UGC NET COMMERCE December 2018 Q31
- Option : D
- Explanation : To begin with, we consider the mean deviation and standard deviation. To calculate mean deviation, absolute deviations are used whereas the calculation of standard deviation calls for squaring the deviations before averaging them and taking the square root. The squaring of deviations places relatively larger weights to the bigger deviation values. The result is that the standard deviation is always higher than the mean deviation. Further, quartile deviation is always smaller than the standard deviation and the mean deviation. The relationship between the three measures is defined precisely in respect of a normal distribution.
That mean deviation is about 80 per cent of the standard deviation. Conversely, the standard deviation is about 1.25 times the mean deviation. Further, quartile deviation is approximately two-thirds of the standard deviation and five-sixths of the mean deviation. Thus, the relationships given here may be summarized as follows:
4 SD = 5 MD = 6 QD
Here, SD is standard deviation, MD is mean deviation and QD is quartile deviation.
