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# Simple Stats

vCalc.Simple Stats

The **SImple Statistics **calculator computes the most common statistics for a set of comma separated number values (**x**). The statistics include count, min, max, sum, sum of squares, mean, median, mid point, variance and standard deviation.

**INSTRUCTIONS:** Enter the following:

- (
**x**) This is the set of comma separated numeric values (e.g. 4,-1.2,8,9 ) - (
**S**) Choose a statistic from the list:

**STATISTICS:** The calculator returns the chosen descriptive statistics. Note, once the values of x are entered, you can choose any or all of the statistics and they will be displayed in turn without re-entering the values of x. This calculator is a prominent feature with other statistical functions in the College Level Statistics Calculator (Stat Calc).

#### Statistics Calculators

- sort a list of numeric values
- create a random subset of the a list of numeric values
- create a frequency distribution from your data
- compute the standard deviation of a sample's data set (σ)
- compute the standard deviation of a population's data set (SD)
- compute the z-score of a value in your data
- see an on-line elementary statistics tutorial using vCalc calculators
- examine the basics of probability used in elementary statistics
- get a random number from a range you specify

### Common Descriptive or Observational Statistics

The following statistics can be applied to the set of input values:

**count**- this is the number (n) of values in a set.**min**- this is the minimum observed value**max**- this is the maximum value in the set.**sum(Σx)**- this is the sum of the values in a set.**Σx²**- this is the sum of the squared values**(Σx)²**- this is the square of the summed 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.**range**- this is the difference between the max and the min.**rand**- this randomly returns one of the observations in the list**sort up**- this returns a comma separated list of the observations in ascending order.**sort down**- this returns a comma separated list of the observations in descending 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

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

Σx²`= sum(x^2)`

#### square of the sum

(Σx)² = `(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

**Simple Stats**, references 1 equation/constant.

**Equations and Constants **

**Simple Stats**, is used in 1 calculator.

**Calculators**

**Simple Stats**, is listed in 9 Collections.

- Elementary Statistics - Quantification Collection
- Elementary Statistics - Measures of Central Tendency Collection
- Elementary Statistics - A Simple View of Mathematics Collection
- Elementary Statistics Collection
- Elementary Statistics - Frequency Distributions Collection
- Elementary Statistics - Population Versus Sample Collection
- Elementary Statistics - Variability Collection
- Elementary Statistics - Probability Collection
- Elementary Statistics - A Sampling of Applied Probabilities Collection
- more...