Let's first define the terms 'mean' and 'median':
- **Mean** is the average of the numbers. It is found by adding up all the numbers and then dividing by the quantity of numbers.
- **Median** is the middle value in the list of numbers. If there is an even number of observations, the median will be the average of the two middle numbers.
According to your problem, we know that:
- The mean of four numbers (2, 5, a, b) is 9.
- The median of four numbers (2, 5, a, b) is 6.
1. To find the mean, add up all the numbers and divide by the quantity of numbers:
(2 + 5 + a + b ) / 4 = 9
7 + a + b = 36
a + b = 36 - 7
a + b = 29
2. Since the median is 6, and we have an even number of values (4), the median is the average of the two middle numbers. The numbers should be sorted in ascending order, so we know 2 and 5 are the first and second numbers. Thus, 'a' should be next and less than or equal to 'b'. As a result, 'a' and 'b' are the two middle numbers.
Therefore, (a + b) / 2 = 6
a + b = 12
From (1) and (2), we can see that 'a + b' cannot simultaneously be 29 and 12. It appears there might be a mistake in the information provided.
If the total is 29, with 'a' as 5 and 'b' as 24 or vice versa, then, the arrangements can be {2, 5, 5, 24}, with a median of (5+5)/2=5, not 6. If the total is 12, with 'a' as 3 and 'b' as 2, then, the arrangements could be {2, 2, 3, 5}, with a median of (2+3)/2=2.5, not 6. Please check the provided information again.
