Question

Which of the following is true in respect of ‘Median’?
A. It is based on all observations
B. It is the best measure of central tendency
C. It is NOT at all affected by extreme values
D. It is rigidly defined
E. It coincides with the second quartile
Choose the correct answer from the options given below:

• A. A, B and C only
• B. B, C and D only
• C. C, D and E only
• D. A, D and E only

Hint:

To remember the characteristics of median: think of it as a spatial or physical midpoint. Outliers on the extreme edges do not pull the midpoint, making it highly robust compared to the mean.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In statistics, the median is a positional average that divides an ordered dataset into two equal halves.
It is a crucial measure of central tendency, especially useful when analyzing skewed distributions or datasets containing outliers.

Step 2: Detailed Explanation:
Let us analyze each statement individually:
- Statement A (It is based on all observations): This is incorrect.
Unlike the arithmetic mean, the calculation of the median only depends on the position of the middle term (or terms) and does not utilize the actual values of all other observations in the dataset.
- Statement B (It is the best measure of central tendency): This is incorrect.
There is no single "best" measure of central tendency.
While the median is superior for highly skewed data, the arithmetic mean is generally preferred for symmetric distributions and mathematical treatments because of its algebraic properties.
- Statement C (It is NOT at all affected by extreme values): This is correct.
Since the median is a positional value, changing the extreme values (outliers) on either end of the ordered list does not shift the middle position or alter the median value.
- Statement D (It is rigidly defined): This is correct.
The mathematical definition of the median is unique and unambiguous, ensuring that different observers obtain the same value for a given dataset.
- Statement E (It coincides with the second quartile): This is correct.
By definition, the second quartile (\(Q_2\)) marks the \(50^{\text{th}}\) percentile of the dataset, which is precisely identical to the median.
Thus, statements C, D, and E are correct.

Step 3: Final Answer:
The correct option is (C).