# Standard deviation larger than the mean.

I am doing physical activity reseach. A number of papers may say something like the amount of activity per day in minutes is mean 25, standard deviation 29.

Can anybody explain to me how the SD can be more than the mean please?

In my head this would mean that some people would be doing a negative amount of PA which isn't possible.

Many thanks.
Original post by suzywoozyG
I am doing physical activity reseach. A number of papers may say something like the amount of activity per day in minutes is mean 25, standard deviation 29.

Can anybody explain to me how the SD can be more than the mean please?

In my head this would mean that some people would be doing a negative amount of PA which isn't possible.

Many thanks.

The data could be skewed so a few examples with a very large value. As the variance is simply a statistic, it would be consistent with these values, but imagining it as a symmetric normal distribution would be incorrect.

Though it probably means a normal distribution (assuming mean and variance refer to a normal distribution) isnt a great fit for the data. An exponential distribution has identical mean and standard deviation values for instance, but its very different from nomal distribution. A poisson distribution is similar in that the variance is equal to the mean.
(edited 7 months ago)
Original post by suzywoozyG
I am doing physical activity reseach. A number of papers may say something like the amount of activity per day in minutes is mean 25, standard deviation 29.

Can anybody explain to me how the SD can be more than the mean please?

In my head this would mean that some people would be doing a negative amount of PA which isn't possible.

Many thanks.

Concrete example: suppose you have 6 people, 5 do no exercise, one does 150 minutes. Mean is 25, s.d.is sqrt(3125)>50.
Original post by mqb2766
The data could be skewed so a few examples with a very large value. As the variance is simply a statistic, it would be consistent with these values, but imagining it as a symmetric normal distribution would be incorrect.

Though it probably means a normal distribution (assuming mean and variance refer to a normal distribution) isnt a great fit for the data. An exponential distribution has identical mean and standard deviation values for instance, but its very different from nomal distribution. A poisson distribution is similar in that the variance is equal to the mean.

yeah - and tbh I'd actually expect a weird (not normal) distribution for something like minutes of activity per day*. You'd want to eyeball a histogram of the data before trying to summarise it.

*cos many people do next to nothing and some people have physically active full time jobs so you might get a double hump (bimodal distribution) or any sort of odd shape really.
Original post by Joinedup
*cos many people do next to nothing and some people have physically active full time jobs so you might get a double hump (bimodal distribution) or any sort of odd shape really.

The bold refers to the distribution and not the people?

Its one of those common things where as soon as you see mean/variance (or std dev) you immediately think of a symmetric normal distribution whereas "all" distributions have these statistics. The quotes around the all is obv for cauchy ...
(edited 7 months ago)
Original post by mqb2766
The bold refers to the distribution and not the people?

Its one of those common things where as soon as you see mean/variance (or std dev) you immediately think of a symmetric normal distribution whereas "all" distributions have these statistics. The quotes around the all is obv for cauchy ...

I suppose the most everyday example is income statistics as shown here https://www.dummies.com/article/academics-the-arts/math/statistics/how-to-interpret-standard-deviation-in-a-statistical-data-set-169772/

If the star player gets enough of a raise you'd get an SD so large it could make it look like some people were paying to be allowed to be in the team if you insisted on assuming a normal distribution.

(course there's not really an upper limit on income whereas you can't do more than 24 hours of physical exercise per 24 hours.)