I essentially have a situation where heights are normally distributed and I'm given the top 25% of heights and bottom 25% of heights. How would I find the mean and stdev? This is my first week of stats so I haven't learned much yet and we use python for a lot of the questions (I also don't know much about python yet). Is there a simple way to understand how to find these values either by hand or using python? I've looked for similar questions but they often include z-score calculations and we haven't gotten to z-score tables yet, so I assume I need to figure out how to code this situation in python. I'd appreciate any help.
2026-03-31 01:02:03.1774918923
Finding Mean And Standard Deviation Given the Values for the Top 25% and Bottom 25%
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It is very strange for a statistics class to be taught without $z$-score.
To find the mean, recall that the normal distribution is symmetrical. Hence you just have to average out the two numbers.
As for standard deviation, if one refuse to use $z$-score directly, another possible way is that by fixing the mean, the CDF is monotonic, hence you can consider solving the problem using binary search.