Descriptive Statistics Calculator

About this Calculator

Calculator online for descriptive statistics. Descriptive statistics describe the main features of a data set in quantitative terms. This calculator will generate certain descriptive statistics for a sample data set with 4 or more values and up to 150 values. Enter values separated by commas such as 1, 2, 4, 7, 7, 10, 2, 4, 5.

If you need additional statistical values calculated send me a calculation request.

Below is a listing of the statistical values calculated and generally how they are determined with this calculator.

Descriptive Statistics Formulas and Calculations

Minimum

The smallest value in a sample data set.

Maximum

The largest value in a sample data set.

Range

The range from the minimum to the maximum;
range = max - min

Sum

The total of all data values.
(x1 + x2 + x3 + ... + xn)

Count (n)

The total number of data values in a data set.

Mean

The sum of all of the data divided by the count;
mean = sum / n.

Median

The numeric value separating the higher half of the ordered sample data from the lower half. If n is odd the median is the center value.  If n is even the median is the average of the 2 center values.

Mode

The value or values that occur most frequently in the data set.

Standard Deviation (s)

The square root of the variance;
²√variance or variance = s²

Variance

The sum of the squared differences between data values and the mean, divided by the count - 1;
[ (x1 - mean)² + (x2 - mean)² + (x3 - mean)² + ... + (xn - mean)² ] / [n - 1]

Midrange

The average of the minimum and maximum of the data set. (min + max)/2

Quartiles

The median is the second quartile Q₂. It divides the ordered data set into higher and lower halves.  The first quartile, Q₁, is the median of the lower half not including Q₂. The third quartile, Q₃, is the median of the higher half not including Q₂.  This is 1 of several methods for calculating the quartiles.^[1]

Interquartile Range

The range from Q₁ to Q₃ is the interquartile range (IQR).
[Q₃ - Q₁]

Sum of Squares

The sum of the squared differences between data values and the mean;
[ (x1 - mean)² + (x2 - mean)² + (x3 - mean)² + ... + (xn - mean)² ]

Mean Deviation (Mean Absolute Deviation)^[2]

The sum of the differences between data values and the mean, divided by the count;
[ (x1 - mean) + (x2 - mean) + (x3 - mean) + ... + (xn - mean) ] / n

Root Mean Square (RMS)

The square root of, the sum of the squared data values divided by n
²√[ (x1² + x2² + x3² + ... + xn²) / n ]

Standard Error of the Mean

The standard deviation divided by the square root of the count;
s / ²√n

Skewness^[3]

The sum of the cubed differences between data values and the mean, divided by the count minus 1 times the cubed standard deviation;
[ (x1 - mean)³ + (x2 - mean)³ + (x3 - mean)³ + ... + (xn - mean)³ ] / [ (n - 1) * s³ ]

Kurtosis^[3]

The sum of the fourth power of differences between data values and the mean, divided by the count minus 1 times the fourth power of the standard standard deviation;
[ (x1 - mean)⁴ + (x2 - mean)⁴ + (x3 - mean)⁴ + ... + (xn - mean)⁴ ] / [ (n - 1) * s⁴ ]

Coefficient of Variation

The standard deviation divided by the mean;
s / mean

Frequency

The number of occurrences for each data value in the data set.

References

[1] http://en.wikipedia.org/wiki/Quartile

[2] http://mathworld.wolfram.com/MeanDeviation.html

[3] http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm