There are several statistics which measure the shape of a distribution,
- mean - where is the average for the distribution
- median - where is the middle-point for the samples
- variance - how tightly clustered the samples are around the mean
- standard-deviation - square root of variance
- skewness - this is whether the curve is weighted left or right
- kurtosis - this measures how steep the peak of a curve
Assuming you have fair dice, then you need not consider that as a factor.
Adding (subtracting) a constant value to the dice roll would increase (decrease) the mean.
Adding more dice of the same type will increase the kurtosis, the height of the peak, and reduce the variance (more results closer to the mean).
Mixing dice with different numbers of sides would average the mean between the expected mean from the different ranges, and stretch (flatten) the curve.
discarding low (high) dice would skew the curve higher (lower).
Rolling N dice and keeping the highest K < N will skew the distribution right.
Rolling N dice and keeping the lowest K < N will skew the distribution left.
Changing the numbers on the faces can shift the curve low or high (depending upon the numbers chosen for the faces).
dividing (multiplying) by a dice face (ex: 3d6/6) would increase height of curve, reduce range.
A few examples,
A single d6, d8, d10, d12 or d20 produces a uniform distribution.
Two d6 added together produce a triangular distribution. Three d6 added together produce a steeper triangular distribution.
A d12+2 produces a uniform distribution shifted right.
Two d6+6 produces a triangular distribution shifted right.
Four d6/4 produces a curve with a higher kurtosis, but range similar to d6
What do the following look like?