Scatter Plots

Grade 8 · statistics · 100 practice problems · read aloud

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📊 Scatter Plots: Seeing Relationships in Data

What is a Scatter Plot?

A scatter plot is a graph that uses dots to show the relationship between two different sets of data. It helps us see if there is a correlation (a connection or pattern) between them. For example, you could use one to see if there's a link between study time and test scores!

How to Create and Read a Scatter Plot

  1. Label Your Axes: Put the first variable (e.g., "Study Time in Hours") on the x-axis and the second (e.g., "Test Score") on the y-axis.
  2. Plot the Points: For each pair of data, find the x-value, go up to the y-value, and place a dot. For (1 hour, 75%), you'd go to 1 on the x-axis and up to 75 on the y-axis.
  3. Look for a Trend: Step back and see what pattern the dots make. Do they go up? Down? Or are they just a random cloud?
  4. Describe the Correlation:
    • Positive: Dots trend upwards to the right. (As x increases, y increases.)
    • Negative: Dots trend downwards to the right. (As x increases, y decreases.)
    • No Correlation: Dots are spread out with no clear pattern.

Visual Examples

Example 1: Study Time vs. Test Score

Data: (1, 65), (2, 75), (1.5, 70), (3, 90), (0.5, 60)

Interpretation: The points generally go up and to the right. This shows a positive correlation—more study time is associated with higher test scores.

Example 2: Video Game Time vs. Test Score

Data: (4, 60), (2, 80), (5, 65), (3, 75), (6, 55)

Interpretation: The points generally go down and to the right. This shows a negative correlation—more video game time is associated with lower test scores.

⚠️ Common Mistakes to Avoid

  • Confusing Correlation with Causation: Just because two things are related does NOT mean one causes the other. (e.g., More ice cream sales don't cause more drownings; summer causes both!).
  • Incorrectly Labeling Axes: Always double-check which variable goes on which axis.
  • Forgetting the Trend: Look at the overall pattern, not just one or two dots that might be outliers.

💡 Tips & Tricks

  • Memory Aid: Think of the line "uP and to the right" for Positive correlation.
  • Draw a Trend Line: Lightly sketch a straight line that goes through the "middle" of all the dots. This makes the trend easier to see.
  • Strength of Correlation: The closer the dots are to a straight line, the stronger the relationship is.

How to Practice

To get better at scatter plots, try these activities:

  • Collect your own data! Measure your phone screen time and your quiz scores for a week, then plot it.
  • Find scatter plots in news articles or online and practice interpreting them.
  • Use graph paper or free online graphing tools to create plots from given data sets.

Practice problems

6 of the 100, worked through step by step — try them before opening the answer.

1 √(49) + 3² = ?

Hint: Remember to evaluate the square root first, then the exponent, and finally combine the results.

Show the answer

Answer: 16

  1. Identify the operations in the problem. We have: √(49) + 3²
  2. Evaluate the square root. √(49) means the positive square root of 49. Since 7 × 7 = 49, we get: √(49) = 7
  3. Evaluate the exponent. 3² means 3 × 3. 3 × 3 = 9
  4. Add the results. 7 + 9 = 16
  5. Final answer. The expression √(49) + 3² equals 16.

Let's solve step by step.

2 √(64) + 4² - 2³ = ?

Hint: Remember to evaluate each mathematical operation in the correct order, starting with exponents and roots before addition and subtraction.

Show the answer

Answer: 16

  1. Evaluate the square root: √(64) = 8
  2. Evaluate the exponents: 4² = 16 and 2³ = 8
  3. Substitute back into the expression: 8 + 16 - 8
  4. Perform addition and subtraction from left to right: 8 + 16 = 24, then 24 - 8 = 16

The answer is 16.

3 √(81) + 4³ - 2⁵ = ?

Hint: Remember to calculate each term separately before combining them. For example, in an expression like √(36) + 2³ - 3², you would first find the square root, then the exponent values, and finally perform the addition and subtraction.

Show the answer

Answer: 41

  1. Calculate the square root: √(81) = 9
  2. Calculate the first exponent: 4³ = 4 × 4 × 4 = 64
  3. Calculate the second exponent: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32
  4. Substitute the values: 9 + 64 - 32
  5. Perform addition: 9 + 64 = 73
  6. Perform subtraction: 73 - 32 = 41

The answer is 41.

4 √(81) + 5² - 2³ = ?

Hint: Remember to evaluate each mathematical operation in the correct order, starting with exponents and roots before addition and subtraction.

Show the answer

Answer: 26

  1. Evaluate the square root: √(81) = 9
  2. Evaluate the exponent: 5² = 25
  3. Evaluate the other exponent: 2³ = 8
  4. Substitute back into the expression: 9 + 25 - 8
  5. Perform addition: 9 + 25 = 34
  6. Perform subtraction: 34 - 8 = 26

The answer is 26.

5 (3.2 × 10⁴) ÷ (8.0 × 10²) = ?

Hint: When dividing numbers in scientific notation, divide the coefficients and subtract the exponents of the powers of 10.

Show the answer

Answer: 40

  1. Divide the coefficients: 3.2 ÷ 8.0 = 0.4
  2. Subtract the exponents: 4 - 2 = 2
  3. Combine the results: 0.4 × 10²
  4. Convert to standard form: 0.4 × 100 = 40

The answer is 40.

6 (4.2 × 10⁵) ÷ (7.0 × 10²) = ?

Hint: When dividing numbers in scientific notation, divide the coefficients and subtract the exponents separately.

Show the answer

Answer: 600

  1. Divide the coefficients: 4.2 ÷ 7.0 = 0.6
  2. Subtract the exponents: 5 - 2 = 3
  3. Combine the results: 0.6 × 10³
  4. Convert to standard form: 0.6 × 1000 = 600

The answer is 600.

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