I am wondering, can 'fluctuation' be mentioned in a bar chart like this:

the bar chart depicts the fluctuation of the number of pets per certain category.

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Whether or not fluctuation is a good word to use depends on two factors:

  • What is on the X-axis of the bar chart?
  • How is the data behaving?

First, consider this bar chart:
I wouldn't consider this fluctuation, because the graph is merely depicting the condition of a pet store at a particular moment in time. Nothing is really fluctuating; the graph simply shows that there were more puppies than kittens at the pet store at the time this data was collected.

Now, consider this bar chart:
This comes closer to fluctuation, but I think a better word would be growth.

NOAD defines fluctuation as:

fluctuation (n.) rise and fall irregularly in number or amount

In the second graph, the sales numbers are rising, but not falling; therefore, the pet store has had steady growth in feline sales since 2011, not fluctuating sales since 2011.

Finally, let's consider this graph:
Now we have some fluctuation. The data has been collected over a period of time, and, during this time span, there were times when sales were increasing (2010 through 2012), and times when sales were decreasing (2012 through 2013). Therefore, sales have been fluctuating during the time depicted on the graph.

  • Thanks @J.R. , Do you know any websites or books in order to digest in explaining such bar charts clearly? I really want to improve myself in this area. – Hakan May 4 '14 at 8:35

Since fluctuation means a continual change or variation it can be used in a bar chart to express the relation between two variables.

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