Question

the first three moments of a distribution about the mean are 0,81,-144 respectively. what is the moment coefficient of skewness for the distribution.
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Answer 1

Step-by-step explanation:

1. - Coefficient of Variation …..Pg 01 2. - Correction Of Mean & SD …..Pg 04 1. - Karl Pearson's Coefficient of Ske - JK Shah Classes

Q1. Calculate the coefficient of variation. 3 , 5 , 7 , 9 , 11. STEP 1 : x x – x (x – x )2. 3 -4 16. 5 2 4. 7 0 0. 9 2 4. 11 4 16 ... coefficient of skewness is –0.8 . If Q1 = 44.1 and Q3 = 56.6 , find the median of the distribution.

Answer 2

Answer:

The required moment coefficient of skewness is found to be equal to -0.1975.

Step-by-step explanation:

Skewness:

• Skewness is a method of measure of symmetry,  more specifically lack of symmetry. The dataset is symmetric if it looks the same on the left and right sides of the centre.
• If the dataset is not symmetric, the dataset is said to be distorted. If the tail of the dataset is long to the right (left), the dataset is said to be positively (negative) distorted. Skewness is measured by its coefficient.

Calculation:

We know that the moment coefficient of skewness for a distribution whose moments about the mean are given to us is calculated by the following expression:

$\gamma=\frac{m_3}{(m_2)^{\frac{3}{2}}}$

Where, $\gamma$ is the moment coefficient of the skewness for a distribution,

and $m_2, m_3$ are the second and third moments of a distribution,

Now, we are given the first three moment coefficient of skewness as 0, 81, -144.

Substituting this in the above mentioned expression, we get:

$\gamma=\frac{-144}{(81)^{\frac{3}{2}}}$

We can write 81 as square of 9, so:

$\gamma=\frac{-144}{(9)^{2\times\frac{3}{2}}}$

We get:

$\gamma=\frac{-144}{(9)^{3}}$

Simplifying this, we get:

$\gamma=\frac{-144}{729}$ or -0.1975

Thus, the moment coefficient of skewness for the associated distribution is found out to be: γ = -0.1975.

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