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This is not a question about how to insert images at the top, but rather asking whether or not this is common practice.

The template I've received from my university automatically inserts figures at the top of a page if no other flags are given using \begin{figure}[t] as default.

Personally, I find it a bit awkward to be introduced to a certain image before reading about the respective explanation within the text. But I got a feeling that top-positioned images are the way one usually writes LaTeX documents.

At the end of the day, it's a question about preference, but I really want to know which of the two following is "the way to go": Left or right?

enter image description here

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You are asking a question about page layout. What is common may not be what is best for readers to understand. One of the issues with having a picture in the middle of text is that you often end up with a few lines of text above or below the figure. As a consequence, the eye often has difficulty distinguishing between what's part of the figure and what's part of the regular flow of text. That's particularly awkward if it's just one, two, or three lines of text. This does not happen if you put figures at the top or the bottom of the page, and consequently that's what most style guides recommend.

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I would say it isn't common. As you suggest it is a bit awkward. Perhaps the intent is just to get the figure onto the correct page of the manuscript, expecting that you will make adjustments.

However, since you were given the template by the university, you should probably inquire from them why it was done that way and if you are bound to it in any way.

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