Math Problem Statement

The scatter plot below compares students' heights to the number of text messages they send daily. What would be the best prediction of the number of text messages

sent by a student who is 68 inches tall?

Studext essage and

Text Messages

Sent Daily

160

140

120

100

80

40

20

60 61 62

63 64 65 66 67 68

Height (in inches)

A.

20

B.

45

C. 110 D. The scatter plot shows no association, so it is not possible

to make a prediction.

Solution

To determine the best prediction for the number of text messages sent by a student who is 68 inches tall:

  1. Look at the scatter plot and observe the general trend or association between height and the number of text messages sent daily.

    • If the points show a consistent increase or decrease, there's a positive or negative association.
    • If the points are scattered randomly, there may be no association.
  2. Find 68 inches on the x-axis (height) and locate the corresponding y-value (text messages sent daily) using the trend.


Answer Explanation:

  • If there's a clear positive or negative trend, estimate the y-value for 68 inches based on the line or general direction of the points.
  • If there’s no discernible pattern, the answer is D ("no association").

Let me know if you'd like me to analyze further with more context or details from the scatter plot!


Questions:

  1. What does a positive association between two variables mean in a scatter plot?
  2. How can we determine a line of best fit for a scatter plot?
  3. What other types of correlation (besides positive and negative) can scatter plots exhibit?
  4. Why might data in a scatter plot not allow for a prediction?
  5. How does interpolation differ from extrapolation in scatter plot analysis?

Tip:

When analyzing scatter plots, always identify trends (linear, quadratic, etc.) before making predictions or concluding an association.

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Math Problem Analysis

Mathematical Concepts

Data Analysis
Scatter Plots
Trends and Associations
Prediction

Formulas

No explicit formulas used, but interpretation of data trends

Theorems

Concept of Correlation in Data Analysis

Suitable Grade Level

Grades 6-8