PLEASE HELP ... i drew a box plot for the distribution 85,85,90,90,90,110,110,110,125 and it looked like a solid box because my median was same as Q1. Is it ok for the median to be the same as Q1??

Question

median =90

Q1 =90

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Lv / Q3 Lv

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85 90 95 100 105 110 115 120 125

Answer 1

There are 9 values you are summarizing. The median is the one in the middle (or average of the two in the middle if number of values is even) after they've been sorted from low to high. In this case the median is the 5th value = 90.

The first quartile is the value in the n x 0.25-th position, ROUNDED UP TO THE NEXT INTEGER if the product is not an integer. 9 x 0.25 = 2.25, not an integer, so rounding up to the next integer = 3-rd value. In this case the 1st quartile = 90.

So YES, it is possible for the 1st quartile and the median to take on the same value.