When should I use the median instead of the mean?

Use the median when the data are skewed or contain outliers, because the median is resistant: extreme values barely change it. The mean uses every value, so an outlier drags it toward itself and can misrepresent the typical value. For symmetric data with no outliers, the mean and standard deviation are appropriate; for skewed data, prefer the median and interquartile range.

What is the five-number summary in a box plot?

The five-number summary is the minimum, the first quartile, the median, the third quartile, and the maximum. In a box plot, the box spans the first to third quartile (the interquartile range), the line inside the box is the median, and the whiskers extend to the minimum and maximum. The range is max minus min, and the IQR is the third quartile minus the first.

How do I describe the association in a scatterplot?

Name four features: form (linear if the points follow a line, nonlinear if curved), direction (positive if y rises as x rises, negative if y falls), strength (strong if the points cluster tightly around a line, weak if scattered), and any outliers or clusters. Direction is about up versus down; strength is about how tightly the points follow the trend.

What do the slope and intercept of a line of best fit mean?

The slope is the predicted change in the response for each one-unit increase in the explanatory variable, a rate. The y-intercept is the predicted response when the explanatory variable is zero. Interpret both in context and with hedged language: say the slope is associated with a change, not that it causes one, and predict by substituting an x-value.

What does the correlation coefficient r tell me?

The correlation coefficient r runs from negative 1 to 1. Its sign gives the direction of a linear relationship (positive or negative), and its magnitude gives the strength: values near 1 in absolute value mean a strong linear relationship, values near 0 mean weak or no linear relationship. So r equals negative 0.92 is a strong negative linear relationship.

Why does correlation not imply causation?

A strong correlation shows that two variables move together, but a hidden lurking variable can cause both. Ice-cream sales and drownings are correlated because hot weather drives both, not because ice cream causes drowning. To establish causation you need a controlled experiment, so from a correlation you may only say the variables are associated, never that one causes the other.

GeorgiaMaths

Georgia Milestones Algebra: a complete guide to data and statistical reasoning

A deep-dive Georgia Milestones Algebra: Concepts & Connections guide to data and statistical reasoning, the statistics connection (about 15 percent of the EOC). Covers one-variable displays, center and spread and comparing distributions, scatterplots and association, lines of best fit and regression, and correlation, causation, and residuals.

Generated by Claude Opus 4.815 min readA.DSRUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

Jump to a section

What this part of the course demands
Displaying one-variable data
Center, spread, and comparing distributions
Scatterplots and two-variable data
Lines of best fit
Correlation, causation, and residuals
How this strand is examined
Check your knowledge

What this part of the course demands

This guide covers Data and Statistical Reasoning, the A.DSR domain, the statistics connection that is about 15 percent of the EOC. It runs from one-variable displays through two-variable data, fitting a line, and the interpretive checks (correlation, causation, residuals) that keep a model honest. These are very learnable points and a reliable way to add to a score above Proficient. Each dot-point page carries its own worked Milestones-style questions: displaying one-variable data, center, spread, and comparing distributions, scatterplots and two-variable data, lines of best fit, and correlation, causation, and residuals.

Displaying one-variable data

Show one-variable data with a dot plot (small sets, every value), a histogram (larger sets, frequency over intervals), or a box plot (the five-number summary). The box spans $Q_1$ to $Q_3$ (the IQR), the inside line is the median, and whiskers reach the extremes. Describe shape as symmetric, skewed right (long tail right), or skewed left.

Center, spread, and comparing distributions

Center: mean (uses all values) or median (resistant to outliers). Spread: range, IQR (resistant), and standard deviation (consistency). Use the mean and standard deviation for symmetric data, the median and IQR when there is skew or outliers. Compare two distributions by center, spread, and shape, using the same measures for both.

Scatterplots and two-variable data

A scatterplot shows paired data. Describe the association by form (linear or not), direction (positive or negative), strength (tight or scattered), and outliers. Direction is up-versus-down; strength is how tightly the points follow the trend.

Lines of best fit

A line of best fit $\hat{y} = a + bx$ summarizes a linear trend. The slope is the predicted change in $y$ per unit of $x$ ; the y-intercept is the predicted $y$ at $x = 0$ . Predict by substituting an $x$ -value; predicting within the data is interpolation (safe), far outside is extrapolation (risky).

Correlation, causation, and residuals

The correlation coefficient $r$ runs from $-1$ to $1$ : sign is direction, magnitude is strength. Correlation is not causation (a lurking variable can explain it). A residual is actual minus predicted ( $y - \hat{y}$ ); a residual plot with no pattern means a line fits, while a pattern means a line is the wrong model.

How this strand is examined

Numeric entry. Compute mean, median, IQR, a residual, or a prediction.
Multiple choice. Identify shape, interpret $r$ , or spot a correlation-causation fallacy.
Hot spot. Identify an outlier on a scatterplot or a feature of a box plot.
Constructed response. Compare distributions, interpret a fitted line, or read a residual plot.

Check your knowledge

Work these as you would for credit on the EOC.

Find the mean and median of $5, 7, 8, 8, 22$ . (2 points)
A box plot has $Q_1 = 10$ , $Q_3 = 22$ . Find the IQR. (1 point)
A distribution has a long tail to the right. Describe its shape. (1 point)
A scatterplot's points fall as $x$ rises, tightly clustered. Describe direction and strength. (1 point)
For $\hat{y} = 20 + 5x$ , interpret the slope and predict $y$ when $x = 4$ . (2 points)
Interpret $r = -0.88$ . (1 point)
A line predicts $\hat{y} = 40$ where the actual value is 36. Find the residual. (1 point)

Sources & how we know this

Georgia's K-12 Mathematics Standards (Algebra: Concepts & Connections) — Georgia Department of Education (2023)
Georgia Milestones Assessment System — Georgia Department of Education (2024)