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I want to display data that is of my own personal job applications/replies/offers between two different time periods. One where my name was a certain way, and one after I changed my name, but I want this to be on the same chart so it highlights the difference.

would a line chart that signifies the point where the name change occurred be appropriate? how is data that compares the introduction or change of a variable typically displayed?

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There are many possible ways to visualize this. Line chart is one option and probably would work if you want to show change over time. If you don´t need time, you could get rid of it by showing the variables per week or some other time unit. This will allow you to use some other chart types - for example barplots. You can even squeeze all the variables into the same star/radar plot - sometimes it works nicely.

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