1. What is Mean and Standard Deviation?

The mean (average) is a measure of central tendency that represents the sum of all values divided by the number of values. The standard deviation is a measure of dispersion that shows how much variation exists from the average.

2. How the Calculator Works

The calculator uses the following formulas:

Where:

• \( x \) — Individual data points
• \( \bar{x} \) — Mean of the data
• \( n \) — Number of data points
• \( \sum \) — Summation of values

3. Importance of These Statistics

Details: The mean provides a central value of the dataset, while standard deviation indicates how spread out the values are. Together they provide a quick summary of data distribution.

4. Using the Calculator

Tips: Enter numerical values separated by commas or spaces. The calculator will ignore non-numeric values. At least two data points are recommended for meaningful standard deviation.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between population and sample standard deviation?
A: Population SD divides by n (used here), while sample SD divides by n-1. Use sample SD when working with a subset of a larger population.

Q2: When is standard deviation most useful?
A: SD is most meaningful for normally distributed data. For skewed distributions, median and IQR might be better.

Q3: What does a high standard deviation indicate?
A: A high SD relative to the mean suggests data points are spread out over a wider range of values.

Q4: Can I calculate these for categorical data?
A: No, mean and SD are only meaningful for numerical (quantitative) data.

Q5: How many decimal places should I report?
A: Typically report one more decimal place than the original measurements.