# 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

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### 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.

### Moment (mathematics)

**momentsmomentraw moment**

Moment (mathematics)

; the mode about

### 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**

### 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.