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Distinguish Patterns: Mini-Lesson Review

Distinguish Patterns: Mini-Lesson Review

Distinguish Patterns: Mini-Lesson Review

Mini Lesson Question

Question #1: Distinguish Patterns

Which statement best describes the scatter plot? 

scatter plot with x from -1 to 11 and y from 0 to 8 plot points: (0.25,6), (1, 5),(1,6),(1, 7.5)(1.75, 4.5), (2,4), (2.5,3.5), (2.75,5.75), (3.5,3.5)(4,2.75), (4.5,2.5)(5,3.5), (5.5,2.5),(6.3.5)(6.25, 2.75), (6.75,4.75)(7,4)(7.5,5.75),(8.5,5.25), (9,7.25),(9.5,6.26)

  1. There is an increasing linear pattern.
  2. There is a decreasing linear pattern.
  3. There is no pattern.
  4. There is a nonlinear pattern.

Distinguish Linear Patterns from Nonlinear Patterns 

A scatter plot is a graph of numerical data with two variables. If two variables vary together in a predictable way, we say there is a statistical relationship between the two variables.

  • When the points of the scatter plot seem to fall along a line, the scatter plot is linear.
  • Nonlinear patterns seem to follow a curve.
  • If the scatter plot shows no pattern, it means there is no relationship between the variables.
Scatter plot with eight black points on a grid. Points are scattered in a U-shape. The x-axis ranges from -3 to 4 and the y-axis from 10 to 35. Scatter plot with eight black points on a grid. Points display a positive trend as the x-values increase. The x-axis ranges from -3 to 4 and the y-axis from 10 to 35. Scatter plot with nine black data points showing a varied distribution. Dots are unevenly spread, no clear trend visible. Both the x-axis and y-axis range from 0 to 6.
There is a relationship. There is a relationship. There is no relationship.
It appears to be an increasing linear pattern. It appears to be nonlinear.
Examples of scatter plots illustrating linear, nonlinear, and no relationships between variables, with corresponding descriptions.

Try it

Distinguish Linear Patterns from Nonlinear Patterns

At a dinner party, every person shakes hands with every other person present. The scatter plot shows the number of people, x, and the number of handshakes, y.

Scatter plot illustrating the relationship between the number of people and the number of handshakes. The data show a positive upward trend that is growing at a faster rate as the number of people increases.

Is the relationship linear or nonlinear? Be prepared to show your reasoning.

Here is how to describe the relationship:

The scatter plot shows that the number of handshakes increases as the number of people increases. The increase is not at a constant rate, so the relationship is nonlinear.

Check Your Understanding

Which statement best describes the scatter plot?

Scatterplot with thirteen black points on a grid. The points include (1, 1), (1, 2), (1,75, 2.1), (1.7, 3.4), (2.2, 2.6), (2.3, 3.4), (3.4, 4.1), (3.5, 2.8), (3.8, 3.75), (4, 4.2), (4.2, 5.3), (4.8, 4.5), (5.1, 5.3)

  1. There is an increasing linear pattern.

  2. There is no pattern.

  3. There is a decreasing linear pattern.

  4. There is a nonlinear pattern.

There is an increasing linear pattern.

Check yourself: The points on this graph seem to increase from left to right and cluster in a way that forms that shape of a line.

Video: Distinguishing Linear Patterns

Scatter Plots Example

Watch the video to see scatter plots that show the relationship between study time, shoe size, and test score.

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