# average (mean)

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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 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