Central tendency

The normal distribution, a very common probability density, useful because of the central limit theorem.

Central or typical value for a probability distribution.

- Central tendency

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Statistical dispersion

Extent to which a distribution is stretched or squeezed.

Example of samples from two populations with the same mean but different dispersion. The blue population is much more dispersed than the red population.

Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions.

Average

Average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list .

Comparison of arithmetic mean, median and mode of two log-normal distributions with different skewness

The mode, the median, and the mid-range are often used in addition to the mean as estimates of central tendency in descriptive statistics.

Median

Value separating the higher half from the lower half of a data sample, a population, or a probability distribution.

Finding the median in sets of data with an odd and even number of values
Geometric visualization of the mode, median and mean of an arbitrary probability density function
Comparison of mean, median and mode of two log-normal distributions with different skewness

The median is 2 in this case, (as is the mode), and it might be seen as a better indication of the center than the arithmetic mean of 4, which is larger than all-but-one of the values.

Level of measurement

Classification that describes the nature of information within the values assigned to variables.

In single variable calculus, a function is typically graphed with the horizontal axis representing the independent variable and the vertical axis representing the dependent variable. In this function, y is the dependent variable and x is the independent variable.

The mode, i.e. the most common item, is allowed as the measure of central tendency for the nominal type.

Outlier

Outlier is a data point that differs significantly from other observations.

Figure 1. Box plot of data from the Michelson–Morley experiment displaying four outliers in the middle column, as well as one outlier in the first column.
Relative probabilities in a normal distribution

Estimators capable of coping with outliers are said to be robust: the median is a robust statistic of central tendency, while the mean is not.

Statistics

Discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The normal distribution, a very common probability density, useful because of the central limit theorem.
Scatter plots are used in descriptive statistics to show the observed relationships between different variables, here using the Iris flower data set.
Gerolamo Cardano, a pioneer on the mathematics of probability.
Karl Pearson, a founder of mathematical statistics.
A least squares fit: in red the points to be fitted, in blue the fitted line.
Confidence intervals: the red line is true value for the mean in this example, the blue lines are random confidence intervals for 100 realizations.
In this graph the black line is probability distribution for the test statistic, the critical region is the set of values to the right of the observed data point (observed value of the test statistic) and the p-value is represented by the green area.
The confounding variable problem: X and Y may be correlated, not because there is causal relationship between them, but because both depend on a third variable Z. Z is called a confounding factor.
gretl, an example of an open source statistical package

Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other.

Arithmetic mean

Sum of a collection of numbers divided by the count of numbers in the collection.

Comparison of two log-normal distributions with equal median, but different skewness, resulting in different means and modes

While the arithmetic mean is often used to report central tendencies, it is not a robust statistic, meaning that it is greatly influenced by outliers (values that are very much larger or smaller than most of the values).

Mid-range

The normal distribution, a very common probability density, useful because of the central limit theorem.

In statistics, the mid-range or mid-extreme is a measure of central tendency of a sample (statistics) defined as the arithmetic mean of the maximum and minimum values of the data set:

Frequency (statistics)

Event of times the observation occurred/recorded in an experiment or study.

The normal distribution, a very common probability density, useful because of the central limit theorem.

This assessment involves measures of central tendency or averages, such as the mean and median, and measures of variability or statistical dispersion, such as the standard deviation or variance.

Interquartile range

Measure of statistical dispersion, which is the spread of the data.

Boxplot (with an interquartile range) and a probability density function (pdf) of a Normal Population
Box-and-whisker plot with four mild outliers and one extreme outlier. In this chart, outliers are defined as mild above Q3 + 1.5 IQR and extreme above Q3 + 3 IQR.

The median is the corresponding measure of central tendency.