Q.6.43 - Elementary Statistics

Question

 In the paper "Cloudiness: Note on a Novel Case of Frequency" (Procedings of the Royul Sociery of London, Vol. $62$. pp.$287-290$), K. Pearson examined data on daily degree of cloudiness, on a scale of 0 to 10 , at Breslau (Wroclaw), Poland, during the decade $1876-1885$. A frequency distribution of the data is presented in the following table.

a. Draw a frequency histogram of these degree-of-cloudiness data.

b. Based on your histogram, do you think that degree of cloudiness in Breslau during the decade in question is approximately normally distributed? Explain your answer.

Step-by-Step Solution

Answer

(a)

(b) The degree of cloudiness in Breslau over the decade does not follow a normal distribution. 

Part (a) Step 1: Given information

Given in the question that,  In the paper "Cloudiness: Note on a Novel Case of Frequency" (Procecdings of the Royal Sociery of London, Vol. $62$, pp. $287-290$), K. Pearson examined data on daily degree of cloudiness, on a scale of $0$ to $10$ , at Breslau (Wroclaw), Poland, during the decade $1876-1885$. A frequency distribution of the data is presented in the following table.

We need to draw a frequency histogram of these degree-of-cloudiness data. 

Part (a) Step 2: Explanation

A frequency histogram is a sort of bar graph that displays the frequency, or number of times, a data set's outcome happens. To graphically show the data, it has a title, an $x$-axis, a $y$-axis, and vertical bars.

The given data is

Degree	Frequency
$0$	$751$
$1$	$179$
$2$	$107$
$3$	$69$
$4$	$46$
$5$	$9$
$6$	$21$
$7$	$71$
$8$	$194$
$9$	$117$
$10$	$2089$

The degrees of cloudiness data can be represented as a frequency histogram as follows:

Part (b) Step 1: Given information

Given in the question that,  In the paper "Cloudiness: Note on a Novel Case of Frequency" (Procecdings of the Royal Society of London, Vol. $62$, pp. $287-290$), K. Pearson examined data on daily degree of cloudiness, on a scale of $0$ to $10$ , at Breslau (Wroclaw), Poland, during the decade $1876-1885$. A frequency distribution of the data is presented in the following table.

Based on the histogram we need to explain that whether the degree of cloudiness in Breslau during the decade in question is approximately normally distributed.

Part (b) Step 2: Explanation

Degree	Frequency
$0$	$751$
$1$	$179$
$2$	$107$
$3$	$69$
$4$	$46$
$5$	$9$
$6$	$21$
$7$	$71$
$8$	$194$
$9$	$117$
$10$	$2089$

The degrees of cloudiness data can be represented as a frequency histogram as follows:

The form of the distribution is far from the normal curve, as can be seen above. As a result, the degree of cloudiness in Breslau over the decade does not follow a normal distribution.