Q.2.139 - Elementary Statistics

Question

We have drawn a smooth curve that  represents a distribution, 

a. Identify the shape of the distirbution with regard to modality.

b. Identify the shape  of the distribution with regard to symmetry (or non symmetry)

c . If the distribution is unimodal and non symmetric, classify it as either right skewed or left skewed.

Step-by-Step Solution

Answer

a) The shape of the graph is multimodal 

(b) The shape of the graph is non-symmetric 

(c) The skewness of the distribution  cannot be determined

Part(a) Step 1 : Given Information

The given graph is:

we have to  Identify the shape of the distirbution with regard to modality.   

Part (a) Step 2 : Explanation

A probability distribution with more than one peak, or "mode," is known as a multimodal distribution. The term "unimodal" refers to a distribution having only one peak. The term "bimodal" refers to a distribution with two peaks. A multimodal distribution has two or more peaks.

There are three peaks in the given graph. 

Part (b) Step 1: Given Information

The given graph is:

we have to Identify the shape  of the distribution with regard to symmetry (or non symmetry)    

Part (b) Step 2: Explanation

When a distribution's shape is broken into two sections, one of them is the mirror image of the other, the distribution is said to be symmetric. The graph in question cannot be divided into two equal halves, one of which is a mirror image of the other.

Part (c) Step 1: Given Information

The given graph is:

We have to classify  the distribution as either right skewed or left skewed If the distribution is unimodal and non symmetric.    

Part(c) Step 2: Explanation

A probability distribution with more than one peak, or "mode," is known as a multimodal distribution.

A skewed (non-symmetric) distribution is one in which mirror-imaging is not possible.