NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.2

Question 3

Step 1: First, recall what each term means:

• Mean: It is the average of the data values.
• Median: It is the middle value of the data when arranged in order.
• Mode: It is the value that occurs most frequently.

Step 2: The statement says that mean, median, and mode of grouped data will always be different.

Step 3: But this is not true. For some types of data, especially when the data is symmetric (evenly spread on both sides), all three can be equal.

Example: In a perfectly symmetric distribution like the marks of students forming a bell-shaped curve, we get:

Mean = Median = Mode

Step 4: Therefore, they are not always different. They can sometimes be the same.

Final Conclusion: The statement is False.