Understanding the Median

The median is the middle value in a dataset that has been arranged in ascending or descending order. It is a measure of central tendency. The method for finding the median depends on whether the dataset has an odd or even number of data points.

Calculating the Median for an Even Dataset

When a dataset contains an even number of observations, the median is the average (arithmetic mean) of the two middle values. Here are the steps:

1. Arrange the data points in ascending order.
2. Identify the two middle data points.
3. Calculate the mean of these two middle data points. This mean is the median of the dataset.

Finding the Median of 5, 8, 25, 22, 34, 18

We are given the dataset: 5, 8, 25, 22, 34, 18.

First, let's arrange these numbers in ascending order:

5, 8, 18, 22, 25, 34

The dataset has 6 numbers, which is an even number of data points. The two middle numbers are the 3rd and 4th numbers in the sorted list.

The 3rd number is 18.

The 4th number is 22.

To find the median, we calculate the average of these two numbers:

Median $= \frac{\text{3rd number} + \text{4th number}}{2}$

Median $= \frac{18 + 22}{2}$

Median $= \frac{40}{2}$

Median $= 20$

Therefore, the median of the dataset 5, 8, 25, 22, 34, 18 is 20.