Measures of dispersion, Applied Statistics

 

Other Measures of Dispersion

In this section, we look at relatively less used measures of dispersion like fractiles, deciles, percentiles, quartiles, interquartile range and finally quartile deviation. Quartile deviation is also referred to as semi-interquartile range.

Fractiles are similar to percentages. If we say that in CFA level I, the pass percentage was 35, we understand that out of every 100 candidates who appeared for the examination, 35 candidates passed the examination. Similar to this, in a frequency distribution also there are always some elements which lie at or below the given fractile. For instance, the median is 0.50 fractile as half of the data is less than or equal to this value. Further in any distribution, 25 percent of the data lies at or below the 0.25 fractile. Interfractile range is the difference between the values of two fractiles. Therefore, this is also necessarily a measure of dispersion between the two fractiles in a frequency distribution. Depending on the number of equal parts into which we divide the data we call them as deciles, percentiles and quartiles. A decile is a fractile which divides the data into ten equal parts, percentile is a fractile which divides the data into 100 equal parts and finally a quartile is the one which divides the data into four equal parts. While computing fractiles we ought to arrange the elements in an increasing order.

Interquartile Range: Since range, interfractile and interquartile range typically from what we call as distance measures of dispersion, the interquartile range looks at how far one should go from the median on either side of it before one-half of the data points are included. As we have seen above, quartiles are fractiles which divide the data into four equal parts such that each quartile consists 25 percent of the data points. The quartiles are the highest data points in each of these four parts. Interquartile range is the difference between the last value in the third quartile (usually denoted by Q3) and the last value in the first quartile denoted by Q1.

Quartile Deviation: It is the difference between the third and the first quartile divided by two. It is expressed as Q.D.

Q.D.

= 1077_quartile deviation.png

where,

         Q1 = first quartile

         Q3 = third quartile

Posted Date: 9/14/2012 3:01:58 AM | Location : United States







Related Discussions:- Measures of dispersion, Assignment Help, Ask Question on Measures of dispersion, Get Answer, Expert's Help, Measures of dispersion Discussions

Write discussion on Measures of dispersion
Your posts are moderated
Related Questions
Large Sample Test for Proportion A random sample of size n (n > 30) has a sample proportion p of members possessing a certain attribute (success). To test the hypothesis that t

for this proportion, use the +-2 rule of thumb to determine the 95 percent confidence interval. when asked if they are satisfied with their financial situation, .29 said "very sat

The manager of Pizza Hut provides a delivery service for customers who telephone in an order. The manager would like to give callers an idea of the time it will take to deliver an

In recent years a number of calculators are available for doing statistical calculations over and above the usual addition, subtraction, multiplication and division. The fx-82 mode

In reduced rank regression (RRR), the dependent variables are first submitted to a PCA and the scores of the units are then used as dependent variables in a series of

A file on DocDepot in the assignments folder on doc-depot called bmi.mtp contains data on the Body Mass Index (BMI) of a population of Ottawa residents. The first column identifies

Pneumatic Actuator Design Matrix: The range of actuator design parameters have been provisionally assessed and are presented in Table. You are required to determine the following

Advantages By definition, mode is the most typical or representative value of a distribution. Hence, when we talk of modal wage, modal size of shoe or modal size of family i

what is the use of applied statistic in our daily routin life

how do i determine the 40th percentile in an ogive graph