Difference between revisions of "Median (statistics)"
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| + | A '''median''' is a common type of [[mean]] for a set of numbers. | ||
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== Definition == | == Definition == | ||
| − | The | + | The median of a [[finite]] [[set]] of [[real number]]s is the middle [[element]] of the set when the elements are written in order (i.e. least to greatest). When the number of elements is even, there are two middle elements and so the [[arithmetic mean]] of the two is taken to be the median. |
| − | For example, the median of the set <math>\{2, 3, 5, 7, 11, 13, 17\}</math> is 7. In order to find the median of the set {5, 3, 9, 7}, we would first write it in order {3, 5, 7, 9}. Then, to find the median, we take <math> | + | For example, the median of the set <math>\{2, 3, 5, 7, 11, 13, 17\}</math> is 7. In order to find the median of the set <math>\{5, 3, 9, 7\}</math>, we would first write it in order {3, 5, 7, 9}. Then, to find the median, we take <math>\frac{5+7}{2}=6</math>. |
The median is one of several different [[mean]]s for a set of numbers. It appears most frequently in the field of [[statistics]] and also occasionally on mathematical contests. | The median is one of several different [[mean]]s for a set of numbers. It appears most frequently in the field of [[statistics]] and also occasionally on mathematical contests. | ||
== Problems == | == Problems == | ||
| − | Find the median of {3, 4, 5, 15, 9}. | + | ===Pre-introductory=== |
| + | Find the median of <math>\{3, 4, 5, 15, 9\}</math>. | ||
| + | ===Introductory=== | ||
| + | ===Intermediate=== | ||
| + | ===Olympiad=== | ||
{{problems}} | {{problems}} | ||
Revision as of 21:22, 24 November 2007
A median is a common type of mean for a set of numbers.
Contents
Definition
The median of a finite set of real numbers is the middle element of the set when the elements are written in order (i.e. least to greatest). When the number of elements is even, there are two middle elements and so the arithmetic mean of the two is taken to be the median.
For example, the median of the set 
is 7. In order to find the median of the set 
, we would first write it in order {3, 5, 7, 9}. Then, to find the median, we take 
.
The median is one of several different means for a set of numbers. It appears most frequently in the field of statistics and also occasionally on mathematical contests.
Problems
Pre-introductory
Find the median of 
.
Introductory
Intermediate
Olympiad
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