Chapter 1.1, Problem 1TY

To determine

To describe: Two datasets for each level of the four levels of measurements.

Answer to Problem 1TY

Nominal level of measurement:

Dataset 1:

Student	1	2	3	4	5	6	7	8	9	10
Gender	Female	Female	Male	Male	Male	Female	Male	Female	Female	Male

Dataset 2:

The dataset shows the nationality of 10 employees:

Indian, American, Nigerian, Sri Lankan, Pakistani, Russian, German, Tibetan, Brazilian, Argentines.

Ordinal level of measurement:

Dataset 1:

The dataset shows the top 10 football teams around the world:

Netherland, Brazil, England, North Korea, Germany, Portugal, Spain, Italy, Sweden and Chile.

Dataset 2:

The performance rating for an electronic gadget is given below:

3, 5, 2, 1, 4, 3, 5, 2, 1 and 4.

Interval level of measurement:

Dataset 1:

The dataset shows the temperatures measured in degrees during the months of May:

32, 34, 35, 30, 31.5, 29.2, 32.5, 30.5, 28.8 and 35.7.

Dataset 2:

The temperatures measured in Fahrenheit for 10 patients are given below:

101.5, 100, 102.6, 103, 100.8, 108, 106.3, 104.3, 99.5 and 106.

Ratio level of measurement:

Dataset 1:

The height of 10 students measured in centimetres is given below:

172, 170.5, 173, 185, 165.7, 150.2, 177, 183.8, 178.4 and 170.

Dataset 2:

The dataset shows the number of mistakes occurred while printing 5 books:

5, 10, 7, 8 and 9.

Explanation of Solution

Justification:

Level of measurements:

Nominal level of measurement:

If the data takes labels, names or other characteristics where mathematical operations are impossible then the level of measurement is nominal.

Ordinal level of measurement:

A data takes ordinal level of measurement if the entries or numerical values can be arranged according some order or rank. But, the differences between the values are not meaningful.

Interval level of measurement:

It consists of ordered values and also contains one more property of having equal distances or intervals between the values. Interval scale does not contain the values of absolute zero. In this level of measurement, the difference between the numbers is meaningful.

Ratio level of measurement:

It also consists of ordered values and equal distances or intervals between the values with one more property, that it contains absolute zero point in the values. In this level of measurement ratio of the numbers is meaningful.

Examples for Nominal data:

Dataset 1:

The dataset gender of the students

The dataset deals with the gender of students in a class. The gender (male and female) takes non-numerical entities where mathematical operations are not possible.

Dataset 2:

The dataset shows the nationality of 10 employees

The dataset deals with the nationality of employees in a company. The nationality takes non-numerical entities where mathematical operations are not possible.

Examples for Ordinal data:

Dataset 1:

The dataset shows the top 10 football teams around the world:

The dataset deals with the top 10 football teams in the world. The top 10 list takes non-numerical entities and the list can be arranged in some order. But doing mathematical calculations are impossible. Thus, the data follows ordinal level of measurement.

Dataset 2:

The performance rating for an electronic gadget is given below:

The respondents were asked to rate the performance of an electronic gadget in a 5 point scale. The rating can be arranged in order but performing mathematical calculations makes no sense. Thus, the data follows ordinal level of measurement.

Examples for interval data:

Dataset 1:

The dataset shows the temperatures measured in degrees during the months of May:

The dataset deals with the average temperatures measured during the months of May. The values can be arranged in order. There is no absolute zero on this scale. That is, a zero value represents the starting point on this scale. Finding difference between two values is also meaningful. Thus, the data follows interval level of measurement.

Dataset 2:

The temperatures measured in Fahrenheit for 10 patients are given below:

The dataset deals with the average temperature measured for 10 patients. The values can be arranged in order. There is no absolute zero on this scale. That is, a zero value represents the starting point on this scale. Finding difference between two values is also meaningful. Thus, the data follows interval level of measurement.

Examples for ratio data:

Dataset 1:

The height of 10 students measured in centimetres is given below:

The dataset deals with the sample height of students in a college. The values can be arranged in order. There is absolute zero on this scale. Finding difference between two values is also meaningful. A value can be expressed a multiple of another value. Thus, the data follows ratio level of measurement.

Dataset 2:

The dataset shows the number of mistakes occurred while printing 5 books:

The dataset deals with the number of mistakes occurred while printing 5 books. The values can be arranged in order. There is absolute zero on this scale. Finding difference between two values is also meaningful. Thus, the data follows ratio level of measurement.