Median Math Example 4

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Example 4

medium
The ordered data set {2,5,8,x,14,18}\{2, 5, 8, x, 14, 18\} has median 10.510.5. Find xx.

Solution

  1. 1
    There are 66 values, so the median is the average of the 3rd3^{\text{rd}} and 4th4^{\text{th}} values.
  2. 2
    Set up the equation: 8+x2=10.5\frac{8 + x}{2} = 10.5.
  3. 3
    Multiply by 22: 8+x=218 + x = 21, so x=13x = 13.

Answer

x=13x = 13
For an even-sized ordered data set, the median depends only on the two middle positions. Once those are identified, the problem becomes a simple algebra equation.

About Median

The median is the middle value of an ordered data set โ€” half of the values are above it and half are below it.

Learn more about Median โ†’

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