Error bars & confidence intervals in Grapher

Uncertainty is a critical component of scientific and engineering data. In Grapher, error bars and bands transform static plots into precise communication tools by visualizing measurement reliability and statistical spread. Grapher can display error bars on line plots, scatter plots, line/scatter plots, horizontal bar charts, vertical bar charts, 3D ribbon plots, 3D wall plots, 3D horizontal bar charts, and 3D vertical bar charts.

Error bar types

Grapher automates the most common statistical workflows by providing built-in calculation methods for rapid data analysis. These presets allow you to apply uncertainty indicators without manual preprocessing. For complex datasets requiring unique parameters, the manual data variable option offers full control over custom error values. You can toggle between these methods in the Property Manager on the Error Bars tab.

• Read from Data Variable
  • Choose this option to display custom error bar values that have been pre-calculated and stored in your worksheet.
  • This is the only selection available when plotting both vertical and horizontal error bars simultaneously.
• Average Value Only
  • Displays the average Y value for each corresponding X value (for vertical error bars) or the average X value for each Y value (for horizontal error bars).
  • Useful when you want to show a representative or central tendency value along with your data points.
• Sample Standard Deviation
  • This option illustrates the sample standard deviation of the Y values for each X value (for vertical error bars) or the X values for each Y value (for horizontal error bars). It calculates the standard deviation from the subset of sampled data points.
  • Provides insight into the variability of data points around the mean, especially when dealing with a sample of data.
• Population Standard Deviation
  • Select when you want to show the population standard deviation of Y values for each X value with vertical error bars or X values for each Y value with horizontal error bars.
  • Useful for representing variability when you have data for the entire population, not just a sample.
• Standard Error of the Mean
  • Use when you want to display the standard error of the mean of Y values for each X value with vertical error bars or X values for each Y value with horizontal error bars.
  • Particularly valuable when you want to convey the precision of the mean as an estimate of the true population mean, especially with large datasets.

Visualizing Confidence Intervals

Grapher supports the visualization of Confidence Intervals (CIs) to help you communicate the stability and margin of error inherent in your results. By plotting these intervals, you can demonstrate the reliability of your findings based on sample size and variability, allowing for a more statistically rigorous presentation of your data.

Graph showing a 95% Confidence Interval for the data.

Source: National soil geochemistry data provided by the U.S. Geological Survey (USGS). 

Samples collected between 2007–2010 across the conterminous United States.

Customizing Error Bars and Bands

Grapher offers advanced styling options that allow you to extend standard whiskers into shaded "Error Bands" by connecting error data points. This visualization technique is highly effective for highlighting uncertainty trends across continuous data, such as time-series or distance-based measurements, providing a cleaner and more professional aesthetic for complex plots.

Vertical bar chart with positive and negative error bars.	Error Bands (Only show the fill between the error bars)

1. In the Object Manager, select your plot.
2. In the Property Manager, click the Error Bars tab.
3. Change the Direction field to Vertical, Horizontal, or Vertical and Horizontal.
4. Set the error bar properties in the General section. If you have selected Vertical and Horizontal, the properties being displayed in the General section are for the direction selected in the Properties to edit field.

Graph displaying custom error bars from worksheet

Source: National soil geochemistry data provided by the U.S. Geological Survey (USGS). 

Samples collected between 2007–2010 across the conterminous United States

1. Follow the step in the Connect and fill between your error bars section above.
2. In the the Property Manager, select the Error Bars tab.
3. In the Error Bars section, set the Cap width field to zero.
4. In the the Property Manager, select the Line tab.
5. In the Error Bar Line Properties section, in the Error Bars section, set the Style field to Invisible.
6. In the Error Bar Line Properties section, in the Vertical Error Bar Connection Line section, set the Style field to Invisible.
7. In the the Property Manager, select the Fill tab.
8. In the Plot Fill Properties section, in the Vertical Error Bar Connection Line section, set the Pattern field to Solid.
9. In the Plot Fill Properties section, in the Vertical Error Bar Connection Line section, set the Color field to Solid to your desired color.

Graph showing data points and Population Standard Deviation

Source: National soil geochemistry data provided by the U.S. Geological Survey (USGS). 

Samples collected between 2007–2010 across the conterminous United States

Error Bar & Confidence Interval resources and customization

The customizations showcased on this page are just a subset of what's possible with error bars. For comprehensive details on adjusting their appearance and settings, see the following topics in the Grapher Help:

• Error Bars 
  • Error Bar - Line Properties.
• Confidence Intervals
  • Confidence Intervals Property Manager tabs
    • Plot     |     Data Limits     |     Symbol     |     Line     |     Fill
       

Data References

• Smith, D.B., Cannon, W.F., Woodruff, L.G., Solano, F., Kilburn, J.E., and Fey, D.L., 2013, Geochemical and mineralogical data for soils of the conterminous United States: U.S. Geological Survey Data Series 801, 19 p., https://pubs.usgs.gov/ds/801/.