Question

if every item in a series is increased by the same quantity,the quartile deviation​

Answer 1

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The Quartile Deviation

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)

Answer 2

Answer:

If every item in a series is increased by the same quantity, the quartile deviation​ remains same.

Concept:

Quartile Deviation:  Quartile deviation is defined as half of the difference between the upper and lower quartile. The upper quartile (Q₃) is the middle number between median and largest observation. the lower quartile (Q₁) is the middle number between median and smallest observation. The second quartile (Q₂) is the median of observations. Mathematically, Quartile deviation is expressed as,

QD = 1/2(Q₃ - Q₁)

Quartile deviation is independent of change of origin but depends on change of scale.

Change of Origin:  It means addition or subtraction of a quantity (number) in each of the observations.

Change of scale: It means multiplying or dividing each of the observations by a quantity (number).

Explanation:

In this question, we are given that each item is increased by the same quantity which means the change of origin is taking place.

Quartile deviation is independent of change of origin, means it will not be affected by the change of origin.

Hence, if every item in a series is increased by the same quantity, the quartile deviation​ remains same.

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