# Can this be done because of the relationship between the Standard Deviation and the Median?

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.

• You might want to add the self-study tag to the question. Jul 2, 2017 at 3:13
• 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 Jul 2, 2017 at 3:53
• 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) Jul 2, 2017 at 3:56