Notes > Foundations of Computing > Types of Average
The mode is the most frequently occuring value in a set of data. The modal class in a grouped set of data is the group with the most occurences. If two adjacent groups have the same maximum amount of occurences the mode can be estimated using inspection. A set of data is bi-modal if it has two equally occuring maximum values or modes.
The median is the middle value in a set of ordered data. It therefore has an equal number of values above it and below it in the set of data. If there are two values sharing the middle location in a set of data, the mid-point between these two values is taken as the median.
The median is not always necessarily a value that occurs in the set of data and may not be a whole number. The median cannot describe the distribution or the set of data though i.e. whether the values are equally spread across the range or whether they are bunched at the ends of the range for example.
To calculate the median that occurs within a group or class in a grouped set of data, it is assumed that the values within classes are evenly spread. Interpolation used to work out an estimate as to where the median is likely to occur. Alternatively, a cumulative frequency graph can be drawn and the middle quartile (median) can be read off the vertical axis.
The arithmetic mean is the sum of all occuring values divided by the total number of values. The mean is given in terms of the units that the original data is in but it doesn't actually represent a value that has occured.
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