# Tutorial:Descriptive Statistics

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## Contents |

## Summary

Origin provides comprehensive Descriptive Statistics support including basic statistics (mean, median, variance, etc.), frequency counts, and correlation coefficients of data you select. In addition to strong plotting features, Origin's statistical tools help you summarize and analyze your data.

This tutorial will show you how to:

- Use the
**Statistics on Column**Dialog to calculate descriptive statistics for grouped data. - Copy statistical results to a new worksheet for further processing.
- Unstack Columns to a graph.
- Analyze data sets with the
**Correlation Coefficient**Tool.

Minimum Origin Version Required: Origin 8.0 SR6

## Finding Frequency Information for Groups

Start with some data. We can use the **Discrete Frequency** Tool to quickly obtain frequency information for groups of data.

- Start with a new project or a new workbook. Import the data file
*\Samples\Statistics\automobile.dat*by using**Import Single ASCII** - Highlight the first two columns. Select
**Statistics: Descriptive Statistics: Discrete Frequency**to open a dialog. Column A and Column B are automatically picked as Input Data. Click**OK**

## Calculating Descriptive Statistics on Grouped Data

Using the **Statistics on Columns** tool, we can find basic statistics for each group of data.

- Switch back to the first sheet.
- Select
**Statistics: Descriptive Statistics: Statistics on Columns**to open the**Statistics on Columns**dialog. - Open the
**Range 1**branch and click the**interactive button**. The dialog will "roll up" and you can set**Data Range**as Column C ~ Column G by selecting C(Y) and dragging to G(Y) in the Worksheet. Click the button in the rolled up dialog to restore the dialog. To set**Group Range**to**B(Y): Make**, click the**triangle button**next to**Grouping Range**and select**B(Y) : Make**. - Here, we will show how to make a box plot for the grouped data and put all groups in a graph for a quick comparison. Do the following: 1) Expand the
**Output Settings**branch and the**Graph Arrangement**sub-branch. Select the**Arrange Plots of Same Type in One Graph**check box. 2) Expand the**Plots**branch, and select the**Box Charts**check box.

- Click the
**OK**button to get the results in a report sheet.

You can double-click to open the graph containing the box plot and customize the graph. Click the |

## Using Statistical Results for Further Operations

After using the **Statistics on Columns** dialog to produce a report tree, you may wish to do further analysis and plotting on the statistical results.

For example, to get average attribute values (i.e. horsepower, 0-60 mph time, weight, mileage) by vehicle Make from 1992 to 2004, perform the following:

- In the report sheet, right-click on the title of the Descriptive Statistics table and select
**Create Copy as New Sheet**from the short-cut menu.

- When the new sheet is active, select
**Worksheet: Unstack Columns**. - In the dialog that comes up, set columns D and E as
**Data to be Unstacked**. Since the**triangle button**fly-out menu supports only one selection, you need to use the**interactive button**. - Set
**column A**as**Group Variables**. - Select the
**Include Other Columns**check box and set**Other Columns**to column B. - Set
**Put Grouping Info. to**to**Long Name**. Click the**OK**button.

- In the result of
**Unstack Columns**, we get the mean and standard deviation of Power, 0~60 mph time, Weight, Gas Mileage and Engine Displacement for the 18 different car makes. - Highlight the whole result worksheet. Select
**Plot: Multi-Curve: Stack**from the main menu. - In the pop-up dialog, all columns in the worksheet are automatically set as
**Input**. Set**Plot Type**to**Scatter**and click the**OK**button.

In the above screenshot, the top X-Axis Tick Labels have been rotated 45 degrees for clarity. To do this, double-click on the tick labels to open the **X-Axis** dialog. Set the **Rotation** on the **Custom Tick Labels** tab.

## Analyzing the Relationship between different Indicators

We can use a correlation coefficient to explore the relationship between columns of our automobile data. In addition, we can plot a scatter matrix with a confidence ellipse to get a graphical representation of the correlation.

- Go to the original worksheet with the source data. Highlight the last five columns.
- Select
**Statistics: Descriptive Statistics: Correlation Coefficient**from the Origin menu to open the**Correlation Coefficient**tool. Note that**Pearson**is the default selection. This method is suitable for quantitative data. - Under the
**Plots**branch, select the**Add Confidence Ellipse**check box. The**Scatter Plot**check box should then be automatically selected. This means that the tool will create a scatter matrix with a confidence ellipse added to each scatter plot. Click**OK**.

Note the high positive correlation between **Engine Displacement** and **Power** and the high negative correlation between **Gas Mileage** and **Engine Displacement**.

Categories: Tutorials for 8.1 Booklet | P3 | DuPont Training | Tutorials for 8.5 Booklet | Descriptive Statistics (Tutorials) | Training Manual

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