Question

For a symmetrical distribution:

• A. \(\text{Mean}>\text{Median}>\text{Mode}\)
• B. \(\text{Mean}<\text{Median}<\text{Mode}\)
• C. \(\text{Mean}=\text{Median}=\text{Mode}\)
• D. None of these

Hint:

For distributions: \[ \text{Symmetric} \Rightarrow \text{Mean}=\text{Median}=\text{Mode} \] \[ \text{Positively Skewed} \Rightarrow \text{Mean}>\text{Median}>\text{Mode} \] \[ \text{Negatively Skewed} \Rightarrow \text{Mean}<\text{Median}<\text{Mode} \]

Answer 1

The Correct Option is C

Concept: A symmetrical distribution is perfectly balanced about its center. Examples include the ideal normal distribution where the left and right halves are mirror images of each other.

Step 1: Understand the position of the mean. The arithmetic mean lies at the balancing point of the distribution.

Step 2: Understand the position of the median. The median divides the distribution into two equal halves. In a symmetrical distribution, this point coincides with the center.

Step 3: Understand the position of the mode. The mode is the value with maximum frequency. For a symmetrical distribution, the peak occurs exactly at the center.

Step 4: Compare all three measures. Since all three occupy the same central position, \[ \text{Mean} = \text{Median} = \text{Mode}. \] Hence Option (C) is correct. Conclusion: \[ \boxed{\text{Mean}=\text{Median}=\text{Mode}} \] Therefore, the correct answer is Option (C).