Math Problem Statement

The data shown below was collected from a random survey about the number of hours people spent at a mall and the amount of money they spent.  

Time at Mall (hours)

Money Spent (dollars)

1.0

8

2.0

12

2.5

20

3.0

24

3.5

25

4.0

28

4.5

80

5.0

50

Considering these data, John concluded that the money spent by people at the mall shows a strong positive linear association with the amount of time they spend at the mall.

What is the value of the correlation coefficient for the data supporting John’s conclusion? Round your answer to the nearest hundredth.

Solution

The correlation coefficient for the data is 0.80. This indicates a strong positive linear association between the time spent at the mall and the amount of money spent.

Would you like more details on how to interpret this result, or do you have any questions? Here are some related questions to consider:

  1. What does a correlation coefficient of 0.80 imply about the relationship between two variables?
  2. How can outliers in the data affect the correlation coefficient?
  3. What are other methods to analyze the relationship between these variables?
  4. Can we use this data to predict future spending based on time at the mall?
  5. How can we visualize this data to better understand the relationship?

Tip: Always visualize data with a scatter plot to see the relationship clearly before concluding on correlation.

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation

Formulas

Pearson correlation coefficient formula: r = (Σ(xy) - n(μx)(μy)) / (√[Σ(x^2) - n(μx)^2] * √[Σ(y^2) - n(μy)^2])

Theorems

Properties of correlation coefficients

Suitable Grade Level

Grades 9-12

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