To find the median of a data set, follow these steps:
- Order the data from smallest to largest.
- Identify the middle value(s):
- If the number of observations (data points) is odd , the median is the middle number in the ordered list.
- If the number of observations is even , the median is the average of the two middle numbers.
Detailed Explanation:
- For an odd number of data points, the median is the value at position n+12\frac{n+1}{2}2n+1, where nnn is the number of data points. For example, if there are 15 numbers, the median is the 8th number in the sorted list.
- For an even number of data points, the median is the average of the values at positions n2\frac{n}{2}2n and n2+1\frac{n}{2}+12n+1. For example, if there are 14 numbers, the median is the average of the 7th and 8th numbers in the sorted list.
Example 1 (Odd number of data points):
Data: 3, 13, 7, 5, 21
Sorted: 3, 5, 7, 13, 21
Median = middle value = 7
Example 2 (Even number of data points):
Data: 3, 13, 7, 5, 21, 23
Sorted: 3, 5, 7, 13, 21, 23
Middle values = 7 (3rd) and 13 (4th)
Median = (7 + 13) / 2 = 10 This method ensures the median divides the data
into two halves, where half the numbers are below the median and half are
above it
