Q. 6.138 - Elementary Statistics

Question

In 1902, W. R. Macdonell published the article "On Criminal Anthropometry and the Identification of Criminals" (Biometrika, Vol. 1. Pp. 177-227). Among other things. the author presented data on the left middle finger length, in centimeters. The following table provides the midpoints and frequencies of the finger-length classes used.

Use these data and the technology of your choice to assess the normality of middle finger length of criminals by using

a. a histogram.

b. a normal probability plot.

Step-by-Step Solution

Answer

a. The above constructed histogram has bell shaped which implies that the data has been taken from the normally distributed population.

b. Thus, it could be said that the data set is normally distributed.

Part (a) Step 1: Given Information

A histogram for the provided data set.

Part (a) Step 2: Explanation

The data is: 

A histogram for the provided data set.

$\begin{array}{|rr|}\hline \text{ Mid point }& \text{ Frequency }\\ 9.5& 1\\ 9.8& 4\\ 10.1& 24\\ 10.4& 67\\ 10.7& 193\\ 11& 417\\ 11.3& 575\\ 11.6& 691\\ 11.9& 509\\ \hline\end{array}$

$\begin{array}{|rr|}\hline 12.2& 306\\ 12.5& 131\\ 12.8& 63\\ 13.1& 16\\ 13.4& 3\\ \hline\end{array}$

Part (a) Step 3: Explanation

Histogram for the provided data set could be constructed as:

The above constructed histogram has bell shaped which implies that the data has been taken from the normally distributed population.

Part (b) Step 4: Given Information

A normal probability plot for the provided data set.

Part (b) Step 5: Explanation

A normal probability plot for the provided data set can be constructed as:

Since, all the data points follow the linear pattern. Thus, it could be said that the data set is normally distributed.