Question 10

Explanation

Given the data: $55, a, 73, b$. The average of these numbers is $68$.

The difference between $b$ and $a$ is $22$.

We eliminate equations (1) and (2).

Add both equations:

Substitute $b = 83$ into equation (1):

Thus, the four numbers are $55, 61, 73, 83$. These are already ordered. The median is the middle value of the sorted data. For 4 data points, the median is the average of the 2nd and 3rd values.

So, the median of the four data points is $67$.