Question

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Answer 1

Explanation:

Quartiles

A median divides a given dataset (which is already sorted) into two equal halves similarly, the quartiles are used to divide a given dataset into four equal halves. Therefore, logically there should be three quartiles for a given distribution, but if you think about it, the second quartile is equal to the median itself! We’ll deal with the other two quartiles in this section.

The first quartile or the lower quartile or the 25th percentile, also denoted by Q1, corresponds to the value that lies halfway between the median and the lowest value in the distribution (when it is already sorted in the ascending order). Hence, it marks the region which encloses 25% of the initial data.

Similarly, the third quartile or the upper quartile or 75th percentile, also denoted by Q3, corresponds to the value that lies halfway between the median and the highest value in the distribution (when it is already sorted in the ascending order). It, therefore, marks the region which encloses the 75% of the initial data or 25% of the end data.

The Quartile Deviation

Formally, the Quartile Deviation is equal to the half of the Inter-Quartile Range and thus we can write it as – [Math Processing Error] Therefore, we also call it the Semi Inter-Quartile Range.

The Quartile Deviation doesn’t take into account the extreme points of the distribution. Thus, the dispersion or the spread of only the central 50% data is considered.

If the scale of the data is changed, the Qd also changes in the same ratio.

It is the best measure of dispersion for open-ended systems (which have open-ended extreme ranges).

Also, it is less affected by sampling fluctuations in the dataset as compared to the range (another measure of dispersion).

Since it is solely dependent on the central values in the distribution, if in any experiment, these values are abnormal or inaccurate, the result would be affected drastically.

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