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Negative Direction

Negative Direction

A way of describing the scatterplot of negatively associated data.

 

 

See also

Positive direction

Example

Problem: A teacher records the number of hours students spent watching TV per week and their test scores. The data are: (2, 92), (5, 85), (8, 78), (10, 70), (14, 60). Describe the direction of the scatterplot.
Step 1: Plot the points on a coordinate plane with hours of TV on the horizontal axis and test score on the vertical axis.
Step 2: Observe the pattern: when TV hours increase from 2 to 14, the test scores decrease from 92 to 60.
Step 3: Since the points trend downward from left to right — as one variable goes up, the other goes down — the scatterplot has a negative direction.
Answer: The scatterplot shows a negative direction because test scores decrease as hours of TV watching increase.

Another Example

Problem: A car dealership tracks the age of used cars (in years) and their selling price (in thousands of dollars). The data are: (1, 28), (3, 22), (5, 17), (7, 11), (10, 6). What direction does the scatterplot show?
Step 1: Identify the variables: car age (horizontal axis) and selling price (vertical axis).
Step 2: Check the trend: a 1-year-old car sells for 28,000,whilea10−year−oldcarsellsfor28,000, while a 10-year-old car sells for6,000. As age increases, price decreases.
Step 3: The points fall from left to right, so the scatterplot has a negative direction.
Answer: The scatterplot has a negative direction because selling price decreases as the car's age increases.

Frequently Asked Questions

How can you tell if a scatterplot has a negative direction?
Look at the overall pattern of the data points from left to right. If the points trend downward — meaning the y-values generally decrease as the x-values increase — the scatterplot has a negative direction. You can also imagine drawing a line of best fit; if that line has a negative slope (tilts downward to the right), the direction is negative.
Is negative direction the same as negative correlation?
They are closely related but not identical. Negative direction describes the visual trend you see in a scatterplot (points falling from left to right). Negative correlation is a more precise statistical measurement, often given by a correlation coefficient between −1 and 0, that quantifies how strongly the two variables are linearly related. A scatterplot with a negative direction will have a negative correlation coefficient.

Negative Direction vs. Positive Direction

Negative direction means data points slope downward from left to right — as one variable increases, the other decreases. Positive direction means data points slope upward from left to right — as one variable increases, the other also increases. Both describe the overall trend of a scatterplot, but they indicate opposite relationships between the variables.

Why It Matters

Identifying the direction of a scatterplot is one of the first steps in analyzing bivariate data. When you recognize a negative direction, you know that the two variables have an inverse relationship, which helps you make predictions — for example, predicting that more screen time is associated with lower test scores. Understanding direction also prepares you for calculating the correlation coefficient and fitting regression lines in more advanced statistics courses.

Common Mistakes

Mistake: Confusing the direction of a scatterplot with its strength.
Correction: Direction (positive or negative) tells you whether the variables increase together or move in opposite directions. Strength (strong, moderate, weak) tells you how closely the points cluster around a line. A scatterplot can have a negative direction but be either strong or weak.
Mistake: Thinking a few points that go up means the direction is not negative.
Correction: Direction describes the overall trend, not every individual point. In real data, some points may deviate from the general pattern. Focus on whether the majority of points trend downward from left to right.

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