Mode (statistics)

modemodalmodesaveragemodal averagemodal valuemode valuemode(s)most commonmost common class
The mode of a set of data values is the value that appears most often.wikipedia
157 Related Articles

Median

averagesample medianmedian-unbiased estimator
Like the statistical mean and median, the mode is a way of expressing, in a (usually) single number, important information about a random variable or a population.
The median is 2 in this case, (as is the mode), and it might be seen as a better indication of central tendency (less susceptible to the exceptionally large value in data) than the arithmetic mean of 4.

Normal distribution

normally distributednormalGaussian
The numerical value of the mode is the same as that of the mean and median in a normal distribution, and it may be very different in highly skewed distributions. In symmetric unimodal distributions, such as the normal distribution, the mean (if defined), median and mode all coincide.
\mu is the mean or expectation of the distribution (and also its median and mode),

Mean

mean valuepopulation meanaverage
Like the statistical mean and median, the mode is a way of expressing, in a (usually) single number, important information about a random variable or a population.
In descriptive statistics, the mean may be confused with the median, mode or mid-range, as any of these may be called an "average" (more formally, a measure of central tendency).

Probability mass function

mass functionprobability massmass
It is the value x at which its probability mass function takes its maximum value.
The value of the random variable having the largest probability mass is called the mode.

Probability distribution

distributioncontinuous probability distributiondiscrete probability distribution
The mode is not necessarily unique to a given discrete distribution, since the probability mass function may take the same maximum value at several points x 1, x 2, etc. The most extreme case occurs in uniform distributions, where all values occur equally frequently. When the probability density function of a continuous distribution has multiple local maxima it is common to refer to all of the local maxima as modes of the distribution. A mode of a continuous probability distribution is often considered to be any value x at which its probability density function has a locally maximum value, so any peak is a mode.
Mode: for a discrete random variable, the value with highest probability (the location at which the probability mass function has its peak); for a continuous random variable, a location at which the probability density function has a local peak.

Symmetric probability distribution

symmetricsymmetric distributionSymmetry
In symmetric unimodal distributions, such as the normal distribution, the mean (if defined), median and mode all coincide.
If a symmetric distribution is unimodal, the mode coincides with the median and mean.

Level of measurement

quantitativescaleinterval scale
Unlike mean and median, the concept of mode also makes sense for "nominal data" (i.e., not consisting of numerical values in the case of mean, or even of ordered values in the case of median).
The mode, i.e. the most common item, is allowed as the measure of central tendency for the nominal type.

Arithmetic mean

meanaveragearithmetic
A most widely encountered probability distribution is called the normal distribution; it has the property that all measures of its central tendency, including not just the mean but also the aforementioned median and the mode (the three M's ), are equal to each other.

Multimodal distribution

bimodalbimodal distributionmultimodal
Such a continuous distribution is called multimodal (as opposed to unimodal).
In statistics, a bimodal distribution is a continuous probability distribution with two different modes.

Skewness

skewedskewskewed distribution
The numerical value of the mode is the same as that of the mean and median in a normal distribution, and it may be very different in highly skewed distributions.
If the distribution is both symmetric and unimodal, then the mean = median = mode.

Central tendency

Localitycentral locationcentral point
Central tendency
The most common measures of central tendency are the arithmetic mean, the median and the mode.

Unimodality

unimodalunimodal distributionunimodal function
Such a continuous distribution is called multimodal (as opposed to unimodal).
In mathematics, unimodality means possessing a unique mode.

Log-normal distribution

lognormallog-normallognormal distribution
A well-known class of distributions that can be arbitrarily skewed is given by the log-normal distribution.
The mode is the point of global maximum of the probability density function.

Descriptive statistics

descriptivedescriptive statisticstatistics
Descriptive statistics
Measures of central tendency include the mean, median and mode, while measures of variability include the standard deviation (or variance), the minimum and maximum values of the variables, kurtosis and skewness.

Summary statistics

summary statisticSummarizationdata summarization
Summary statistics
Common measures of location, or central tendency, are the arithmetic mean, median, mode, and interquartile mean.

Arg max

arg minargmaxargument of the maximum
Arg max
Mode (statistics)

Random variable

random variablesrandom variationrandom
Like the statistical mean and median, the mode is a way of expressing, in a (usually) single number, important information about a random variable or a population.

Statistical population

populationsubpopulationsubpopulations
Like the statistical mean and median, the mode is a way of expressing, in a (usually) single number, important information about a random variable or a population.

Discrete uniform distribution

uniform distributionuniformly distributeduniformly at random
The mode is not necessarily unique to a given discrete distribution, since the probability mass function may take the same maximum value at several points x 1, x 2, etc. The most extreme case occurs in uniform distributions, where all values occur equally frequently.

Maxima and minima

maximumminimumlocal maximum
When the probability density function of a continuous distribution has multiple local maxima it is common to refer to all of the local maxima as modes of the distribution.

Probability density function

probability densitydensity functiondensity
A mode of a continuous probability distribution is often considered to be any value x at which its probability density function has a locally maximum value, so any peak is a mode.

Interval (mathematics)

intervalopen intervalclosed interval
In order to estimate the mode of the underlying distribution, the usual practice is to discretize the data by assigning frequency values to intervals of equal distance, as for making a histogram, effectively replacing the values by the midpoints of the

Histogram

histogramsbin sizebin
In order to estimate the mode of the underlying distribution, the usual practice is to discretize the data by assigning frequency values to intervals of equal distance, as for making a histogram, effectively replacing the values by the midpoints of the

Kernel density estimation

kernelkernel densitykernel density estimate
An alternate approach is kernel density estimation, which essentially blurs point samples to produce a continuous estimate of the probability density function which can provide an estimate of the mode.