Median Calculation for Given Data

To find the median of a dataset, follow these steps:

1. Arrange the data in ascending order.
2. Identify the middle value(s).
3. Calculate the median based on whether the number of data points is odd or even.

Step 1: Order the Data

First, arrange the given numbers in ascending order:

7, 19, 19, 20, 26, 34, 44, 81, 88, 90

Step 2: Identify Middle Values

Count the total number of data points. In this case, there are 10 data points (an even number).

For an even number of data points, the median is the average of the two middle numbers.

The two middle positions are the $ \frac{n}{2} $ position and the $ (\frac{n}{2} + 1) $ position.

Here, $ n = 10 $, so the positions are $ \frac{10}{2} = 5^{th} $ and $ (\frac{10}{2} + 1) = 6^{th} $.

The 5th number in the ordered list is 26.

The 6th number in the ordered list is 34.

Step 3: Calculate the Median

Calculate the average of the two middle numbers identified in Step 2.

Median $ = \frac{\text{Sum of the two middle numbers}}{2} $

Median $ = \frac{26 + 34}{2} $

Median $ = \frac{60}{2} $

Median $ = 30 $

The median of the given data is 30.