Constructing mean, median, and mode from ordered prices

One lookback, three constructions

Mean, median, and mode are three constructions of a single representative value for the same set of observations.

Editorial interpretation: TradersWeek treats the single number pulled from a lookback as a construction choice. The same ordered tape can be reduced to a full-sample mean, a mid-rank quantile, or a frequency mode.

Building the mean from every observation

An arithmetic mean is constructed by summing every observation in a lookback and dividing by the observation count.

For a nine-value series that sums to 483, the mean is 53.67. Substituting 97 for the final 57 raises the sum to 523 and the mean to 58.11, a result larger than every observation except that last value.

The mean uses the full sample, including outliers. One extreme observation displaces it more when the lookback is short than when it is long.

Building the median as a mid-rank quantile

A median is constructed by ordering the observations and taking the middle rank. With an even count the two central ranks are averaged.

After substituting 97 for 57 in the worked series, the ordered median remains 54, so the mid-rank quantile is unchanged by that outlier.

Quantile analysis reduces ordered price, volume, or breadth observations to an explicit rank-based baseline, such as a median, over a stated lookback.

Building the mode from a frequency distribution

A mode is the most frequent value and need not be unique. A frequency table with 52 counted three times and 55 counted three times has two modes.

A frequency distribution counts how often each value appears and is used to locate modes and activity clusters.

Point of control as a session mode

Market-profile session construction treats the price with the greatest activity as the point of control, which is the mode of that session's frequency distribution.

Editorial interpretation: TradersWeek reads that point of control as the session-level version of the same mode construction.

Medians already used as central lines

Some chart constructions already build their central line from medians rather than means, including point-and-figure column centers and Ichimoku cloud components.