Quartile Deviation, Statistics, Basic Statistics

Quartile Deviation

The range as a measure of dispersion discussed above has certain limitations. It is based on two extreme items and it fails to take account of the scatter within the range. From this there is reason to believe that if the dispersion of the extreme items is discarded, the limited range thus established might be more instructive for this purpose there has been developed a measure called the interquartile range the range which includes the middle 50 per cent of the distribution that is one quarter of the observations at the lower end another quarter of the observations at the upper end of the distribution are excluded in computing the interquartile range. In other works, interquartile range represents the difference between the third quartile and the first quartile.

Symbolically,

Interquartile range = Q3 – Q1

Very often the interquartile range is reduced to the form of the semi-tier quartile range or quartile deviation by dividing it by 2

Symbolically

Quartile deviation or Q. D = (Q3 – Q1) / 2

Quartile deviation given the average amount by which the two quartiles differ from the median. In asymmetrical distribution the two quartiles Q1 and Q3) are equidistant from the median med - 1 = Q3 – med. And as such the difference can be taken as a measure of dispersion. The median ± covers exactly 50 per cent of the observations.

In reality however one seldom finds a series in business and economic data that is perfectly symmetrical. Nearly all distributions of social series are asymmetrical. In an say metrical distribution Q1and Q3 are not equidistant from the median. As a result an asymmetrical distribution includes only approximately 50 per cent of observations.

When quartile deviation is very small it describes high uniformity or small variation of the central 50% items and a high quartile deviation means that the variation among the central items is large.

Quartile deviation is an absolute measure of dispersion. The relative measure corresponding to this measure, called the coefficient of quartile deviator is calculated as follows.

Coefficient of Q.D = (Q3 – Q1) / 2 / (Q3 + Q1)/2 = Q3 – Q1 / Q3 + Q1

Coefficient of quartile deviation can be used to compare the degree of variation in different distributions.

Computation of quartile deviation the process of computing quartile deviation is very simple we have just to compute the values of the upper and lower quartiles the following illustrations would clarify calculations.
Posted Date: 1/31/2012 11:40:36 PM | Location : United States







Related Discussions:- Quartile Deviation, Statistics, Assignment Help, Ask Question on Quartile Deviation, Statistics, Get Answer, Expert's Help, Quartile Deviation, Statistics Discussions

Write discussion on Quartile Deviation, Statistics
Your posts are moderated
Related Questions
1 Compute SX; SXY ; and SY . > # Put your R code here. 2 Compute the sample correlation matrix (q_p) between the X and Y variables. Test individual correlations for significance

Use the “best subsets” method to identify a “best” model for the data. Explain what you think is the best model and why.

I want to simulate observed variables for structural equation modeling. In real data it is assumed that observed variables are not error free variables, so should i also simulate e

hi i just want to knw my husband done b.com n doing job as a accountant in private firm can u suggest me it is better for my husband to do m.ba or either some professional course

Financial sales and building sensible financial help Conceptual structure can be identified as a structure. It is a structured design of connected goals and fundamental concept

Court-ordered withholdings Paycheck accounting also includes withholdings for items other than payroll taxation. For example, legal courts of law may purchase business employer


You have recently joined XYZ, an international company that produces a wide range of office supplies and stationary goods. In your new role as Group Management Accountant your firs

Let f (?) be the production function associated with a single-output technology, and let Y be the production set. Show that Y satisfies constant returns to scale if and only if f (