Standard Deviation Calculator
A comprehensive statistics calculator that finds the standard deviation, variance, mean, median, and mode for a set of numbers. Supports both sample and population data sets for accurate statistical analysis. Simply enter your data to get a full statistical summary.
Inputs
Enter the required values to calculate.
Result
The calculated result will appear here.
More Information
Understanding the Standard Deviation Calculator
Standard deviation is a crucial concept in statistics that measures the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the values tend to be close to the mean (or expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Sample vs. Population
It is critical to choose the correct data type for an accurate calculation:
- Population: Choose this if your data set includes every single member of the group you are studying (e.g., the test scores of every student in a single classroom). The formula divides the sum of squared differences by n.
- Sample: Choose this if your data is a smaller subset of a larger group (e.g., the test scores of 50 students chosen to represent an entire school district). The formula divides by n-1. This is known as Bessel's correction and provides a more accurate estimate of the population's standard deviation.
Other Statistical Measures Calculated
- Mean: The average of all the numbers in the data set.
- Median: The middle value of the data set when it is sorted in order.
- Mode: The number that appears most frequently in the data set.
- Variance: This is the average of the squared differences from the Mean. Standard deviation is simply the square root of the variance, which returns the measure to the original units of the data, making it more intuitive to interpret.
- Range: The difference between the highest and lowest values in the set.
- Quartiles & IQR: Quartiles divide your data into four equal parts. The Interquartile Range (IQR) is the range between the first quartile (Q1) and the third quartile (Q3) and represents the middle 50% of your data.