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Standard Deviation Calculator

Use our Standard Deviation calculator, a free online conversion tool to calculate and perform Standard Deviation of the numbers

Standard Deviation Formula

x is the set of the numbers

x̄ or mean is the average of the set of the numbers

n is the size of the set

SD or σ is the standard deviation

Standard Deviation

How Standard Deviation is Calculated

It is difficult to understand the standard deviation solely from the standard deviation formula. There are two general interpretations that can be useful in understanding the standard deviation.

1. The standard deviation may be thought of as the average difference between an observation and the mean, ignoring the sign.

2. The standard deviation may be thought of as the average difference between any two data values, ignoring the sign.

Application of Standard Deviation

  • The standard deviation enables us to determine with a great deal of accuracy, where the values of a frequency distribution are located in relation to the mean.
  • Summarizes the deviation of a large distribution from mean in one figure used as a unit of variation.
  • Indicates weather the variation is real or due to special reason
  • Helps in comparing two samples
  • Helps in finding the suitable sample size for valid conclusion