What is a Logarithmic Chart?
A logarithmic chart uses a logarithmic scale, not a linear value. A linear scale is what most charts commonly use, where values are equally spaced out like a ruler. With logarithmic scales, while the end value could be the same as the linear value, the spaces between the values are different. This offers a range of benefits, but it primarily helps to display numerical data over a large range of values in a far more compact form.
Logarithms are non-linear. For example, 10 and 20 compared to 80 and 90 are not equally spaced apart; instead 10 and 100 and 60 and 600 will be equally spaced apart because they both represent a 100 percent increase.
Basic Logarithmic Math
“Logs” are another way of writing exponential equations. This allows the separation of the exponent on one side of an equation. For instance, 42 = 16 can be rewritten as log4 16 = 2, although you would say “log to the base 2 of 16 is 4.” Log is the exponent, in this example, 4.
The equation y = Logb (x) shows that y is the exponent or power that b is raised in order to get x.
Why Use a Logarithmic Scale?
People use logarithmic scales because not everything is equal. The difference one feels between 60 degrees and 65 degrees is minimal. However, the difference between 105 degrees and 110 degrees is very noticeable. So while they are linear in nature, and if they are mapped onto a scale, they are the same distance apart; the temperature change between 105 degrees and 110 degrees feels a lot more noticeable.
A commonly understood logarithmic scale is the Richter scale. This measures the release of energy. Ask anyone who has experienced many earthquakes; they can barely feel a magnitude 2.5 or 3.5 earthquake, and it’s hard to assess the difference between them. However, the same one magnitude difference between 5.5 and 6.5 is very noticeable. And if you’ve been unfortunate enough to experience the difference between a 7.5 and an 8.5, it’s terrifying. While a linear scale is regular, each magnitude increase represents a tenfold increase in amplitude.
Other common applications of logarithmic (or exponential) functions include decibel measurements, star brightness, data storage capability (Moore’s Law), and pH balance.
When Should a Logarithmic Scale be Used?
A logarithmic scale is used when:
- Data covers a large range of values. The use of logarithms instead of linear values can reduce an axis or chart to a more manageable size.
- Data may contain exponential laws, such as the Richter scale.
A logarithmic chart is ideal to be used in two scenarios:
- When there is skewness towards large values or when some points are much smaller or larger than the remainder of the data. For instance, if a chart is displaying the profits of 100 branches of a department store and two or three branches have huge sales compared to the other branches. This will make the other 98 stores’ data more compressed and harder to see.
- To show a percentage shift or factors of multiplication. For instance, if a store sold one product in the first year, and then each year thereafter doubled the number of products sold. A traditional chart would show a long period of a small number of products and then a sharp uptick. However, a logarithmic scale will show a doubling each year; a straight line from bottom left to top right, which is far more accurate for this example.
The linear shows the number of products over time, while the logarithmic chart shows the rate of change.
Examples in Business for Logarithmic Charts
Possibly one of the more familiar uses of logarithmic charts and scales in business is for stock prices. This is because with price, a $1 increase in price becomes less influential while the price gains in value, as it is less of a percentage change.
Logarithmic charts are used for a long term analysis of price changes on a stock or share price. They are commonly used by technical analysts and traders who want to see a percentage change, not a specific dollar value change. Traders want to be able to quickly see and assess patterns.
A logarithmic scale means charts will show a visual move for a percentage move, unlike a linear chart. This is great for analysis of assets that are not volatile, helping a trader to visualize how far a price will need to move in order to attain a sell or buy target price.
What Kind of Charts Work with Logarithmic Scales?
There are a few different chart types that work well with logarithmic scales. Not all chart types will be effective or suitable. For instance, bar charts do not work well because they require visual length assessment.
A dot chart makes a chart which is far less cluttered than a bar chart. They clearly show values and can do so on a horizontal or vertical scale. They are particularly good for logarithmic scales as the dots do not show a value in themselves, unlike a bar or column chart.
Another common chart to use with logarithmic scales is a line chart. These can clearly show trend lines, which are a particular strength of logarithmic charts.
Specialized Stock and Share Charts
There are a number of share price charts that show trends and patterns. These include candlestick charts, Kagi charts, and Renko charts. These charts show a range of information such as buy and sell prices, price trends, and general sentiment about specific shares. These should be part of any share trader’s arsenal of charts to analyze data, but they work alongside logarithmic scale charts.
Benefits of a Logarithmic Chart
Trends are Easier to See
Because the figures are a true reflection of what is actually happening, it’s easier to see trends with a logarithmic chart. Once trend lines are drawn on the chart, it’s easy to see the difference between a logarithmic and linear chart, and which has a more accurate representation.
Useful for Long Term Perspectives
Over a long term, things can change. Using a logarithmic scale can be easier to see long term perspectives, which often have huge periods of change and growth on a scale. On a linear scale, these may not be easy to display.
A Wider Range of Data Can be Displayed
Because a linear scale is equally spread out, there are a few outliers. Outliers can squeeze all the other data together, making it difficult to see clearly. A logarithmic scale can avoid this problem and make it far easier to see the individual data points.
Disadvantages of a Logarithmic Chart
On a logarithmic scale there is no absolute zero (a value cannot be to the power of zero), so the chart cannot start at zero. For some charts, this will not present a problem, but for others this can be problematic. There is no way to “solve” this, but it is something the chart-maker needs to keep in mind.
Difficult to Analyze
For people wanting to see values, or expecting to see something specific, then a logarithmic chart will be difficult to interpret. These charts are not designed to show an actual figure but trends.
The person reviewing the chart must understand that it is logarithmic, not linear. This should be clear on the scale of the chart.
No Negative Values
You cannot plot positive and negative numbers on the same logarithmic chart. This is because there cannot be logarithmic negative numbers.