Construct and interpret scatter plots

Detailed Explanation: Construct and interpret scatter plots

A scatter plot shows how two quantitative variables are paired. Each data pair is written as an ordered pair $(x,y)$ and plotted where the horizontal and vertical coordinates meet.

Example

A teacher records the number of hours students studied and their test scores.

1. Choose and label the axes

Use the variable that may help explain or predict the other variable on the horizontal axis.

• Horizontal axis: Hours studied
• Vertical axis: Test score

Label both axes and include units when appropriate.

2. Choose an appropriate scale

The hours range from $1$ to $6$, so the horizontal axis could go from $0$ to $6$, counting by $1$.

The scores range from $55$ to $88$, so the vertical axis could go from $50$ to $90$, counting by $5$ or $10$.

The scale should be even and large enough to include every data value.

3. Plot each ordered pair

Rewrite the data as ordered pairs:

For example:

• Plot $(1,55)$ by moving to $1$ on the horizontal axis and up to $55$ on the vertical axis.
• Plot $(2,62)$ by moving to $2$ and up to $62$.
• Plot $(2,67)$ separately. Two students studied for $2$ hours, so there must be two points with $x=2$.
• Continue until every ordered pair is plotted.

Do not rearrange the values. In $(5,60)$, the $5$ means $5$ hours studied and the $60$ means a test score of $60$.

Interpret the pattern

Look for the direction, form, and strength of the association.

• Direction: The plot has a positive association because test scores generally increase as study hours increase.
• Form: The points follow a roughly linear pattern, meaning they tend to lie around a straight line.
• Strength: The association is moderately strong because most points are fairly close to the upward trend, although not all points fit it perfectly.
• Possible outlier: The point $(5,60)$ is unusual. A student who studied for $5$ hours scored much lower than the other students who studied for several hours.

A reasonable conclusion is:

In this group, students who studied more hours generally earned higher test scores. The pattern is roughly linear and moderately strong, but $(5,60)$ may be an outlier.

An association does not prove that studying more caused the higher scores. Other factors, such as prior knowledge or test difficulty, could also affect the results.