Measures of dispersion, Applied Statistics

Assignment Help:

 

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


Related Discussions:- Measures of dispersion

Index number, Index Number Meaning and Definitions of Index Number ...

Index Number Meaning and Definitions of Index Number The index numbers are the special type of averages which are presented in percentages and computed on certain base.

Regression, The 4 assumptions of regression: 1.       Variables are norm...

The 4 assumptions of regression: 1.       Variables are normally distributed 2.       Linear relationship between the independent and dependent variables 3.       Homosced

Professional Counselor, A researcher hypothesized that the pulse rates of ...

A researcher hypothesized that the pulse rates of long-distance athletes differ from those of other athletes. He believed that the runners’ pulses would be slower. He obtained a ra

Carpal tunnel statistics, Cindy, the Assistant Vice President of Engineerin...

Cindy, the Assistant Vice President of Engineering/Administrative Services at Blue Cross Blue Shield Rhode Island (BCBSRI), has seen all of the OSHA statistics: In 2000, 1

Median for grouped data, Grouped Data  In order to find the median, the...

Grouped Data  In order to find the median, the median class is to be first located and then interpolation is to be used by assuming that items are evenly spaced over the entire

Research tool, what are the characteristics of research tool?

what are the characteristics of research tool?

Accident proneness, Accident proneness  A personal psychological issue w...

Accident proneness  A personal psychological issue which affects the individual's probability of suffering the accident. The concept has been studied statistically under the num

Stat, solve problems

solve problems

Che, Chebychev inequality

Chebychev inequality

Correlation coefficient, Consider three stocks A, B and C costing $100 each...

Consider three stocks A, B and C costing $100 each. The annual returns on the three stocks have mean $5 and variance $10. a. Suppose that the returns on the three stocks are i.i

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd