A scatter plot displays paired numerical data as points on a coordinate plane, one point for each pair. It helps show whether two quantities have a pattern or relationship: points rising from left to right show a positive association, points falling show a negative association, and a shapeless cloud shows no association.
Each dot is one student. The cloud rises from left to right, so more hours studied tends to go with higher scores: a positive association. The orange point breaks the pattern.
Formal definition and notation
A scatter plot displays bivariate quantitative data(x1, y1), (x2, y2), …, (xn, yn) as n points in the plane, usually with the explanatory variable on the horizontal axis. It is read for direction (positive or negative), form (linear or nonlinear), strength (how tightly the points cluster), and unusual features such as outliers and clusters.
For used cars of one model, a trend line for value y (thousands of dollars) against age x (years) is y = −2.4x + 30. Predict the value of a 5-year-old car and explain the slope.
Substitute x = 5: y = −2.4(5) + 30 = −12 + 30 = 18.
The slope −2.4 means the value tends to drop by about 2.4 thousand dollars for each extra year of age.
The y-intercept 30 is the predicted value at age 0: about 30 thousand dollars.
The data show an association with age; the trend line describes it but does not, by itself, prove that age is the only cause.
Answer: A 5-year-old car is predicted to be worth about 18 thousand dollars; the value falls about 2.4 thousand dollars per year.
Common mistakes
✗ MistakeIce cream sales and sunburns rise together, so ice cream causes sunburns.
✓ InsteadBoth go up in hot, sunny weather. The scatter plot shows an association, not a cause.
A scatter plot shows association, but association alone does not prove cause. A third factor can drive both variables.
✗ MistakeConnecting the points from left to right like a line graph.
✓ InsteadLeave the points unconnected, and draw at most one trend line through the cloud.
The points are separate individuals, not a sequence in time, so a zigzag path has no meaning.
✗ MistakeWith y = 3.5x + 60, a student who studies 20 hours will score 130.
✓ InsteadPredict only within the range of the data (here 1 to 8 hours); the score cannot pass 100 anyway.
A trend line describes the data you have. Extending it far beyond that range (extrapolation) often gives impossible answers.
A line plot (dot plot) shows one variable, stacking dots above a number line. A scatter plot shows two variables, with one point for each (x, y) pair.
Scatter Plotvs.Line graph
A line graph connects points in order, usually over time, such as temperature each hour. A scatter plot leaves the points unconnected because the pairs have no order.
Quick check: 3 questions
Question 1 of 3
The points (1, 9), (2, 7), (3, 6), (4, 4), (5, 2) are plotted. What kind of association do they show?
Show answer and explanation
Answer: B. As x increases, y decreases, so the points fall from left to right: a negative association. Positive would rise, and no association would show no clear direction.
Question 2 of 3
For children aged 5 to 12, a scatter plot shows a strong positive association between shoe size and reading level. Which conclusion is best?
Show answer and explanation
Answer: D. Older children tend to have bigger feet and read at higher levels, so age drives both. Choices A and B claim a cause the data cannot show, and C ignores the strong association.
Question 3 of 3
A trend line is y = 4x + 20. What does it predict when x = 7?
Show answer and explanation
Answer: A.y = 4(7) + 20 = 28 + 20 = 48. Choice B adds 4 + 7 + 20, C multiplies 4 × 27, and D adds 7 to 20 and skips the slope.
Scatter Plot: frequently asked questions
What is a trend line on a scatter plot?
A trend line, or line of best fit, is a straight line drawn through the middle of the points so that it follows their overall direction, with about as many points above it as below. Its equation, such as y = 3.5x + 60, lets you summarize the pattern and make predictions inside the range of the data.
How do you describe a scatter plot?
Give the direction (positive, negative or none), the form (linear or curved), the strength (points tight around the pattern or spread out), and anything unusual, such as outliers or separate clusters. Then say what it means in context, for example: more hours studied goes with higher scores.
What is the difference between a scatter plot and a line graph?
A scatter plot shows the relationship between two variables measured on the same individuals, and its points are not joined. A line graph shows how one quantity changes, usually over time, and joins consecutive points with segments. Use a scatter plot to look for association, and a line graph for change over time.
