1. What is Standard Deviation?

Standard Deviation (SD) is a measure of how spread out numbers are from their mean value. It quantifies the amount of variation or dispersion in a set of data values.

2. How Does the Calculator Work?

The calculator uses the sample standard deviation formula:

Where:

• \( SD \) — Standard Deviation
• \( x_i \) — Individual data points
• \( \bar{x} \) — Mean of all data points
• \( n \) — Number of data points

Explanation: The formula calculates the square root of the average of the squared differences from the Mean.

3. Importance of Standard Deviation

Details: Standard deviation is widely used in statistics to measure variability. It helps determine how much variation exists from the average (mean) value.

4. Using the Calculator

Tips: Enter numerical values separated by commas (e.g., 5, 10, 15, 20). You need at least 2 values to calculate standard deviation.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between population and sample SD?
A: Population SD divides by N, sample SD divides by N-1 (Bessel's correction) for unbiased estimation.

Q2: What does a high standard deviation indicate?
A: High SD means data points are spread out over a wider range of values.

Q3: When is standard deviation most useful?
A: For normally distributed data, about 68% of values lie within ±1 SD from the mean.

Q4: What are the units of standard deviation?
A: SD has the same units as the original data points.

Q5: How does SD relate to variance?
A: Variance is the square of the standard deviation.