# Simple Stats

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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).

### 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