Use this free online calculator to determine the standard deviation for grouped data. Input your class intervals and their corresponding frequencies to quickly understand the spread and variability within your frequency distribution. Ideal for students, statisticians, and researchers needing accurate statistical analysis for both sample and population data.
Formula:
The standard deviation for grouped data is a measure of how spread out the numbers are in a frequency distribution.
The formula depends on whether you are calculating for a sample or a population:
Sample Standard Deviation (s) = √[ Σ(f * (M - x̄)²) / (Σf - 1) ]
Population Standard Deviation (σ) = √[ Σ(f * (M - μ)²) / Σf ]
Where:
- s (or σ) = Standard Deviation
- f = Frequency of the class interval
- M = Midpoint of the class interval
- x̄ (or μ) = Mean of the grouped data
- Σf = Total number of data points (sum of all frequencies, also denoted as N)
The main difference lies in the denominator: (Σf - 1) for a sample (to correct for bias) and Σf for a population.