average (mean)

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Equation / Last modified by KurtHeckman on 2019/02/18 16:43
`M = `
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vCalc.average (mean)
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The Average (Mean) calculator computes arithmetic mean (a.k.a simple average) for a set of comma separated number values (x). 

INSTRUCTIONS: Enter the following:

  • (x) This is the set of comma separated numeric values (e.g. 4,-1.2,8,9 )

MEAN: The  calculator returns the arithmetic mean for the entered values.

RELATED CALCULATORS:

  • To compute the observation statistics for a set including min, max, mean, mid-point, median, count, population and sample variance and standard deviation, CLICK HERE.
  • To sort a list of numeric values, CLICK HERE.
  • To create a random subset of the a list of numeric values, CLICK HERE.

Descriptive Statistics

The following statistics are available for the set of input values: 

  • count - this is the number (n) of observed values
  • min - this is the minimum observed value
  • max - this is the maximum observed value
  • sum - this is the sum of the observed values
  • mean - the is the mean (average) of the observed values
  • median - the middle ordered value
  • mid point - this is the mid point of the observation range.
  • rand - this randomly returns one of the observations in the list
  • sort - this returns a comma separated list of the observations in ascending order.
  • var-pop - this is the population variance of the values
  • sd-pop - this is the population standard deviation of the values
  • var-sample - this is the sample variance of the values
  • sd-sample - this is the sample standard deviation of the values
  • sum of squares - this is the sum of the squared values
  • square of the sum - this is the square of the summed values.

Thanks to Dr. Lee Hammerstrom, professor of math stats at Eastern Nazarene College, for his advice and testing.

The Math

The formulas for the statistics are as follows:

sum

     `S = sum(x)`

sum of squares

      `SoS = sum(x^2)`

averages

  • mean:     `mu = (sum(x))/n`  where n is the number of observations
  • median:  middle value if in an odd number of observations.  If there is an even number of observations, it's the average of the two middle values.
  • mid-point:  `mp = (min + max)/2`

variance

  • Population Variance: `sigma^2 = (sum_1^n(x_n-mu)^2)/n`
  • Sample Variance: `sigma^2 = (sum_1^n(x_n-mu)^2)/(n-1)`

standard deviation

  • Population Standard Deviation:   `sigma = sqrt((sum_1^n(x_n-mu)^2)/n)`
  • Sample Standard Deviation:   `sigma = sqrt((sum_1^n(x_n-mu)^2)/(n-1))`

Statistics in Culture

"There are three kinds of lies: lies, damn lies and statistics."   Mark Twain