Standard Deviation Calculator

How to Use This Calculator

To use this calculator, you need to input the list of numbers for which you want to calculate the standard deviation. The calculator will then calculate the mean of these numbers and the standard deviation. For example, if you input the numbers 10, 12, 15, 18, and 20, the calculator will calculate the mean as 15 and the standard deviation as approximately 3.58.

The Formula Behind It

The formula for standard deviation is: standard deviation = sqrt(sum((x - mean)^2) / (n - 1)), where x is each number in the list, mean is the average of the numbers, and n is the total count of numbers.

The variable x represents each individual number, the mean is the average of all numbers, and n is the total count of numbers.

Practical Examples

• If you have the following stock prices for the last 5 days: 50, 55, 60, 58, and 62, the calculator will output a standard deviation of approximately 4.47.
• For the exam scores of 5 students: 80, 90, 70, 85, and 95, the calculator will output a standard deviation of approximately 7.75.
• If you have the daily sales of a shop for the last 5 days: 100, 120, 110, 130, and 105, the calculator will output a standard deviation of approximately 9.68.

Common Questions

What is standard deviation used for?

Standard deviation is used to measure the amount of variation or dispersion in a set of values. A low standard deviation means the values tend to be close to the mean, while a high standard deviation means the values are spread out.

Can standard deviation be negative?

No, standard deviation cannot be negative because it is calculated as the square root of the variance, and the square root of a number is always non-negative.

How does standard deviation relate to the mean?

The standard deviation is calculated based on the mean of the numbers, and it measures how much each number deviates from the mean.

What is the difference between population and sample standard deviation?

The main difference is that the population standard deviation is calculated using all the data points in the population, while the sample standard deviation is calculated using a subset of the data points.

Is a high standard deviation always bad?

Not always, a high standard deviation can be bad in some cases, such as in finance where it can indicate high risk, but in other cases, such as in sports, it can indicate a high level of performance variability.