What is the difference between arithmetic and logarithmic scales?

What is the difference between arithmetic and logarithmic scales? And why does it matter for data visualization? In this blog post, we will explore these two types of scales and how they affect the way we interpret graphs and charts.

Arithmetic scale

An arithmetic scale, also known as a linear scale, is a scale where the distance between each unit is equal. For example, on an arithmetic scale from 0 to 10, the distance between 1 and 2 is the same as the distance between 9 and 10. This means that each unit represents the same absolute change in value.

Arithmetic scales are useful for showing absolute changes and comparisons. For example, if we want to compare the population of two countries over time, we can use an arithmetic scale to see how much each country has grown or shrunk in terms of number of people.

However, arithmetic scales can also be misleading when dealing with large numbers or exponential growth. For example, if we want to compare the number of COVID-19 cases in different countries, using an arithmetic scale might make it seem like some countries have very few cases compared to others, when in fact they might have similar rates of infection. This is because an arithmetic scale does not account for the relative change in value.

Logarithmic scale

A logarithmic scale, also known as a log scale, is a scale where the distance between each unit is proportional to the value of the unit. For example, on a logarithmic scale from 1 to 1000, the distance between 1 and 10 is the same as the distance between 10 and 100, or between 100 and 1000. This means that each unit represents the same relative change in value.

Logarithmic scales are useful for showing relative changes and trends. For example, if we want to compare the growth rate of two companies over time, we can use a logarithmic scale to see how fast each company is increasing or decreasing its revenue. A logarithmic scale can also help us visualize data that spans several orders of magnitude, such as the size of planets or the frequency of sound waves.

However, logarithmic scales can also be confusing when dealing with small numbers or linear growth. For example, if we want to compare the height of two people, using a logarithmic scale might make it seem like one person is much taller than the other, when in fact they might have similar heights. This is because a logarithmic scale does not account for the absolute change in value.

Conclusion

Arithmetic and logarithmic scales are two different ways of representing data on a graph or chart. They have different advantages and disadvantages depending on the type and range of data we are dealing with. It is important to choose the appropriate scale for our data visualization goals and to be aware of how it affects our perception and interpretation of the data.