Q. 2.16 - Elementary Statistics

Question

Another important type of data is ordinal data, which is data about order or rank given on a scale such as $1,2,3,\dots$ or $A, B, C,...$ Following are several variables. Which, if any, yield ordinal data? Explain your answer.

a. Height

b. Weight

c. Age

d. Sex

e. The number of siblings

f. Religion

g. Place of birth

h. High school class rank

Step-by-Step Solution

Answer

(a) The height produces ordinal data.

(b) The weight produces ordinal data. 

(c) The age produces ordinal data. 

(d) The Sex does not produce ordinal data.

(e) The Number of siblings produces ordinal data. 

(f) Religion does not produce ordinal data. 

(g) The Place of Birth does not produce ordinal data. 

(h) The High school class rank produces ordinal data. 

Part(a) Step 1: Concept Introduction

The given data is height.

Ordinal data is a categorical, statistical data type in which the variables are divided into natural, ordered categories with no known distances between them. These statistics are on an ordinal scale, one of S. S. Stevens' four levels of measurement described in $1946$.

Part(a) Step 2: Explanation

Ordinal data is information regarding order or rank expressed on a scale of $1,2,3,\dots$ or $A,B,C,\dots$.

On a scale of $1,2,3,\dots$ or $A,B,C,\dots$, the height values can be sorted or ordered. As a result, height produces ordinal data.

Part(b) Step 1: Concept Introduction

The given data is weight.

Ordinal data is a categorical, statistical data type in which the variables are divided into natural, ordered categories with no known distances between them. These statistics are on an ordinal scale, one of S. S. Stevens' four levels of measurement described in $1946$.

Part(b) Step 2: Explanation

Ordinal data is information regarding order or rank expressed on a scale of $1,2,3,\dots$ or $A,B,C,\dots$.

 On a scale of $1,2,3,\dots$ or $A,B,C,\dots$, the weight values can be sorted or ordered. As a result, weight produces ordinal data.

Part(c) Step 1: Concept Introduction

The given data is age.

Ordinal data is a categorical, statistical data type in which the variables are divided into natural, ordered categories with no known distances between them. These statistics are on an ordinal scale, one of S. S. Stevens' four levels of measurement described in $1946$.

Part(c) Step 2: Explanation

Ordinal data is information regarding order or rank expressed on a scale of $1,2,3,\dots$ or $A,B,C,\dots$.

On a scale of $1,2,3,\dots$ or $A,B,C,\dots$, the age values can be sorted or ordered. As a result, age yields ordinal data.

Part(d) Step 1: Definition

The given data is sex.

Ordinal data is a categorical, statistical data type in which the variables are divided into natural, ordered categories with no known distances between them. These statistics are on an ordinal scale, one of S. S. Stevens' four levels of measurement described in $1946$.

Part(d) Step 2: Explanation

$A,B,C,\dots$Ordinal data is information regarding order or rank expressed on a scale of $1,2,3,\dots$ or .

As qualitative data, sex values cannot be ranked or arranged on a scale of $1,2,3,\dots$ or $A,B,C,\dots$. As a result, Sex does not produce ordinal data.

Part(e) Step 1: Concept Introduction

The given data is the Number of siblings.

Ordinal data is a categorical, statistical data type in which the variables are divided into natural, ordered categories with no known distances between them. These statistics are on an ordinal scale, one of S. S. Stevens' four levels of measurement described in $1946$.

Part(e) Step 2: Explanation

Ordinal data is information regarding order or rank expressed on a scale of $1,2,3,\dots$ or $A,B,C,\dots$.

On a scale of $1,2,3,\dots$ or $A,B,C,\dots$, the number of siblings' values can be sorted or ordered.   As a result, the number of siblings yields ordinal data.

Part(f) Step 1: Given Information

The given data is Religion.

Ordinal data is a categorical, statistical data type in which the variables are divided into natural, ordered categories with no known distances between them. These statistics are on an ordinal scale, one of S. S. Stevens' four levels of measurement described in $1946$.

Part(f) Step 2: Explanation

Ordinal data is information regarding order or rank expressed on a scale of $1,2,3,\dots$ or $A,B,C,\dots$ .

As qualitative data, Religion values cannot be ranked or arranged on a scale of $1,2,3,\dots$ or $A,B,C,\dots$. As a result, Religion does not produce ordinal data.

Part(g) Step 1: Given Information

The given data is Place of Birth.

Ordinal data is a categorical, statistical data type in which the variables are divided into natural, ordered categories with no known distances between them. These statistics are on an ordinal scale, one of S. S. Stevens' four levels of measurement described in $1946$.

Part(g) Step 2: Explanation

Ordinal data is information regarding order or rank expressed on a scale of $1,2,3,\dots$ or $A,B,C,\dots$.

As qualitative data, Place of Birth values cannot be ranked or arranged on a scale of $1,2,3,\dots$ or $A,B,C,\dots$. As a result, Place of Birth does not produce ordinal data.

Part(h) Step 1: Given Information

The given data is High school class rank

Ordinal data is a categorical, statistical data type in which the variables are divided into natural, ordered categories with no known distances between them. These statistics are on an ordinal scale, one of S. S. Stevens' four levels of measurement described in $1946$.

Part(h) Step 2: Explanation

Ordinal data is information regarding order or rank expressed on a scale of $1,2,3,\dots$ or $A,B,C,\dots$.

On a scale of $1,2,3,\dots$ or $A,B,C,\dots$, the high school class rank values can be sorted or ordered. As a result, high school class rank yields ordinal data.