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Mode is a measure of central tendency useful for data at any level of measurement. Like the statistical mean and median, the mode is a way of expressing, in a single number, important information about a random variable or a population. Karl Pearson uses the term mode interchangeably with maximum-ordinate. In a footnote he says, "I have found it convenient to use the term mode for the abscissa corresponding to the ordinate of maximum frequency." Mode is the most frequently occurring number in a set of scores or values. In a series of numbers there is frequently more than one mode. Other measures of central tendency are the median and the mean.
The mode is one of several measures of central tendency that statisticians use to indicate the point, or points, on the scale of measures where the population is centered. It is the score in the population that occurs most frequently. The mode is not the frequency of the most numerous score. Mode is the value of that score itself.
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. - Zhang, C; Mapes, BE; Soden, BJ (2003). "Bimodality in tropical water vapour."
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. For
samples, if it is known that they are drawn from a symmetric unimodal
distribution, the sample mean can be used as an estimate of the population mode.
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 x1, x2, etc. The most extreme case occurs in uniform distributions, where all values occur equally frequently.
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.