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Chapter 2: Q. 2.157 (page 83)

Forearm Length. In 1903, K. Pearson and A. Lee published the paper "On the Laws of Inheritance in Man. I. Inheritance of Physical Characters" (Biometrika, Vol. 2, pp. 357-462). The article examined and presented data on forearm length, in inches, for a sample of 140 men, which we present on the Weiss Stats site.

a. use the technology of your choice to identify the modality and symmetry (or non-symmetry) of the distribution of the data set.

b. if unimodal, classify the distribution as symmetric right-skewed. or left-skewed.

Short Answer

Expert verified

a) The distribution is unimodal and symmetric.

b) The skewness is not applicable.

Step by step solution

01

Part (a) Step 1: Given Information 

To determine the modality and symmetry of the distribution.

02

Part (a) Step 2: Explanation 

The frequency distribution is,

The frequency histogram will have the bars of height equal to frequency so,

Because there is just one peak in the distribution, it is unimodal.

Because the apex of the distribution lies nearly in the middle of the graph, the distribution is roughly symmetric.

Bimodal:

Having or involving two modes, especially two maxima (of a statistical distribution).

03

Part (b) Step 1: Given Information

To find the shape of the distribution is right-skewed or left-skewed.

04

Part (b) Step 2: Explanation

The skewness does not apply because the distribution is not unimodal or symmetric.

Symmetric and non-symmetric:

If you understand that symmetrical means that both sides of something are identical, it should be simple to understand that asymmetrical means that the two sides are different in some way. Things that are asymmetrical are irregular and crooked and do not match up perfectly when folded in half.

A "skewed right" distribution has the tail on the right side. The tail of a "skewed left" distribution is on the left side.

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