Math Problem Statement

Casey surveyed 40 people about their reading habits.  She created the scatterplot below to show the ages of the people she surveyed and the number of hours per week each spends reading.

Which statement is MOST strongly supported by the scatterplot?

A. 

There is a positive correlation between the age of a person and the amount of time they spend reading.

B. 

There is a negative correlation between the age of a person and the amount of time they spend reading

C. 

There is no correlation between the age of a person and the amount of time they spend reading

D. 

There is both a positive correlation and a negative correlation between the age of a person and the amount of time they spend reading

Solution

To determine the most strongly supported statement by the scatterplot, we need to interpret the general trend of the points.

  1. Positive correlation: If older individuals tend to spend more time reading, the points on the scatterplot would show an upward trend as age increases.
  2. Negative correlation: If older individuals tend to spend less time reading, the points would show a downward trend as age increases.
  3. No correlation: If there is no apparent trend (points scattered randomly), it means no correlation exists.
  4. Both positive and negative correlation: This would indicate distinct sections of the scatterplot where there are upward and downward trends, suggesting mixed results.

Given the options:

  • If the scatterplot shows an upward trend overall, the answer is A.
  • If the scatterplot shows a downward trend overall, the answer is B.
  • If the scatterplot shows no discernible trend, the answer is C.
  • If there are clear sections of both upward and downward trends, the answer is D.

From the description alone, option A ("There is a positive correlation...") is most likely correct, provided the scatterplot demonstrates an overall increasing trend.

If you can describe or upload the scatterplot, I can confirm this for you. Would you like to proceed?


Expanding Questions:

  1. What patterns can help identify positive or negative correlation in a scatterplot?
  2. How do outliers in a scatterplot affect correlation interpretation?
  3. How can correlation strength (e.g., strong, weak) be visually assessed in a scatterplot?
  4. What are some real-life examples where positive correlations are commonly observed?
  5. How can a scatterplot with no correlation still provide useful data?

Tip: Always look for the direction of the overall trendline when interpreting scatterplots.

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Math Problem Analysis

Mathematical Concepts

Scatterplots
Correlation
Data Interpretation

Formulas

No explicit formulas used; relies on visual interpretation of scatterplot trends.

Theorems

No specific theorems; general principles of correlation and data visualization.

Suitable Grade Level

Grades 6-8