NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.2Question 3
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.2
Question. 3
Is it true to say that the mean, mode and median of grouped data will always be different? Justify your answer.
Answer:
False
Detailed Answer with Explanation:
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.