If data set a has a larger standard deviation than data set b, what would be different about their distributions?

To understand the difference consider the figure below.

Standard deviation is square root of variance. Larger standard deviation means larger variance which means larger spread of distribution. So data set A has wider and flatter spread with more data in both tails as compared to data set B. Smaller standard deviation of data set B means data is more clustered around the mean.

hi,

you half the rectangle that you ae asking about so then you would see the scale factor of 1/2 the one u have selected, the one on top is half.

hope this !