Question

"The first three moments of a distribution about the mean are 1, 4 and 0. The distribution is:​

Answer 1

Answer:

The distribution is: "Symmetrical"

Answer 2

The distribution is symmetric

Given

• first three moments of a distribution about the mean are 1, 4 and 0.

1. first Central moment,m1 = 1
2. second Central moment, m2= 4
3. 3rd Central moment,m3 = 0

To find

• The nature of the distribution.

Solution

we are provided with three Central moments and are asked to comment on the nature of the distribution of the observations.

we know that moments are useful statistical measurement or values which are used to judge the nature of the distribution understand the pattern of graph, etc.

Moments are of two type raw moment and central moment. Central moments are estimated keeping the mean of the observation as a reference point and raw moment are estimated using any random point a as a reference point.

the nature of the Observation or skewness could be found by using the standard equation, given by,

B = (m3)^2/(m2)^3

or, B = 0/4^3

or, B = 0

since the skewness, B is zero the observation graph would be symmetric.