Question

Given below are two statements, one is labelled as Assertion (A) and other one labelled as Reason (R).
Assertion (A) : A good measure of dispersion needs to be least affected by change in the sampling.
Reason (R) : Standard deviation is the best measure of dispersion.
In light of the above statements, choose the most appropriate answer from the options given below:

• A. Both (A) and (R) are not correct and (R) is not the correct explanation of (A).
• B. Both (A) and (R) are correct and (R) is the correct explanation of (A).
• C. (A) is correct but (R) is not correct.
• D. (A) is not correct but (R) is correct.

Hint:

To remember why Standard Deviation is the best measure of dispersion:
Unlike the Range (which only uses two extreme values) or Quartile Deviation (which only uses the middle 50% of data), Standard Deviation uses every single data point and has the highest sampling stability.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In descriptive statistics, dispersion measures how spread out or scattered a set of data is.
A good measure of dispersion must satisfy several criteria, such as being rigidly defined, based on all observations, easy to calculate, and least affected by sampling fluctuations (sampling stability).

Step 2: Detailed Explanation:
Let us evaluate the Assertion and the Reason:
- Assertion (A): "A good measure of dispersion needs to be least affected by change in the sampling."
This is a correct statement. Sampling stability is a prerequisite for any robust statistical measure.
If we draw different random samples from the same population, the values of our dispersion measure should remain relatively stable and not fluctuate wildly.
- Reason (R): "Standard deviation is the best measure of dispersion."
This is a correct statement. Standard deviation is widely considered the best and most reliable measure of dispersion because:
1. It is based on all observations.
2. It is rigidly defined.
3. It has high sampling stability (it is least affected by sampling fluctuations compared to range, quartile deviation, or mean deviation).
4. It is highly suitable for further mathematical and algebraic treatments.
Let us analyze the relationship:
Because standard deviation possesses high sampling stability (i.e. it is least affected by changes in sampling), it satisfies this crucial criterion of a good measure, making it the best overall measure of dispersion.
Therefore, both (A) and (R) are correct, and (R) is the correct explanation of (A).

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