DataData are facts or values collected to answer a question, such as survey answers, measurements or counts. Numerical data are numbers you measure or count, like heights; categorical data are labels or groups, like favorite colors. Data are organized in tables and shown in graphs so patterns are easy to see.Statistics · Grade 2, Grade 3, Grade 6OutlierAn outlier is a data value that is far away from most of the other values in a set. In 4, 5, 6, 7, 50, the value 50 is an outlier. A common test flags any value more than 1.5 times the interquartile range below the first quartile or above the third. Outliers pull the mean strongly.Statistics · Grade 6, Grade 7, Grade 8Line of Best FitA line of best fit is a straight line drawn through a scatter plot that shows the overall trend of the data as closely as possible. It passes through the middle of the points, with about as many above it as below. Its equation, ŷ = mx + b, lets you predict one variable from the other.Statistics · Grade 8, Algebra 1, StatisticsCorrelation CoefficientThe correlation coefficient, r, is a number from −1 to 1 that measures how closely the points of a scatter plot follow a straight line. The sign gives the direction (positive slopes up, negative slopes down), and the size gives the strength: near ± 1 is strong, near 0 is weak or none.Statistics · Algebra 1, StatisticsSlopeSlope is a number that measures how steep a line is: the change in y divided by the change in x between any two points on the line, often called rise over run. A positive slope rises from left to right, a negative slope falls, and a horizontal line has slope 0.Algebra · Grade 8, Algebra 1SubstituteSubstitute means to replace a variable with a number or with an equal expression. In 4x − 1, substituting 3 for x gives 4(3) − 1. You substitute to evaluate expressions, to check whether a number is a solution, and to solve systems of equations by swapping in an equal expression.Algebra · Grade 6, Grade 7, Grade 8Y-InterceptThe y-intercept is the point where a graph crosses the y-axis. Every point on the y-axis has x = 0, so you find the y-intercept by putting x = 0 into the equation. In y = mx + b, the y-intercept is b, written as the point (0, b).Algebra · Grade 8, Algebra 1Line PlotA line plot shows data values along a number line, often with marks above each value. Each X or dot stands for one data value, and repeated values stack in a column, so the tallest stack is the mode. Line plots make it easy to see clusters, gaps, outliers and the spread of a small data set.Statistics · Grade 3, Grade 4, Grade 5Dot PlotA dot plot is a graph that shows each data value as a dot above its place on a number line. Dots for repeated values stack up in a column, so the tallest stack shows the mode, and you can see the center, spread, gaps and outliers of the data at a glance.Statistics · Grade 3, Grade 4, Grade 5Number LineA number line is a straight line with numbers placed at equal distances along it, so every point stands for a number. Zero sits in the middle, positive numbers go to the right and negative numbers to the left. Numbers increase from left to right, so a number line shows order, distance and adding as moving.Number System · Grade 2, Grade 3, Grade 6Coordinate PlaneThe coordinate plane is a flat grid formed by a horizontal x-axis and a vertical y-axis crossing at the origin, (0, 0). Every point is located by an ordered pair, x first then y, such as (3, −2). The two axes divide the plane into four quadrants, numbered I to IV counterclockwise from the upper right.Geometry · Grade 5, Grade 6, Grade 7Ordered PairAn ordered pair is two numbers written to locate a point on the coordinate plane. It is written as (x, y): the x-value comes first, and the y-value comes second. From the origin, move x units across, then y units up or down. The order matters: (2, 5) and (5, 2) are different points.Geometry · Grade 5, Grade 6, Grade 7X-AxisThe x-axis is the horizontal number line on the coordinate plane. It crosses the vertical y-axis at the origin, (0, 0). The x-coordinate of a point tells how far to move along the x-axis, and every point on the x-axis has a y-coordinate of 0, such as (5, 0).Geometry · Grade 5, Grade 6, Grade 7CorrelationCorrelation is a measure of how strongly two variables move together in a straight-line pattern. In a positive correlation both rise together; in a negative correlation one rises as the other falls. The correlation coefficient r runs from −1 to 1: values near ± 1 are strong and values near 0 are weak. Correlation does not prove causation.Statistics · Grade 8, Algebra 1, StatisticsCausationCausation means a change in one variable directly produces a change in another: the first is the cause and the second is the effect. Two variables can be correlated without causation, because a lurking variable or chance may link them. A well-designed randomized experiment is the standard way to show causation.Statistics · Grade 8, Algebra 1, StatisticsTwo-Way TableA two-way table shows counts for two categorical variables collected from the same group, with one variable in the rows and the other in the columns. Each inside cell is a joint frequency, and the totals in the margins are marginal frequencies. Dividing a cell by a row or column total gives relative frequencies that reveal associations.Statistics · Grade 8, Algebra 1