Simple Stats

vCalc Reviewed
Equation / Last modified by Administrator on 2019/04/14 07:05
`Stat = `

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:
    • count, min, max, sum (Σx), (Σx²), (Σx)², mean, median, mid point, range
    • var-pop, sd-pop, var-sample, sd-sample
    • sort up, sort down, rand

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

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