Probability Distributions

1. Probability Distributions Some of the more general probability distributions.

2. Probability Distributions • Graphs – the horizontal axis represents the range of values a variable can take and the vertical axis represents the probability of the event.

3. Unimodal Distribution • This graph is an example of a unimodal distribution as it has only one peak.

4. Bimodal Distribution • This graph is an example of a bimodal distribution as it has two peaks. Notice that they do not have to be the same height.

5. Skewed Distribution • A skewed distribution has its peak off to one side (not in the middle).

6. Symmetric Distribution • Symmetric distributions are as the name suggests, symmetric about the central vertical line.

7. Mean • In a symmetric graph, like the one on the left, the mean value will be at the peak. • In a skewed graph, like the one on the right, the mean value will not be at the peak. In this example it will be to the left of the peak.

8. Large standard deviation • This graph has a large standard deviation as it’s peak is wide and short.

9. Small standard deviation • This graph has a small standard deviation as it’s peak it tall and narrow.

10. Area under the curve • The area under the curve indicates what the probability of that outcome is, so for example in this graph it is very likely (about 80%) for an event to occur in the range between the two small vertical lines.

11. Area under the curve • In this graph it is quite unlikely (about 10%) for an event to occur at a value less than the small vertical line.

12. Area under the curve • In this graph it is highly likely (about 90%) for an event to occur at a value greater than the small vertical line.