- vCalc Catalog Home
- average (mean)

# average (mean)

vCalc Reviewed

Equation / Last modified by KurtHeckman on 2019/02/18 16:43
`M = `

Tags:

Rating

Copied from

ID

vCalc.average (mean)

UUID

2342fb9f-f209-11e6-9770-bc764e2038f2

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,
**.** - 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