\)

if any \(x_i\) or weight is negative, return missing; if any \(x_i\) or weight is 0, return 0.

The index number of Minimum in the original (input) dataset.

The index number of Maximum in the original (input) dataset.

\[Q_3-Q_1\,\]

Maximum - Minimum

Request computation of custom percentiles.

This option is only available when Custom Percentile(s) is checked. Percentiles are computed for all the values listed.

\[MAD = median(|{X_i} - median(X)|)\,\]

that is, starting with the residuals (deviations) from the data's median, the MAD is the median of their absolute values.

\[(MAD/norminv(0.75))/Median\,\]

\[d=n-1\,\!\]

\[d=n\,\!\]

\[y=\begin{cases} x_{(k)}, & \mbox{if }g\ne \frac{1}{2}\\ x_{(j)}, & \mbox{if }g=\frac{1}{2} \mbox{ and } j\mbox{ is even} \\ x_{(j+1)}, & \mbox{if }g=\frac{1}{2} \mbox{ and } j\mbox{ is odd} \end{cases}\]

where k is the integer part of \(np+\frac{1}{2}\)

\[y=(1-g)x_{(j)}+gx_{(j+1)}\,\!\]

where \(x_{(n+1)}\,\!\)is taken to be \(x_{(n)}\,\!\)

\[y=(1-g)x_{(j)}+gx_{(j+1)}\,\!\]

where \(x_{(0)}\) is taken to be\(x_{(1)}\)

\(m=\begin{cases} \frac{n}{2},& \mbox{if }n\mbox{ is even}\\ \frac{n+1}{2},& \mbox{if }n\mbox{ is odd} \end{cases}\) \(k=\begin{cases} \frac{m}{2},& \mbox{if }m\mbox{ is even}\\ \frac{m+1}{2},& \mbox{if }m\mbox{ is odd} \end{cases}\)

Then we have:

\(Minimum+x_{(1)}\,\!\) \(Q_1=\begin{cases} x_{(k)},& \mbox{if }m\mbox{ is odd}\\ \frac{1}{2}(x_{(k)}+x_{(k+1)}), & \mbox{if }m\mbox{ is even} \end{cases}\)

\[Q_2=\begin{cases} x_{(m)},& \mbox{if }n\mbox{ is odd}\\ \frac{1}{2}(x_{(m)}+x_{(m+1)}), & \mbox{if }m\mbox{ is even} \end{cases}\]

\[Q_3=\begin{cases} x_{(n-k-1)},& \mbox{if }n\mbox{ is odd}\\ \frac{1}{2}(x_{(n-k)}+x_{(mn-k+1)}), & \mbox{if }m\mbox{ is even} \end{cases}\]

\[Maximum=x_{(n)}\,\!\]

Note: if this method is selected, only quartiles will be computed. Custom percentiles are disabled.

Book

Specifies the destination workbook.

• <none>: Do not output report worksheet tables.

• <source>: The source data workbook.

• <new>: A new workbook.

• <existing>: A specified existing workbook

BookName

Enter the name of the workbook.

Sheet

The target worksheet.

SheetName

Name of the target worksheet.

Column

• <new> Output stats to appended columns.
• <next to source> Output stats to appended or inserted columns.

Results Log

Output the report to the Results Log

Script Window

Output the report to the Script Window

Notes Window

Specify the destination Notes window:

• <none>: Do not output to a Notes window.

• <new>: Output to a new Notes window. Specify a name for the Notes window.