If the difference of mode and median of a data is 24, then the difference of median and mean is

• (a) 12
• (b) 24
• (c) 8
• (d) 36

To solve the problem, we need to understand the relationships between mode, median, and mean in a dataset. Given that the difference between the mode and median is 24, we can express this mathematically as:

Mathematical Relationships

Let:

• Mode = M
• Median = Med
• Mean = Mean

From the information provided:

M - Med = 24

This implies:

M = Med + 24

Finding the Difference Between Median and Mean

In many datasets, especially when they are skewed, the following relationship often holds:

Mean - Med = k, where k is a constant that can vary based on the skewness of the data.

Using the relationship between mode, median, and mean, we can derive:

Med - Mean = (M - Med) - k

Substituting the known difference:

Med - Mean = 24 - k

Evaluating the Options

Now, we need to evaluate the provided options:

• (a) 12
• (b) 24
• (c) 8
• (d) 36

To find the correct answer, we can assume a common scenario where the data is moderately skewed, leading to a typical value for k. If we assume k = 12, then:

Med - Mean = 24 - 12 = 12

Thus, the difference between the median and mean is:

12

Final Answer

The correct choice is (a) 12.