Proportions

The relationship between two quantitative variables.

The center, spread, and shape of univariate data distribution.

Frequencies for different intervals of quantitative data.

The percentage of categories in qualitative data.

The sampling distribution is normal.

The data is biased.

Calculations using the normal curve are not valid.

The proportion of hockey players who broke a bone is exactly 0.95.

The correlation does not imply that more homework causes higher exam scores, as there may be lurking variables or it could be coincidental.

More homework directly causes higher exam scores because correlation always indicates causation in such studies.

Higher exam scores cause students to spend more time on homework since better performance motivates increased studying.

There is no relationship between homework and exam scores; the correlation is purely by chance.

Experiment

Census

Observational study

Survey

$np = 40 \geq 10$ and $n(1-p) = 160 \geq 10$

$np = 2 < 10$ and $n(1-p) = 198 < 10$

$np = 2 \geq 10$ and $n(1-p) = 198 \geq 10$

$np = 40 < 10$ and $n(1-p) = 160 < 10$

Bar graph

Histogram

Scatter plot

Pie chart

Systematic variation

Biased variation

Random variation

Non-random variation

The average value is very high or very low.

The values are spread out over a wide range.

There are many outliers in the data.

The values are close to each other.

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{1}{5}$

$\frac{2}{5}$

Approximately Symmetric Condition: The data distribution is roughly symmetric.

Random Sampling Condition: The data is collected from a random sample.

Large Counts Condition: $np \geq 10$ and $n(1-p) \geq 10$

Small Counts Condition: $np < 10$ and $n(1-p) < 10$