What happens to the distribution when we change the mean and standard deviation?


#1

Question

In the context of this exercise, what happens to the distribution when we change the mean and standard deviation?

Answer

For a normal distribution, knowing the mean and standard deviation values can provide us with a general idea on the shape of the distribution.

The mean value will determine the position that the distribution will be centered around. As a result, changing this value will not effect the shape of the distribution itself, but will essentially change the location, essentially shifting the whole distribution toward whatever the mean is.

The standard deviation will have a more substantial effect on the appearance of the distribution. Smaller standard deviations will make the distribution appear as a thinner curve, because the values will be closely centered around the mean. Larger standard deviations will make the distribution appear similar to a flat and wide curve, also centered around the mean.

If we look at the graph provided in the exercise with the three example normal distributions, we can see that these qualities hold depending on their mean and standard deviation values.