Descriptive Results

Count (n):
Mean:
Median (Q2):
Standard Deviation:
Skewness:
Kurtosis (Excess):
Minimum:
Maximum:
Range:

Note: Standard Deviation, Skewness, and Kurtosis are *sample* statistics.

95% Confidence Interval for the Mean

95% CI:
Margin of Error (± from Mean):
Standard Error:
t-critical (df=):

X-Axis Sketch (Mean & Significance Levels)

Box Plot

Box Plot Summary

Min (Whisker):
Q1 (First Quartile):
Median (Q2):
Q3 (Third Quartile):
Max (Whisker):
IQR (Interquartile Range):
Lower Fence (Outliers <):
Upper Fence (Outliers >):
Outliers:

Horizontal Stem-and-Leaf Plot

How to Use the Confidence Interval Calculator

This tool calculates the confidence interval for the population mean (mu) when you only have sample data and the population variance is unknown. This is the most common real-world scenario, and the calculation uses the Student's t-distribution.

Prepare Your Data

Gather your individual data points (measurements, scores, etc.) from your sample. The calculator needs at least 5 data points to provide reliable results.

Example Data: 10, 12, 8, 11, 15

Enter the Data

In the main input box, enter your numbers. You can separate the values using commas, spaces, or by placing each number on a new line.

Tip: If you use the example data shown on the screen, just press "Calculate" without changing anything.

Click "Calculate"

Press the blue "Calculate" button. The calculator will instantly process your data and display a full results panel below the input area.

Review the Results

The results are broken down into three main areas:

Descriptive Results: See the Sample Size, Mean, Standard Deviation, and Median of your input.
95% Confidence Interval: Find the final range (e.g., [10.25, 12.75]). This means you can be 95% confident the true population mean falls within this range.
Plots and Visualizations: Check the Box Plot and Stem-and-Leaf Plot to understand the distribution and spread of your data.

If you want to run a new analysis, click the "Clear Input" button to quickly reset the form.

Example: Confidence Interval for Reaction Time

A researcher measures the reaction time (in milliseconds) of 8 participants in a new cognitive test. The goal is to estimate the true average reaction time (Population Mean) for the entire population with 95% confidence.

1. Sample Data (n = 8)

210, 195, 205, 220, 190, 215, 200, 210

2. Calculator Results Summary

Descriptive Statistics

Sample Size (n): 8
Sample Mean (X-bar): 205.625 ms
Sample Standard Deviation (s): 9.873 ms

95% Confidence Interval Calculation

Degrees of Freedom (n - 1): 7
t-critical value: 2.365
Standard Error (s / √n): 3.491 ms
Margin of Error: ±8.25 ms

3. Conclusion

Confidence Interval (95% CI): [197.375, 213.875] ms

Interpretation: Based on this sample, we are 95% confident that the true mean reaction time for the entire population lies between 197.375 milliseconds and 213.875 milliseconds.