Question

The second and fourth moments of a distribution about the arithmetic mean are 16 and 162 respectively. Coefficient of Kurtosis is given by

Answer 1

Answer:

34. The second and third moments of a distribution about the arithmetic mean are 16 and -64 respectively. Coefficient of skewness B, is given by (2) (A) -0.25 (B) 1 (C) 4 (D) -1 35. The second and fourth moments of a distribution about the arithmetic mean are 16 and 162 respectively. Coefficient of kurtosis B2 is given by (2 (A) 1 (B) 1.51 (C) 0.63 (D) 1.69

Answer 2

Given

• second Central moment, m2 = 16
• 4th Central moment, m4 = 162

To find

• Coefficient of Kurtosis

Solution

Kurtosis is the measure of peakness of a distribution and there are three types of kurtosis, platykurtic, mesokurtic , Leptokurtic.

we are provided with the fourth Central moment and the second Central moment and are asked you find the kurtosis or measurement of peakness of this distribution which could be found simply by putting the given values in the standard equation

ie, Kurtosis B = m4/ (m2)^2

or, B = 162/(16)^2

or, B = 162/256

or, B = 0.63 ( coefficient of kurtosis)

Now the measure of kurtosis is given by,

G = B - 3

or, G = 0.63 - 3

or, G = -2.3

Therefore we can conclude that the given distribution is platykurtic. (as G less than zero)