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Quiz: Data Analysis and Real-World Applications

Test your understanding of data analysis, scatterplots, correlation, lines of best fit, sequences, and applications with these questions.

1. What is a scatterplot used for?

  1. Displaying one variable over time
  2. Showing the relationship between two variables
  3. Calculating the mean of a dataset
  4. Finding the equation of a line
Show Answer

The correct answer is B. A scatterplot displays paired data as points on a coordinate plane, showing how two variables are related. Each point represents one data pair (x, y), allowing you to visualize patterns, trends, and correlations. Option A describes a time series graph. Option C is a calculation, not a visualization. Option D is done using the data, not the scatterplot itself.

Concept Tested: Scatterplot

See: Creating Scatterplots

2. What does positive correlation mean?

  1. As one variable increases, the other decreases
  2. As one variable increases, the other also increases
  3. The variables are unrelated
  4. The relationship forms a circle
Show Answer

The correct answer is B. Positive correlation occurs when both variables tend to increase together. On a scatterplot, the points form a pattern rising from left to right. Option A describes negative correlation. Option C describes no correlation. Option D doesn't describe a correlation pattern.

Concept Tested: Positive Correlation / Correlation

See: Positive Correlation

3. In a linear regression equation ŷ = 5x + 20, what does the 5 represent?

  1. The y-intercept
  2. The slope
  3. The correlation coefficient
  4. The initial value only
Show Answer

The correct answer is B. In the regression equation ŷ = mx + b, the coefficient of x (here, 5) is the slope. It represents the rate of change—for every 1-unit increase in x, y increases by 5 units. Option A is the constant term (20). Option C is represented by r, not part of the equation itself. Option D confuses slope with initial value.

Concept Tested: Linear Regression / Slope

See: The Regression Equation

4. What is the explicit formula for an arithmetic sequence?

  1. a_n = a₁ · r^(n-1)
  2. a_n = a₁ + (n-1)d
  3. a_n = a₁ + nd
  4. a_n = a₁ · d^n
Show Answer

The correct answer is B. The explicit formula for an arithmetic sequence is a_n = a₁ + (n-1)d, where a₁ is the first term, d is the common difference, and n is the term number. Option A is the geometric sequence formula. Option C forgets the -1. Option D incorrectly uses multiplication with an exponent.

Concept Tested: Arithmetic Sequence

See: Explicit Formula for Arithmetic Sequences

5. Find the 10th term of the geometric sequence 3, 6, 12, 24, ...

  1. 768
  2. 1,536
  3. 384
  4. 3,072
Show Answer

The correct answer is B. The first term is a₁ = 3 and the common ratio is r = 2. Using a_n = a₁ · r^(n-1): a₁₀ = 3 · 2⁹ = 3 · 512 = 1,536. Option A uses 2⁸ instead of 2⁹. Option C uses 2⁷. Option D uses 2¹⁰.

Concept Tested: Geometric Sequence

See: Explicit Formula for Geometric Sequences

6. Which correlation coefficient indicates the strongest relationship?

  1. r = 0.3
  2. r = -0.95
  3. r = 0.5
  4. r = 0
Show Answer

The correct answer is B. The correlation coefficient r ranges from -1 to 1. The strength is determined by the absolute value |r|. Since |-0.95| = 0.95 is closest to 1, it indicates the strongest relationship (even though it's negative correlation). Option A is weak. Option C is moderate. Option D indicates no linear relationship.

Concept Tested: Correlation / Linear Regression

See: Correlation Coefficient

7. Savings grow from $1,000 to $1,500 in 10 years with compound interest at 4% annually. Which formula applies?

  1. 1500 = 1000(1.04)^10
  2. 1500 = 1000 + 1000(0.04)(10)
  3. 1500 = 1000(1.4)^10
  4. 1500 = 1000(0.96)^10
Show Answer

The correct answer is A. Compound interest uses A = P(1 + r)^t, so 1500 = 1000(1.04)^10. The formula compounds the 4% growth each year. Option B is simple interest, not compound. Option C uses the wrong growth factor. Option D uses a decay factor instead of growth.

Concept Tested: Compound Interest

See: Compound Interest

8. What does the line of best fit represent?

  1. The exact relationship between all data points
  2. The average of all y-values
  3. A model that approximates the trend in the data
  4. The median value
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The correct answer is C. The line of best fit is a linear model that best represents the overall trend or pattern in a scatterplot. It minimizes the distances from the points to the line, providing a useful approximation for making predictions. Option A is impossible—data points rarely all lie on one line. Options B and D describe statistical measures, not trend lines.

Concept Tested: Line of Best Fit

See: Line of Best Fit

9. In the sequence 5, 10, 15, 20, ..., what is the common difference?

  1. 2
  2. 5
  3. 10
  4. 15
Show Answer

The correct answer is B. The common difference d is found by subtracting consecutive terms: 10 - 5 = 5, 15 - 10 = 5, 20 - 15 = 5. This arithmetic sequence adds 5 each time. Option A is incorrect. Options C and D give term values, not the difference.

Concept Tested: Arithmetic Sequence / Common Difference

See: Structure of Arithmetic Sequences

10. Which statement best describes negative correlation?

  1. Both variables increase together
  2. As one variable increases, the other decreases
  3. Variables show no pattern
  4. Data points form a horizontal line
Show Answer

The correct answer is B. Negative correlation means that as one variable increases, the other tends to decrease. On a scatterplot, points form a pattern falling from left to right (negative slope). Option A describes positive correlation. Option C describes no correlation. Option D doesn't represent a typical correlation pattern.

Concept Tested: Negative Correlation / Correlation

See: Negative Correlation