Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Mean deviation is about 80% of Standard Deviation.
Reason R: The quartile deviation is about 2/3 of the Standard Deviation.
In the light of the above statements, choose the correct answer from the options given below:

Correct option is B

• Assertion A: "Mean deviation is about 80% of Standard Deviation."

  • This statement is true. In most datasets, the mean deviation is approximately 80% of the standard deviation. This relationship holds because mean deviation (the average of absolute deviations from the mean) tends to be smaller than the standard deviation (which is the square root of the variance). In typical distributions, mean deviation is approximately 0.8 times the standard deviation.

• Reason R: "The quartile deviation is about 2/3 of the Standard Deviation."

  • This statement is also true. The quartile deviation (also known as the semi-interquartile range) is half the difference between the first and third quartiles (Q3 - Q1). It is approximately 2/3 of the standard deviation for a normal distribution, though this can vary slightly depending on the distribution's shape. This is an empirical rule.

However, Reason R does not explain Assertion A, because the relationship between mean deviation and standard deviation is not directly related to the relationship between quartile deviation and standard deviation. Therefore, although both statements are true, Reason R is not the correct explanation of Assertion A.

Information Booster:

1. Mean Deviation and Standard Deviation:
   Mean deviation is calculated as the average of the absolute deviations from the mean, and standard deviation is the square root of the variance. On average, mean deviation is about 80% of the standard deviation in typical distributions.

2. Quartile Deviation and Standard Deviation:
   The quartile deviation (semi-interquartile range) is typically 2/3 of the standard deviation for a normal distribution, though this is a general approximation that works well in many practical cases.