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

Lorenz curve , Lorenz Curve   It is a graphic method of measur...

Lorenz Curve   It is a graphic method of measuring dispersion. This curve was devised by Dr. Max o Lorenz a famous statistician.  He used this technique for wealth it i

Describe the opportunities for statistical learning, 1. Recognize and expla...

1. Recognize and explain the opportunities for statistical learning. 2. Describe how the use of statistics supports student learning. 3. Recognize appropriate data displays a

Simple linear regression, We are interested in assessing the effects of tem...

We are interested in assessing the effects of temperature (low, medium, and high) and technical configuration on the amount of waste output for a manufacturing plant. Suppose that

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

Graphical calculation for mode, For calculating the mode of the grouped dat...

For calculating the mode of the grouped data graphically, the following procedure is adopted. Draw a histogram of the data; the modal class is the tallest rectangle.

Diversity of data , The box plot displays the diversity of data for the tot...

The box plot displays the diversity of data for the totexp; the data ranges from 30 being the minimum value and 390 being the maximum value. The box plot is positively skewed at 1.

Index number of price for paasche’s method, Construct index numbers of pri...

Construct index numbers of price for the following data by applying: i)      Laspeyre’s method ii)     Paasche’s method iii)    Fisher’s Ideal Index number

Poisson distribution, Poisson Distribution The poisson Distribution  wa...

Poisson Distribution The poisson Distribution  was discovered  by French mathematician simon  denis  poisson. It is a discrete probability distribution. Meaning : In bi

Multiple correspondence analysis, Correspondence Analysis (CA) is a general...

Correspondence Analysis (CA) is a generalization of PCA to contingency tables. The factors of correspondence analysis give an orthogonal decomposi:ion of the Chi- square associated

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