In statistics, a population is the totality of the elements of the universe in study (e.g. all the students from University of Cambridge in 1955)

A data sample is a set of data collected and/or selected from a statistical Population by a defined procedure

Set of values (data) obtained from the Population or Sample being studied   (x₁; x₂; x₃; x₄;.............; x_n)

The most popular and well known measure of central tendency, the mean () is equal to the sum of the observations divided by the number of observations.
The mean is strongly influenced by the extreme values of the observations.

Formula:   

Where:

• : Arithmetic mean
• n: Number of Observations

The median divides the previously ordered observations into two halves. When the number of observations is odd, the median is the central value of the ordered series of observations. When the number of observations is even, the median is equal to the mean of the two central values.
The median is not influenced by the extreme values of the observations.

The median of the series (15;25;30;40;50;65;70;85;90) equals 50

The median of the series (15;25;25;30;40;50;65;70;85;90) equals 45

The Mode is the value that appears most often in a set of data.

The Mode of the series (15;25;25;30;40;50;65;70;85;90) equals 25

The series (15;25;30;40;50;65;70;85;90) do not have a Mode

Note: a set of data can present more than one Mode. The WebCalc calculator shows, in these cases, the first Mode found.

The most popular and well known measures of dispersion, the standard deviation (S - also represented by the Greek letter sigma σ) is a measure that is used to quantify the amount of variation or dispersion of a set of data values. It is equal to the square root of the Variance

Variance is the arithmetic mean of the square distance of the observations values from the observations mean.

Formula used for a Sample:   

Formula used for a Population:   

Where:

• S²: Variance
• : Mean
• n: Number of Observations

The smallest observed value in a set of data

The largest observed value in a set of data

The Range of a set of data is the difference between the largest and smallest values

Formula:   

Where:

• S: Standard Deviation
• n: Number of Observations

Is defined as the ratio of the standard deviation (S) to the Mean ().
The CV is widely used in analytical chemistry to express the precision and repeatability of an assay. It is also commonly used in fields such as engineering or physics when doing quality assurance studies.

Formula:   

Where:

• S: Standard Deviation
• : Mean

Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive or negative, or even undefined.

Formula:   

Where:

• n: Number of Observations
• : Mean
• S: Standard Deviation

Kurtosis is a measure of the "tailedness" of the probability distribution of a real-valued random variable

Formula:

Where:

• K: Kurtosis
• n: Number of Observations
• : Mean
• S: Standard Deviation

Sum of the Observations.

Number of Observations.

Splits off the lowest 25% of data from the highest 75%.

Cuts data set in half. It is equal to the Median.

Splits off the highest 25% of data from the lowest 75%.