The following observations are arranged in ascending order. The median of the data is 25 find the value of x.17, x, 24, x + 7, 35, 36, 46

1. Break Down the Problem

We need to find the value of $x$ given that the median of the dataset is 25. The observations are arranged in ascending order: $17, x, 24, x + 7, 35, 36, 46$

2. Relevant Concepts

To find the median:

• For a dataset with an odd number of observations, the median is the middle value.
• For a dataset with an even number of observations, the median is the average of the two middle values.

Here, there are 7 observations. The median will then be the 4th element in the ordered list.

3. Analysis and Detail

Given that the median is 25, we can set up the following condition:

1. Since the arranged observations are: $17, x, 24, (x + 7), 35, 36, 46$ The 4th observation, which is $x + 7$, should equal 25.

Now we can set up the equation: $x + 7 = 25$

2. Now we solve for $x$: $x = 25 - 7 \\ x = 18$

4. Verify and Summarize

We should verify the order of the numbers with $x = 18$:

• The observations become: $17, 18, 24, 25, 35, 36, 46$.
• The fourth observation is indeed 25.

Final Answer

The value of $x$ is $\boxed{18}$.