ฯƒ Standard Deviation Calculator

Standard Deviation

What is Standard Deviation?

Standard deviation measures how spread out values are from the mean. A low standard deviation means data is clustered near the mean; a high value means data is widely spread.

Population ฯƒ = โˆš[ฮฃ(xแตข โˆ’ ฮผ)ยฒ / N]
Sample s = โˆš[ฮฃ(xแตข โˆ’ xฬ„)ยฒ / (Nโˆ’1)]

Steps to Calculate

  1. Find the mean (average) of the dataset.
  2. Subtract the mean from each value; square the result.
  3. Find the average of all squared differences (variance).
  4. Take the square root of the variance.

Frequently Asked Questions

What is the difference between population and sample standard deviation? โ–ผ
Population SD (ฯƒ) divides by N and is used when you have all the data. Sample SD (s) divides by Nโˆ’1 and is used when you have a sample from a larger population. Use sample SD in most real-world cases.
What does a high standard deviation mean? โ–ผ
A high standard deviation means the data values are spread out widely from the mean. A low standard deviation means the values are close to the mean.
What is the standard deviation of 2, 4, 4, 4, 5, 5, 7, 9? โ–ผ
The population standard deviation is 2.0. This is a classic textbook example used to illustrate normal distribution.