When we find lines of position to triangulate our position on a river chart, odds are the three lines will not meet at a single point, as logic dictates they should. Instead, the three lines typically intersect to create a triangle; it's generally accepted that the smaller the triangle, the more accurate your positioning.
So why does this occur? It arises from the presence of errors, be it human error or instrument error. Whenever we obtain a variation in readings where theoretically none should exist, we use statistical analysis to try to find the single truth within the cloud of results. We do this by averaging the various results, working off the assumption that they may well all be slightly inaccurate, but with the exception of a few seriously erroneous outliers, all of our data points are generally hovering around the correct answer.
But what do we mean by averaging? There are many different kinds of averages. For their presentation project, Dante and Erin had the crew find the lines of position for three different landmarks while the ship was stationary. As expected, a range slight variances were found these readings. To approximate the correct reading, they calculated three different methods of averaging their data: the mean, median, and mode.
The the sake of an example, assume that Dante and Erin collected five bearings off a daymarker located on the far side of the Kill Van Kull. Those five bearings read were as follows: 30˚, 28˚, 28˚, 26˚, and 24˚. Which is correct? Are any of them correct?
The mean is the most well-known type of average. To determine the mean, add up the total value of all the data points, then divide by the number of data points. Here, the mean average would be (30+28+28+26+24)/5, or 27.2 degrees.
The median is the "middle" data point. In this case, when all data points are arranged from high to low, the median average indicated that a bearing 28 degrees is probably the most accurate.
The mode is the most commonly found value in a data set. Of five data points, 28˚ is the only value to occur more than once. Thus, the mode also incidates toward a correct bearing of 28 degrees.