Grouped Data Standard Deviation Calculator

Your details

How many class intervals your frequency table has (2 to 8).
Use "sample" when your frequency table represents a subset of a larger population (divides by n-1). Use "population" when it covers every member of the group (divides by n).
Standard Deviation
12.0655

Square root of the variance (same units as your data)

Mean68.25
Variance145.5769
Total observations (n)40
Mean68.25
Std Dev12.0655
Variance145.5769

Standard deviation: 12.0655

  • The sample mean is 68.25 and the standard deviation is 12.0655.
  • The coefficient of variation is 17.7%: moderate spread.
  • About 68% of observations fall roughly within one standard deviation of the mean (56.18 to 80.32), assuming an approximately normal distribution.
  • Total observations: 40. The n-1 (Bessel) correction was applied to estimate the population variance from this sample.

Next stepGrouped data calculations use class midpoints as approximations. For more precise results, use individual (ungrouped) data values when available.

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