Mode

In statistics, the value in a data set which occurs with the greatest frequency. In a bimodal distribution, it may be more relevant to report two modes, rather than the mean or median which may lie between the peaks and be less likely to occur. The term is applied both to probability distributions and to collections of experimental data. Like the statistical mean and the median, the mode is a way of capturing important information about a random variable or a population in a single quantity. The mode is in general different from mean and median, and may be very different for strongly skewed distributions. The mode is not necessarily unique, since the same maximum frequency may be attained at different values. The worst case is given by so-called uniform distributions, in which all values are equally likely. The mode of a probability distribution is the value at which its probability density function attains its maximum value, so, informally speaking, the mode is at the peak. In symmetric unimodal distributions, such as the normal (or Gaussian) distribution (the distribution whose density function, when graphed, gives the famous "bell curve"), the mean, median and mode all coincide. For a sample from a continuous distribution, such as [0.935..., 1.211..., 2.430..., 3.668..., 3.874...], the concept is unusable in its raw form, since each value will occur precisely once. The usual practice is to discretize the data by assigning the values to equidistant intervals (mathematics), as in making a histogram, effectively replacing the values by the midpoints of the intervals they are assigned to. The mode is then the value where the histogram reaches its peak. For small or middle-sized samples the outcome of this procedure is sensitive to the choice of interval width if chosen too narrow or too wide; typically one should have a sizable fraction of the data concentrated in a relatively small number of intervals (5 to 10), while the fraction of the data falling outside these intervals is also sizable. It applies to distributions that resemble a normal distribution.