Given:
Arithmetic mean = 24
Mode = 12

To find:
Median of the data

Solution:
The median is the middle value of a dataset when it is arranged in ascending or descending order.

Since the mode is 12, it means that 12 appears most frequently in the dataset. However, it does not provide any information about the other values in the dataset.

To determine the median, we need to consider the arithmetic mean. The arithmetic mean is the sum of all the values in the dataset divided by the number of values. In this case, the mean is 24.

We can assume that the dataset has an odd number of values, as the median is a single value. If the dataset had an even number of values, the median would be the average of the two middle values.

Assuming the dataset has 2n+1 values:
Let the dataset be: x1, x2, x3, ..., xn, 12, ..., xn, xn+1

The sum of all the values in the dataset is: x1 + x2 + x3 + ... + xn + 12 + ... + xn + xn+1

The sum of the dataset can be expressed as:
2n * 24 + 12

Since the mean is 24, we have the equation:
(2n * 24 + 12) / (2n + 1) = 24

Simplifying the equation, we get:
48n + 12 = 48n + 24
12 = 24

This equation is not possible, which means our assumption that the dataset has 2n+1 values is incorrect.

Assuming the dataset has 2n values:
Let the dataset be: x1, x2, x3, ..., xn, 12, ..., xn, xn+1

The sum of all the values in the dataset is: x1 + x2 + x3 + ... + xn + 12 + ... + xn

The sum of the dataset can be expressed as:
2n * 24 + 12

Since the mean is 24, we have the equation:
(2n * 24 + 12) / (2n) = 24

Simplifying the equation, we get:
48n + 12 = 48n
12 = 0

This equation is also not possible, which means our assumption that the dataset has 2n values is incorrect.

Assuming the dataset has 2n-1 values:
Let the dataset be: x1, x2, x3, ..., xn, 12, ..., xn-1

The sum of all the values in the dataset is: x1 + x2 + x3 + ... + xn + 12 + ... + xn-1

The sum of the dataset can be expressed as:
(2n-1) * 24 + 12

Since the mean is 24, we have the equation:
((2n-1) * 24 + 12) / (2n-1) = 24

Simplifying the equation, we get:
48n - 12 = 48n
-12 = 0

Again, this equation is not possible, which means our assumption that the dataset has 2