What happens if standard deviation is greater than mean

In a perfect normal distribution it can be. And then any standard deviation sigma is possible In the real world we work with datasets, that can often be well descibed by a normal distribution.

Geoff K. Dec 25, Absolutely it can. Explanation: Standard deviation is a measure of how "spread out" a distribution or a data set is. Related questions How are the measures of central tendency and measures of dispersion complementary? Can the standard deviation ever be negative? What is the sample standard deviation formula? If it weren't for the fact we're reasonably confident we've seen the largest datapoint at just over 8 standard deviations away from the mean I'd think we haven't reached the second hump of the bi-modal distribution yet.

Incidentally we have the median which is 13 times smaller than the mean. For the fast answer, the plot does not exist because the mean and standard deviation are dominated by single outliers separated by more than the mean's value. If I set my histogram based on the median, I lose the important part of the graph off the right.

Even in the case when you are dealing with normal distributions, these are examples of a location-scale family of distributions which means I can choose the center mean and spread SD to be anything I want it to be. A normal probability model is a poor choice for modeling time-to-event outcomes.

If the probability model is exponential, the variance is related to the square of the mean, so with an SD greater than the mean, we can infer that there is some evidence the mean is greater than "1" on whichever units you have used to measure the outcome.

But that is purely ad hoc : you would do better to use maximum likelihood to estimate characteristics of the survival times directly, rather than make broad inferences. In the case of one-sample hypothesis testing where your hypothesis is that the mean is 0, we can say a bit more. If you mean to say that the sample mean is less than 2 times the standard error , normal probability laws tell us that there is little evidence to support that the mean is nonzero.

Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. What is implied by standard deviation being much larger than the mean? Ask Question. Asked 5 years, 7 months ago. Active 4 years ago.

Viewed 25k times. Improve this question. Joshua Joshua 1 1 gold badge 2 2 silver badges 7 7 bronze badges. In this situation, the mean is biased by "outliers" or the presence of extreme value observations.

Better measures of location are the median or one of the nonparametric estimators such as Lehman-Hodges Why is my Standard Deviation larger than the mean? Thread starter pianist Start date Mar 12, Tags deviation larger standard. JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding. May 78 7 Australia.

Hello, I have an assignment asking me to calculate the mean and standard deviation for Weekly housing cost. All of the data came from students who filled in the survey. I was given raw data in excel. I attached a notepad file with the raw data i couldnt attach the excel file with the raw data, but if you'd like to double check my calculations, you can copy and paste the data to excel Idont konw why the SD is larger than the mean. It doesn't make sense.

For example, for the 'homecostwk' category, the mean is 84 dollars, and the SD is dollars That means the data spread is from dollars to dollars How is that possible when the raw data values aren't even negative? Did I do the calculations wrong? I had to calculate for other categories too, such as food, entertainment and mobile phone weekly costs. The SD for those categories were also larger than the mean. Sep 1, USA.

There is exactly zero relationship between the standard deviation and the mean. There is no reason to expect the standard deviation to be smaller than the mean in general. Can you explain why you think it should be smaller? Reactions: 1 person. Thanks so much for your reply.

I'm going to try to explain what I mean. When I posted this question, I thought that it was odd that the SD was larger than the mean. However, now that I think about it, it is okay for the SD to be larger than the mean. My concern is that the SD is too large for the mean. For example, regarding the weekly home costs, the mean is 84 dollars. The standard deviation is dollars. This doesn't make any sense to me because how is the standard deviation below the mean a negative value?

The reason that it doesnt make sense to me is that none of the raw data values are negative AND how can it be negative when the data is about home weekly costs? Maybe I did the calculations incorrectly?

May 1, USA. Without seeing either the data or your spreadsheet, almost any answer is going to be a guess. If the number of data elements is small and you used the sample formula rather than the population formula for standard deviation, your computation of the standard deviation may be in error. Let's assume, however, that you made no error in your computation.