Mathematics Asked by murphy on December 3, 2021
I’m having a hard time putting my question into words, so I made a few pictures.
Look at this plot:
Clearly, everyone will agree that these data points are following some nice smooth and continuous function. In the following plot, this is not the case.
What I’m looking for, is a word that describes this difference:
Data set A is much more ??? than data set B.
Is it smooth? Well-behaved maybe? Thanks in advance!
You can use "smoother". And the reason will be following:
You can find the Total Variation (TV) of both the data sets. The variation of B will be much more than A.
The formula of total variation is given by,
$TV(u)=sum_i |u_{i+1}-u_i|$.
Answered by Biswarup Biswas on December 3, 2021
The term you're looking for is "variance." When you look at the data, you fit a curve to it. The curve is smooth, but it's the same curve for both data points. The difference is how much the data varies form the curve, usually measured by $frac{1}{n}sum (f(x)-x)^2$ where $f(x)$ is the equation of the curve. The square root of this quantity is known as the "standard deviation"
You can read more here.
Answered by Stella Biderman on December 3, 2021
It looks like data set A is more smooth than data set B because you can easily see the trend that is there. But, the other thing to know that data set B is [most likely] more well-behaved than data set A because you can get from point to point in set B "freely" without "any traffic" by any points, as compared to set A.
Short answer: Data set A is much more smooth than data set B.
Answered by Obinna Nwakwue on December 3, 2021
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