stats

Individual

An object described in a dataset.

Variable

A characteristic of the individual.

Categorical variable

Places individuals into groups or categories.

Quantitative variable

Takes numerical values with mathematical meaning.

Discrete variable

Quantitative variable that represents counts.

Continuous variable

Quantitative variable that is measured on a scale.

Example of non-quantitative that looks quantitative

ZIP code (numerical-looking label).

Distribution

Describes values of a variable and how often they occur.

Frequency

Raw counts.

Relative frequency

Proportion or percent of the total.

Displays for categorical variables

Bar chart, pie chart, segmented bar chart.

Deceptive categorical displays

3D effects, unequal bar widths, distorted scales, missing labels, axis not starting at zero.

Displays for quantitative variables

Histogram, dotplot, stemplot, boxplot.

Information in all displays

Title, labels, units, scale, legend/key if needed.

Distribution shapes

Symmetric, skewed left, skewed right, uniform, bimodal, multimodal.

Describe a quantitative display (SOCS)

Shape, Center, Spread, Outliers.

Must use when comparing distributions

Comparative language (e.g., "more spread out than").

Stemplot requirement

A key explaining stems and leaves.

Measures of center

Mean (average), Median (middle), Mode (most frequent).

Median shortcut

add the two middle numbers divide by 2

Mean vs median in skewed distribution

Right skew: mean > median. Left skew: mean < median.

When to use mean vs median

Mean: symmetric with no outliers. Median: skewed or outliers present.

Measures of spread

Range (max-min), IQR (Q3-Q1), Variance, Standard Deviation.

IQR and % contained

IQR = Q3 - Q1; contains middle 50% of data.

Variance & standard deviation

Standard deviation = square root of variance.

Interpretation of standard deviation

Typical distance values fall from the mean.

5-number summary

Min, Q1, Median, Q3, Max.

Finding quartiles

Q1 = median of lower half; Q3 = median of upper half.

Outlier rule

Below Q1 - 1.5(IQR) or above Q3 + 1.5(IQR).

What boxplots don't show

Exact shape, mean, modality.

Percentile calculation

(Number of values below x / Total number of values) * 100

Cumulative relative frequency graph

Shows cumulative proportion/percent up to each class boundary.

Z-score formula

z score = value - mean / standard deviation.