Explanation:
To determine the value of \( x \) such that 35 is the median of the data set \( \{21, 7, 45, 33, 62, x\} \), follow these steps:

1. Arrange the Data Set in Ascending Order:

The data set has 6 numbers, so the median will be the average of the 3rd and 4th numbers when arranged in order.

We need to place \( x \) such that the median of the dataset is 35.

2. Determine the Position of \( x \) to Make the Median 35:

- If \( x \) is such that the 3rd and 4th numbers are \( 35 \), then \( x \) needs to be placed so that 35 is the median.

- Let’s test each option to see where \( x \) fits.

3. Testing Different Values of \( x \):

- Testing \( x = 33 \):

Arranging the data set \( \{7, 21, 33, 33, 45, 62\} \):
- The 3rd and 4th numbers are 33 and 33.
- Median = \(\frac{33 + 33}{2} = 33\), which is not 35.

- Testing \( x = 37 \):

Arranging the data set \( \{7, 21, 33, 37, 45, 62\} \):
- The 3rd and 4th numbers are 33 and 37.
- Median = \(\frac{33 + 37}{2} = \frac{70}{2} = 35\), which matches the given median.

Thus, the correct value for \( x \) is \( 37 \), which ensures that the median of the data set is 35.


The value of \( x \) is 37.

The correct answer is C. 37.