Understanding the Problem:

In a test for 20 marks, it is given that 50% of the students scored more than 15 marks and the remaining 50% scored less than 15 marks. We need to find out what 15 marks represent in this scenario.

Calculating the Mean:

To determine the value of 15 marks in this situation, we first need to find the mean score. Since 50% of the students scored more than 15 marks and the remaining 50% scored less than 15 marks, the mean score would be the score that divides the students into these two equal groups.

Finding the Mean:

Let's assume x as the mean score. If 50% of the students scored more than 15 marks, then the average score of this group would be x + 15. Similarly, the average score of the remaining 50% of students scoring less than 15 marks would be x.

Calculating the Mean:

Now, we can calculate the mean using the formula:
Mean = (50% * (x + 15) + 50% * x) / 100%

Solving for x:

By solving the above equation, we get:
Mean = (0.5 * x + 7.5 + 0.5 * x) / 100
Mean = (x + 7.5) / 100

Substituting the Mean:

Now, substituting the mean back into the equation, we get:
15 = (x + 7.5) / 100

Finding the Value of 15 Marks:

By solving the above equation, we find that 15 marks represent the mean score of the test, which is 7.5 marks.

Therefore, in this scenario, 15 marks represent the mean score of the test, which is 7.5 marks.

Median of the data