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If a set of values create a Median of 85 and a Standard Deviation of 5, can you say:

    1-That all the values are between 75 and 95.

    2-That there are not any values greater than 90 and less than 70.

    3-None of the above.

I'm learning by myself, practicing and starting to read about this topic, but I'm having a little trouble with the "Standard Deviation" so I make this question, hope you can help, please.

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    $\begingroup$ You might want to add the self-study tag to the question. $\endgroup$
    – Ami Tavory
    Jul 2, 2017 at 3:13
  • $\begingroup$ To gain intuition you should see how these things behave for yourself. Try making up some data and see how far you can push the largest and smallest values around . For example, look at these data sets I made: Set1: $(70, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 100)$, Set2::$(85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 105)$... Set3::$(65, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85)$. They all have median 85 and sd 5. What do they tell us about your question? How did I manage to make them up just now?...ctd $\endgroup$
    – Glen_b
    Jul 2, 2017 at 3:53
  • $\begingroup$ ctd... (Hint try playing with data sets that only take values 0, 1 or -1 and then try making the sample size larger and smaller. Getting from there to any particular sd and median is simply scaling and shifting.(multiplying and adding appropriate amounts) $\endgroup$
    – Glen_b
    Jul 2, 2017 at 3:56

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You can't say anything just knowing the median and standard deviation about a bound on the values. For instance, you could have a very large concentration of points close to the median (85), with a single outlier less than 70 or above 90 that raises the standard deviation to 5.

In general, all summary statistics (including median/standard deviation) do just that: Summarize. They will tell you things about the group of points as a whole, but will not tell you anything about individual data points.

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