Stats

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40 Terms

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Statistics

The science of collecting, organizing, and interpreting data.

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Individuals

The objects on which data are collected (e.g., students, states, hospitals).

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Variables

Characteristics recorded about individuals.

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Quantitative Variables

Numeric values with meaningful operations (e.g., height, weight).

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Categorical Variables

Groups or categories (e.g., gender, college type).

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Identifier Variables

Unique values assigned to individuals (e.g., ID numbers).

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Bar Charts & Pie Charts

Graphs that represent categorical data.

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Histograms

Graphs that display quantitative data distributions.

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Boxplots

Graphs that compare distributions and identify outliers.

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Dotplots & Density Plots

Graphs that represent distributions and trends.

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Mean (x̄)

Sum of all values divided by the number of values.

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Median (m)

The middle value when data is ordered.

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Range

Difference between the largest and smallest values.

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Interquartile Range (IQR)

Difference between Q3 (75th percentile) and Q1 (25th percentile).

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Standard Deviation (S)

Measures variation around the mean.

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Z-Score

Measure of how far a value is from the mean in standard deviations.

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68-95-99.7 Rule

Describes Normal Distribution percentages.

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Explanatory Variable

The variable suspected to influence another.

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Response Variable

The variable that is measured as an outcome.

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Simpson’s Paradox

When a relationship between two variables reverses due to a lurking variable.

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Proportion

A fraction representing part of a whole (e.g., 0.25 or 1/4).

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Percent

A proportion multiplied by 100 (e.g., 0.25 = 25%).

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Nominal Variables

Categories without a meaningful order (e.g., colors, names).

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Ordinal Variables

Categories with a meaningful order but no consistent difference (e.g., ranking).

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Natural Variables

Ordered with meaningful differences (e.g., temperature, income).

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Standardizing (Z-score)

Z=X−μσ (Tells how many SDs a value is from the mean).

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Shifting

Adding/subtracting a constant affects mean but not spread.

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Scaling

Multiplying/dividing a constant affects both center and spread.

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Correlation (R-Value)

Measures the strength of a linear relationship between two quantitative variables.

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Bimodal Distribution

A distribution with two peaks.

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Skewed Distribution

Distribution where one tail is longer than the other.

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Symmetric Distribution

A distribution where the left and right sides are mirror images.

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Five-Number Summary

Min, Q1, Median, Q3, Max that summarize a dataset.

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Outliers

Data points significantly higher or lower than the rest.

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Frequency Table

Table listing the number of times categories occur.

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Contingency Table

Table showing frequency distribution of variables to examine relationships.

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favstats()

An R function providing summary statistics.

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histogram()

An R function that generates a histogram to visualize distributions.

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tally()

An R function creating frequency tables for categorical data.

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bwplot()

An R function generating boxplots to compare distributions.