Is Interval Scale Discrete or Continuous

In the world of data management, statistics or marketing research, there are so many things you can do with interval data and the interval scale. With this in mind, there are a lot of interval data examples that can be given.

In fact, together with ratio data, interval data is the basis of the power that statistical analysis can show. Both interval and ratio scales represent the highest level of data measurement and help a wide range of statistical manipulations and transformations that the other types of data measurement scales cannot support.

On this page you will learn:

• What is interval data?
  Definition, meaning, and key characteristics.
• A list of 10 examples of interval data.
• Interval vs Ratio data.
• An infographic in PDF for free download.
• A Quick Quiz

As you might know, there are 4 measurement scales: nominal, ordinal, interval, and ratio. Knowing the measurement level of your data helps you to interpret and manipulate data in the right way.

Let's define the interval data:

Interval data refers not only to classification and ordering the measurements, but it also specifies that the distances between each value on the scale are equal. The distance between values is meaningful.

To put it another way, the differences between points on the scale are equivalent. That is why it is called interval data. It is measured on interval scales. The Interval scale is a numeric scale that represents not only the order but also the equal distances between the values of the objects.

The most popular example is the temperature in degrees Fahrenheit. The difference between a 100 degrees F and 90 degrees F is the same difference as between 60 degrees F and 70 degrees F.

Time is also one of the most popular interval data examples measured on an interval scale where the values are constant, known, and measurable.

These characteristics allow interval data to have many applications in the statistics and business intelligence field. However, there is one major disadvantage – the lack of absolute zero.

In the interval scale, there is no true zero point or fixed beginning . They do not have a true zero even if one of the values carry the name "zero."

For example, in the temperature, there is no point where the temperature can be zero. Zero degrees F does not mean the complete absence of temperature.

Since the interval scale has no true zero point, you cannot calculate Ratios . For example, there is no any sense the ratio of 90 to 30 degrees F to be the same as the ratio of 60 to 20 degrees.

A temperature of 20 degrees is not twice as warm as one of 10 degrees.

The lack of the true zero in the interval scales, make it impossible to make conclusions about how many times higher one values is than another.

Thus, interval scale only allows you to see the direction and the difference between the values, but you can not make statements about their proportion and correlation.

So let's sum the key characteristics of the interval data and scales:

• Interval scales not only show you the order and the direction, but also the exact differences between the values.
• The distances between each value on the interval scale are meaningful and equal.
• There is no true zero point or fixed beginning.
• You cannot calculate Ratios.

So, interval scales are great (we can add and subtract to them) but we cannot multiply or divide.

In addition, in the practice, many statisticians and marketers can turn a non-interval ordered values scale into an interval scale to support statistical or data analysis.

Interval data examples:

1. Time of each day in the meaning of a 12-hour clock.

2. Temperature, in degrees Fahrenheit or Celsius (but not Kelvin).

3. IQ test (intelligence scale).

4. Test scores such as the SAT and ACT test scores.

5. Age is also a variable that is measurable on an interval scale, like 1, 2, 3, 4, 5 years and etc.

6. Measuring an income as a range, like $0-$999; $1000-$1999; $2000-$2900, and etc. This is a classic example of turning a non-interval, ordered variable scale into an interval scale to support statistical analysis.

7. Dates (1015, 1442, 1726, etc.)

8.  Voltage e.g. 110 and 120 volts (AC); 220 and 240 volts (AC) and etc.

9.In marketing research, if we ask 2 people how much time do they spend reading a magazine each day, we would know not only who spend more time reading but also the exact difference in minutes (or another time interval) between the two individuals.

10. Grade levels in a school (1st grader, 2nd grader, and etc.)

Interval and Ratio Data

Understanding the difference between interval and ratio data is one of the key data scientist skills.

Interval and ratio data are the highest levels of data measurements. But still, there is important differences between them that define the way you can analyze your data.

As the interval scales, Ratio scales show us the order and the exact value between the units. However, in contrast with interval scales, Ratio oneshave an absolute zero that allows us to perform a huge range of descriptive statistics and inferential statistics.

The ratio scales possess a clear definition of zero. Any types of values that can be measured from absolute zero can be measured with a ratio scale.

The most popular examples of ratio variables are height and weight. In addition, one individual can be twice as tall as another individual.

When it comes to the possibility of analysis, Ratio scales are the king. The variables can be added, subtracted, multiplied, and divided.

So, with ratio data, you can do the same things as with interval data plus calculating ratios and correlations.

Examples of ratio data:

• Weight
• Height
• The Kelvin scale: 50 K is twice as hot as 25 K.
• Income earned in a month.
• A number of children.
• The number of elections a person has voted and etc.

In addition, ratio and interval data are both quantitative data. So, both might also be classified as Discrete or Continuous. See our post discrete vs continuous data.

In many types of research such as marketing research, social, and business research, interval and ratio scales represent the most powerful levels of measurements.

Of course, there are many things that can be done with the two other types of data measurement scales – nominal and ordinal data (see also nominal vs ordinal data). But interval and ratio data support a full-range of statistical manipulations and thus they are very reliable for drawing conclusions.

Download the following infographic in PDF for FREE

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Source: https://www.intellspot.com/interval-data-examples/