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I have two box plots that I'd like to add together to form one box plot representing both plots in one. Here's an example of two box plots:

At a school 200 boys and 200 girls participated in a test. The maximum score were 80 points. I've included an example image of what the box plots could look like.

Example 1

How would I do to add these two box plots together to form one box plot with a total of 400 students and their test results?

Thank you for your help! If you need me to explain what I'm looking for any further, please don't hesitate to ask. Thank you!

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If the only information that you have is the illustration of the two box plots, you cannot determine a single "total" box plot representing 400 subjects. This is because you don't know the exact distributions within the box plots. For example, considering the median point of the whole population (i.e., the central point of the total box plots), we can only say that it is located between the medians of the two box plots. However, its exact location cannot be determined if we don't know the distributions of the left half of the blue box and of the right half of the green box.

To build a total boxplot, it is necessary to know the scores of all subjects. Merging them allows to calculate the new percentiles in the whole population, and to obtain a new, unique box plot.

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