Scales of Measurement

Introduction to Scales of Measurement in Mathematics

Scales of measurement in math are used to classify and/or quantify variables based on certain properties. Each grade of measurement has relevant properties that are crucial to know. Scale of measurement in math is commonly interpreted in the form of graphs. In which it can be described as the mechanism of marks at fixed intervals, which clearly explain the link between the units being used and their illustration on the graph. Data of Measurement scales are basically classified under the four scales of measurement that have frequent applications in statistical analysis:

The 4 types of scales of measurement includes:-

  1. Nominal Scale of Measurement

  2. Ordinal Scale of Measurement

  3. Interval Scale of Measurement

  4. Ratio scales Scale of Measurement

[Image will be Uploaded Soon]


Not to Miss the Properties of Measurement Scales

Getting to know about each property of measurement scale is quite imperative to easily master over the mechanism of measurement scales. Each scale of measurement is considered to fulfill one or more of the below mentioned properties of measurement.

  1. Magnitude: Values on the scale of measurement have a systematized correlation with one another. In other words, some values are bigger and some are smaller.

  2. Equal Intervals: Units of Scale by the side of the scale are equivalent to each other. This implies, for instance, that the difference between 1 and 2 would be equivalent to the difference between 10 and 11.

  3. Identity: Each value on the scale of measurement holds a peculiar description.

  4. A Minimum Value of Zero: The measurement scale has a true 0 point, further down which no values exist.

Let’s take you through the types of measurement scales in math


Types of Measurement Scales in Mathematics

1. Nominal Scale of Measurement

The nominal type of mathematical measurement scale fulfills solely the identity property of measurement. Values that are fed to variables depict a descriptive classification, but have no innate numerical value when it comes to magnitude.


2. Ordinal Scale of Measurement

The ordinal scale is subjected to both measurement properties of identity and magnitude. Every value on the ordinal measurement scale bears a peculiar meaning, and experience a systematic relationship to each other's value on the scale.


3. Interval Scale of Measurement

This measurement scale holds the properties of identity, magnitude, and equal intervals.

An exemplary event of an interval scale is the Fahrenheit (° F) scale to measure temperature. The scale is devised of units of equal temperature, so that the difference between 30 °and 40 ° F is equal to the difference between 40 ° and 50 ° F.


4. Ratio Scale of Measurement

The ratio scale is one that fulfills all 4 properties of measurement.

A suitable example of a ratio scale would be the weight of an object. Each value on the weight scale exhibits an eccentric explanation, weights can be grade ordered, units across the weight scale are equivalent to one another, and the scale has to its name a minimum value of zero— reason being, objects at rest can be weightless, but they also disqualify to have negative weight.

 [Image will be Uploaded Soon]


Solved Example

Let’s get your theoretical understanding tested practically


Problem 1

Take the Celsius scale for measuring temperature. Which of the given measurement properties is fulfilled by the Celsius scale?

  1. Magnitude

  2. Equal intervals

  3. A minimum value of zero.

Your Options are as follows:-

(I). A only

(II). B only

(III). C only

(IV). A and B

(V). B and C


Solution1

The correct answer is no. (IV) i.e. A & B.

Firstly, the scale of Celsius bears the magnitude property. This is because each value on the measuring scale can be graded as higher as or smaller than any other respective value. Secondly, it also has the equal intervals property since the scale is composed of equal units.

Nevertheless, the Celsius scale does not fulfill the property of minimum value of zero because water freezes at 0 ° Celsius, but a temperature grows colder than that.


Problem 2

A Recipe to prepare dough for spring rolls uses 4 cups of wheat flour and 3 cups of water


Solution2

Given the proportion of items used,

That brings, the ratio of flour to water – 4: 3

To make spring rolls for over 50 people attending the birthday party, we might require 5 times the quantity, so we multiply the numbers by 5:

Thus, we do

4×5: 3×5 = 20: 15

That is to say, we would need 20 cups of flour and 15 cups of water

Since, the ratio still remains the same, so the spring rolls should be just as delectable. 


Fun Facts

  • A scale is often referred to as a scale.

  • The measuring tool used for calculating the weight of grocery items or body is also called a scale.

  • Digital scales are widely available scales around us.

 [Image will be Uploaded Soon]

FAQ (Frequently Asked Questions)

1. What is the Use of Nominal Scales of Measurement?

Gender is possibly one the best examples of a variable that is quantified on a nominal scale of measurement. Individuals may be categorized as "male" or "female", but neither value characterizes more or less "gender" than the other. Political and Spiritual/cultural confederations are other examples of variables that are usually quantified on a nominal scale.

2. What is the Use of Ordinal Scales of Measurement?

A typical representation of an ordinal measurement scale in action would be the outcomes of a horse race, announced across the board as "win", "place", and "show". Now, we are aware of the grading order in which horses finished the race. The horse that ‘won’ completed before the horse that placed, and the horse that ‘placed’ finished before the horse that ‘showed’. Despite that, we cannot be acquainted from this ordinal scale whether it was a close competition or whether the winning horse won by a mile.

3. What is the Use of Interval Scales of Measurement?

With an interval scale, you are not just acquainted with whether different values are larger or smaller, you are also familiar how much larger or smaller they are. For instance, suppose it is 45 °F on Saturday and 60 ° F on Sunday. With this you are clear that it was hotter on Sunday, as well how afar is it hotter that it was 15° hotter.