Q.19 - Elementary Statistics

Question

Inauguration Ages. From the information Please Almanac, we obtained the ages at the inauguration for the first 44 presidents of the United States (from George Washington to Barack H. Obama).

a. Identify the classes for grouping these data, using limit grouping with classes of equal width 5 and a firs class of $40-44$.

h. Identify the class marks of the classes found in part (a).

c. Construct frequency and relative-frequency distributions of the inauguration ages based on your classes obtained in part (a).

d. Draw a frequency histogram for the inauguration ages based on your grouping in part (a).

e. Classify the slape of the distribution of inauguration ages for the first $44$ presidents of the United States both generally and specifically.

Step-by-Step Solution

Answer

(a) 

(b) 

(c) 

(d) 

(e) The distribution is almost symmetric. 

Part (a) Step 1: Given information

The given data is 

Part (a) Step 2: Explanation

Individuals are placed into categories by categorical or qualitative criteria, whereas quantitative variables are numerical variables.

Classes with width are

Part (b) Step 1: Given information

The given data is 

Part (b) Step 2: Explanation

A class's classmark is the value that falls exactly in the centre of the class.

The grade is calculated as follows:

Part (c) Step 1: Given information

The given data is 

Part (c) Step 2: Explanation

The frequency and relative frequency for the given classes is given as

Part (d) Step 1: Given information

The given data is 

Part (d) Step 2: Explanation

The histogram is 

Part (e) Step 1: Given information

The given data is 

Part (e) Step 2: Explanation

The number of data values that fall into a class is known as frequency.

Because the peak of the distribution is about in the middle of the histogram, the distribution is roughly symmetric.

As a result, the distribution is almost symmetric.