The mean determines the center of the distribution of a variable. The standard deviation determines its spread—roughly, the average distance from the observations to the mean.
Let's see how changing these parameters affects the distribution of a normal random variable (used here for illustration purposes):
STEP 1: The graph below shows the distribution of a normal random variable with mean 0 and standard deviation 1. Because the mean is set to 0, the curve is centered at zero. And because the standard deviation is set to 1, the observations are, on average, about 1 unit away from the mean.
STEP 2: Use the first slider to change the mean. This shifts the distribution left or right without changing its shape (or spread).
STEP 3: Now, use the second slider to change the standard deviation. Larger standard deviations create wider, flatter distributions because the observations are further away from the mean, on average. By contrast, smaller standard deviations create narrower, taller distributions because the observations are closer to the mean, on average. However, the center stays the same.
Move this slider to see how the mean changes the center of the distribution.
0
Move this slider to see how the standard deviation changes the spread of the distribution.
1
Mean = 0 and Standard deviation = 1
Note: This graph is a density histogram, which shows the distribution of a variable through bins of different heights. The x-axis shows the range of values the variable takes, and the height of the bins indicates the relative proportion of the observations taking those values.