Given that 95% of the values is between 20 and 34, what would be the mean? I think it's 27..but I'm not sure..if it's not 27, what's the right way to solve it? Please explain this to me, thank you.
2026-05-06 05:04:32.1778043872
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Finding mean given information
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The question is poorly worded. It doesn't ask what it (probably) intends to ask. If your data comes from a normal distribution, and the middle 95% of the values lie between 20 and 34, then, by symmetry, the mean must be at 27, as you say. If the question is from a beginning course on statistics, that's probably the answer they're expecting.
But, there is another way to interpret the question. It's possible (I don't know for sure) that you could have a normal distribution with (for example) 2% of its "tail" to the left of 20, and 3% of its other "tail" to the right of 34. This distribution would still have 95% of its values between 20 and 34, but its mean would not be 27. This is a much harder question, and is probably not what was intended.
There is in general no way to know the mean when you only know 95% of the data.
You've used the
normal-distributiontag. Do your values follow a normal distribution? If they do and you know where those 95% of the values are found (for example whether they are the lowest 95%, or the middle 95%, or the highest 95%), you could use a standard normal table to find the mean.