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A scatter plot, also known as a scatter chart or scatter graph, is a tool for visualizing the relationships between variables. Scatter plots are made by plotting ordered pairs on a coordinate plane (or Cartesian plane).

To create a scatter plot, all you need is a sheet of paper, a ruler, and a pencil or pen:

- Draw two perpendicular lines, one horizontal for the $x$ -axis and the other vertical for the $y$ -axis.
- Label the axes according to the data you're comparing, time for example is usually on the $x$ -axis.
- Mark points on both axes to cover the lowest and highest coordinates (ex. if your $x$ variables range from 1 to 9, your $x$ -axis might have a scale from 0 to 10)
- Plot the points on the scatter plot (ex. for the ordered pair $\left(4,3\right)$ , count 4 units to the right from zero, 3 units up, then draw a dot.

Here is an example of data that has been organized by their variables (x,y):

Person's Age in Years ( $x$ ) | Annual Income in USD ( $y$ ) |

32 | 75,000 |

40 | 110,000 |

35 | 90,000 |

36 | 50,000 |

37 | 45,000 |

39 | 60,000 |

34 | 51,000 |

39 | 60,000 |

41 | 40,000 |

45 | 100,000 |

47 | 65,000 |

49 | 68,000 |

53 | 105,000 |

55 | 85,000 |

43 | 80,000 |

44 | 55,000 |

50 | 85,000 |

And this is the resulting scatter plot:

Scatter plots are fantastic ways of finding relationships or correlations between your two variables. You can find outliers in your data, notice groupings of data points, and even draw a line of best fit to more easily visualize correlations, which can be positive or negative as well as weak or strong. You can also find no correlation between variables.

If the value of the $y$ variable on a scatter plot tends to increase with the value of the x variable (and data points rise from the left of the graph to the right of the graph), the variables are said to have a positive correlation. In the example below, the points are scattered widely, which means the variables also have a weak correlation:

If the value of the $y$ variable tends to decrease while the value of the $x$ variable increases (and points fall from the left to the right of the graph), the variables are said to have a negative correlation. While a weak correlation shows points widely scattered, a strong correlation shows points closer in proximity.

If points on a scatter plot don't appear to have a specific tendency, the variables are said to have no correlation. Here is an example of a scatter plot showing no correlation between variables:

a. What does a scatter plot with points that don't seem to rise or fall in any direction show?

No correlation

b. If points on a scatter plot rise from left to right and are close in proximity, what does the data show?

A strong positive correlation between the variables

c. If points show a correlation but are scattered widely, what does this mean?

There is a weak correlation

d. If you graphed women's ages and the number of screwdrivers they own, what type of correlation might you find?

No correlation since these variables are unrelated

e. If you graphed people aged 50 to 80 and their average annual cost of life insurance, what type of correlation might you find?

A strong positive correlation since the annual cost of life insurance often increases steadily for people aged 50+

f. If you graphed the annual cost of auto insurance for drivers aged 16 to 25, what type of correlation might you find?

A strong negative correlation since the annual cost of auto insurance tends to decrease steadily between the ages of 16 and 25.

Common Core: 8th Grade Math Flashcards

MAP 8th Grade Math Practice Tests

Making sense of scatter plots is not always an easy task. A student can feel uncertain of their ability to correctly plot data on the graph and recognize correlations. The good news is there are tutors available to help your student gain a quality understanding of scatter plots. Whether your student wants to work on math assignments or prepare for quizzes and exams, taking part in tutoring can have a significant positive impact on their academics. To learn more about the perks of working with a tutor, contact the Educational Directors at Varsity Tutors.

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