Construct scatter plots

Detailed Explanation: Construct scatter plots

A scatter plot shows how two numerical variables are related. Each data pair is plotted as one point, written as an ordered pair $(x,y)$.

Example

A teacher records how many hours five students studied and their quiz scores.

Step 1: Choose the variables

• The independent variable goes on the horizontal axis, or $x$-axis: hours studied.
• The dependent variable goes on the vertical axis, or $y$-axis: quiz score.

Label the axes with names and units:

• $x$-axis: Hours studied (hours)
• $y$-axis: Quiz score (points)

Step 2: Choose consistent scales

Choose a scale that includes all the data and spaces the numbers evenly.

• On the $x$-axis, label from $0$ to $5$, counting by $1$ hour.
• On the $y$-axis, label from $60$ to $90$, counting by $5$ points.

The same distance on an axis must always represent the same amount.

Step 3: Write the ordered pairs

Match each number of study hours with the quiz score from the same row:

The first number tells the horizontal location, and the second number tells the vertical location. For example, $(3,75)$ means:

1. Move to $3$ hours on the $x$-axis.
2. Move up to a quiz score of $75$.
3. Place a dot there.

Step 4: Plot every pair

Plot the five points:

• $(1,62)$
• $(2,68)$
• $(3,75)$
• $(4,78)$
• $(5,88)$

Do not connect the dots. Each dot represents one student’s paired measurements.

Step 5: Examine the pattern

The points generally rise from left to right. This shows a positive association: students who studied more hours tended to have higher quiz scores. The pattern is not perfectly straight, because real data do not always follow an exact pattern.