Leptokurtic-measure of central tendency, Mathematics

Assignment Help:

Leptokurtic

a) A frequency distribution which is lepkurtic has normally a higher peak than that of the general distribution. The coefficient of kurtosis while determined will be found to be more than 3. Hence frequency distributions along with a value of more than three are definitely leptokurtic

b) Several frequency distributions while plotted may produce a curve similar to that of the general distribution. That frequency distributions are referred to as mesokurtic. The degree of kurtosis is normally equal to 3

c) While the frequency curve contacted produces a peak which is lower than that of a common distribution while such a curve is said to be platykurtic. The coefficient of Leptokurtic is generally less than 3

- This is necessary to calculate the numerical measure of kurtosis. The generally used measure of kurtosis is the percentile coefficient of kurtosis. This coefficient is commonly determined by using the given equation

Percentile measure of kurtosis, K (Kappa) =1971_Leptokurtic-measure of central tendency.png

 

Illustration

Refer to the table above for loans to small business firms/units

Essential

Calculate the percentile coefficient of Kurtosis as

P90 =  (90/100)(n + 1) = 0.9 (610 + 1) 

= 0.9 (611)

= 549.9

The actual loan for a firm in this position

(549.9) = 80.5 + ((549.9 - 538)/40) x 5 = 81.99

P10 = (10/100) (n + 1) = 0.1 (611) = 61.1

The actual loan value given to the firm on this position is

50.5 +((61.1 - 32)/62) x 5 = 52.85

= 0.9 (611)

= 549.9

∴ percentile measure of kurtosis

K(Kappa) =       ½ {(Q3 - Q1)/(P90 - p10)}

 = ½  {(73.82 - 58.53)/(81.99 - 52.85)}

= 0.26

Because 0.26 < 3, it can be concluded that the frequency distribution exhibited by the distribution of loans is platykurtic

Kurtosis is measured also by moment statistics that utilize the exact value of each observation.

i.  M1 the first moment = M1 = (åX)/n = Mean M1 or M1

M2 =  (åX2)/n

M3 =  (åX3)/n

M4 =  (åX4)/n

3. M2 second moment about the mean M2 or f2

M2 = M2 - M12

4. M3 third moment about the mean M3 (a measure of the absolute skew ness)

M3 = M3 - 3M2M1 + 2M13

5. M4 fourth moment about the mean M4 (a measure of the absolute Kurtosis)

M4 = M4- 4M3M1 + 6M2M12 + 3M14

An alternative formula

1172_Leptokurtic.png


Related Discussions:- Leptokurtic-measure of central tendency

Pre-operational stage-development learning maths, Pre-operational Stage : ...

Pre-operational Stage :  This period of a child's cognitive development usually begins at the age of 2, and lasts until about the age of 6. Thus, it usually coincides with the pre

Computation of covariance - ungrouped data, Computation of Covariance ...

Computation of Covariance Ungrouped Data          For a population consisting of paired ungrouped data points {X, Y} where,

Example of linear equations, Example of Linear Equations: Solve the eq...

Example of Linear Equations: Solve the equation 2x + 9 = 3(x + 4). Solution: Step 1. Using Axiom 2, subtract 3x and 9 from both sides of the equation. 2x + 9 = 3(

Sketch the feasible region, Sketch the feasible region for the following se...

Sketch the feasible region for the following set of constraints: 3y - 2x  ≥ 0 y + 8x  ≤  53 y - 2x  ≤  2 x  ≥ 3. Then find the maximum and minimum values of the objective

Example of uniform distribution, Q. Samantha wrote a computer program to r...

Q. Samantha wrote a computer program to randomly generate two-digit numbers between 00 and 99. Let X be the random 2 digit number generated by the computer. Find the distributio

Trig, cot functions

cot functions

Applying percents, If a single person makes $25,00 a year, how much federal...

If a single person makes $25,00 a year, how much federal income tax will he or she have to pay ?And they are gining me a chart that says $0 to $27,050 is 15% of taxes .

Trigonometry, If tanA+sinA=m and m2-n2 = 4vmn, show that tanA-sinA=n

If tanA+sinA=m and m2-n2 = 4vmn, show that tanA-sinA=n

Ellipse, different types of ellipse

different types of ellipse

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