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

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

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

Multiple regression analysis, Complete the multiple regression model using ...

Complete the multiple regression model using Y and your combined X variables.  State the equation.  Next, make sure that you evaluate overall model performance with the Anova table

General algebraic and quantitative expressions, Read the following data on ...

Read the following data on the economy of Angoia and answer/respond to the questions/instructions that follow. Unless otherwise stated, the monetary figures are in real billions o

Business forecasting, Meaning and Definitions of Business Forecasting T...

Meaning and Definitions of Business Forecasting The problem of business  forecasting  refers to the  analysis  of the past and  present economic  conditions. With  the objectiv

Stat, solve problems

solve problems

Calculate the mle estimate for mean, Each section of the SAT test is suppos...

Each section of the SAT test is supposed to be distributed normally with a mean of 500 and a standard deviation of 100. Suppose 5 students in a class took the SAT math test. They r

Pie diagram, Circles or Pie Diagram: Circles or pie diagrams are alter...

Circles or Pie Diagram: Circles or pie diagrams are alternative to squares. These are used  for the same purpose i.e. when  the values are differing  widely in their magnitude

Assignment 1: Testing Hypotheses for Means, Review the Learning Resources a...

Review the Learning Resources and the media programs related to t tests. For additional support, review the Skill Builder: Research Design and Statistical Design and the Skill Buil

Spatial ability test, What would be the cutoff score to indicate a score th...

What would be the cutoff score to indicate a score that is in the top 15% of the scores on a test with a mean of 100 and a standard deviation of 15? This question has multiple p

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