- Subchapter D
- Uncertainty
- For Grades: 6-8
- Learning Goal 1
- How probability is estimated depends on what is known about the situation. Estimates can be based on data from similar conditions in the past or on the assumption that all the possibilities are known.

- Learning Goal 2
- Probabilities are ratios and can be expressed as fractions, decimals, percentages, or odds.

- Learning Goal 3
- The mean, median, and mode tell different things about the middle of a data set.

- Learning Goal 4
- Comparison of data from two groups should involve comparing both their middles and the spreads around them.

- Learning Goal 5
- The larger a well-chosen sample is, the more accurately it is likely to represent the whole. But there are many ways of choosing a sample that can make it unrepresentative of the whole.

- Learning Goal 1
- For Grades: 9-12
- Learning Goal 1
- Even when there are plentiful data, it may not be obvious what mathematical model to use, or there may be insufficient computing power to use some models.

- Learning Goal 2
- When people estimate a statistic, they may also be able to say how far off the estimate might be due to chance.

- Learning Goal 3
- The middle of a data distribution might be misleading when the data are not distributed symmetrically, when there are extreme high or low values, or when the distribution is not reasonably smooth.

- Learning Goal 4
- The way data are displayed can make a big difference in how they are interpreted.

- Learning Goal 5
- Both percentages and actual counts have to be taken into account in comparing different groups; using either category by itself could be misleading.

- Learning Goal 6a
- Considering whether and how two variables are correlated requires inspecting their distributions, such as in two-way tables or scatterplots.

- Learning Goal 6bc
- A correlation between two variables doesn't mean that one causes the other; perhaps some other variable causes them both or the correlation might be attributable to chance alone. A true correlation means that differences in one variable imply differences in the other when all other things are equal.

- Learning Goal 7a
- The larger a well-chosen sample of a population is, the better it estimates population summary statistics.

- Learning Goal 7bc
- For a well-chosen sample, the size of the sample is much more important than the size of the population. To avoid intentional or unintentional bias, samples are usually selected by some random system.

- Learning Goal 8
- A physical or mathematical model can be used to estimate the probability of real-world events.

- Learning Goal 1

- For Grades: 6-8

- Uncertainty