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This essential trains for: SAT-I, GMAT, AMC-8, AMC-10, Math Kangaroo 7-8, Math Kangaroo 9-10.

A data set is a set of values that are not required to be distinct.

Note: This may seem to be in contradiction with the 'well-defined' property of sets which requires them to contain distinct elements. In fact, there is no contradiction. Each value is the result of an experiment of some sort. The fact that two experiments may have yielded the same numeric value for some quantity does not make the experiments one and the same. Presumably, they differ somehow: they may differ in time, location, etc. For example, if we count the number of people that visit a website per hour, we may find that there were 41 visitors from 6 am to 7 am and 41 visitors from 10 am to 11 am. The data point has the same value but is part of two different experiments.

Definition: A data set is a set of related data. The data may be non-numerical (such as: lilliputian, glubbdubdribian, blefuscudian etc.), in which case it is called categorical or it may consist of numbers in which case it is called numerical. (categories from Jonathan Swift's "Gulliver's Travels")

Numerical data is generally ordered in increasing order as in:


Definition: The range of a data set is the difference between the largest value and the smallest value in the set.

In the set D the range is:


Intuitively, the range represents the size of the interval of values that you need in order to plot the values.

Definition: The mode is the value that occurs the most frequently in the set.

The mode of set D is 14.

A data set may be multimodal, i.e. it may have several modes. This one has plenty of modes:


Definition: The median of a data set is "the value in the middle." If there is an even number of values, then the median is the average of the two middle values.

The median of set D is:


Definition: The mean of a data set is the arithmetic mean (i.e. average) of all the values.

The mean of set D is: