The median is a statistical measure that determines the middle value in a given set of numbers. To find the median, you must first arrange the numbers in ascending (or descending) order. Then, if the number of values in the set is odd, the median is the middle number. If the number of values is even, the median is the average of the two middle numbers.
Step-by-Step Process to Find the Median
- Arrange the numbers in ascending order.
- If the total number of values (N) is odd, the median is the value at position (N+1)/2.
- If N is even, the median is the average of the values at positions N/2 and (N/2) + 1.
Example 1: Odd Number of Values
Find the median of the set [7, 3, 1, 9, 5].
Arrange in order: [1, 3, 5, 7, 9]. There are 5 values, so the median is the middle one: 5.
Example 2: Even Number of Values
Find the median of the set [3, 7, 2, 5, 10, 6].
Arrange in order: [2, 3, 5, 6, 7, 10]. There are 6 values, so the median is the average of the 3rd and 4th numbers: (5 + 6) / 2 = 5.5.
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