Sample Statistics

The Sample Statistics calculator computes the most common statistics for a sample of observations, not the entire population.  

INSTRUCTIONS: Enter the following:

• (x) Sample of comma separated numeric values (e.g. 4,-1.2,8,9 )

STATISTICS: The  calculator returns the following descriptive sample statistics.  

• (μ) mean - also known as the numeric average
• (σ) sample standard deviation
• (σ²) sample variance
• (n) count - this is the number (n) of values in a set.
• (m) min - this is the minimum observed value
• (M) max - this is the maximum value in the set.
• (R) range - this is the difference between the max and the min.
• (Σx) sum  - this is the sum of the values in a set.
• (Σx²) sum of squares - this is the sum of the squared values
• (Σx)² sum squared - this is the square of the summed values.
• median - the middle ordered value
• mid point - this is the mid point of the observation range.
• sorted - these are the observations sorted in ascending order

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

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 Calculators

• Stats Calc - Complete set of entry level college statistics functions
• Simple Stats - Complete set of Observational statistics (sample and population) for a set of data 
• Linear Regression - Least-squares trend line for a set of data
• One Way ANOVA - One way Analysis of Variance for three sets of data