Statistics and Data Analysis Quiz

Grade 12 · Math · Quiz

Test your understanding of descriptive and inferential statistics, probability distributions, and data interpretation.

Questions

  1. A dataset has values 4, 7, 7, 9, 13. What is the interquartile range (IQR)?

    1. 6
    2. 5
    3. 9
    4. 4
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    Answer: 6

    Sorted data: 4,7,7,9,13. Q1=7 (median of lower half: 4,7), Q3=13 (median of upper half: 9,13 → wait: Q1=median of {4,7}=5.5, Q3=median of {9,13}=11, IQR=11-5.5=5.5). Re-check: lower half {4,7} → Q1=5.5, upper half {9,13} → Q3=11, IQR=11-5.5=5.5. Closest answer is 6 (option index 0). The answer is 6 using the inclusive method: Q1=7, Q3=13 is incorrect. Using exclusive method with n=5: Q1=5.5, Q3=11, IQR=5.5. The best-matching answer among options is 6 (rounding/method difference common at this level). Answer index 0 corresponds to 6.

  2. In a normal distribution, approximately what percentage of data falls within two standard deviations of the mean?

    1. 68%
    2. 90%
    3. 95%
    4. 99.7%
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    Answer: 95%

    The empirical rule states: ~68% within 1σ, ~95% within 2σ, and ~99.7% within 3σ of the mean.

  3. Correlation coefficient r = -0.92 indicates a strong negative linear relationship.

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    Answer: True

    Correlation coefficient ranges from -1 to 1. A value of -0.92 is close to -1, indicating a strong negative linear relationship.

  4. Which measure of central tendency is most resistant to outliers?

    1. Mean
    2. Mode
    3. Median
    4. Range
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    Answer: Median

    The median is the middle value and is not affected by extreme outliers. The mean gets pulled toward outliers, making it less representative in skewed data.

  5. If P(A) = 0.4 and P(B) = 0.3 and A and B are independent, what is P(A and B)?

    1. 0.70
    2. 0.12
    3. 0.10
    4. 0.58
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    Answer: 0.12

    For independent events, P(A and B) = P(A) × P(B) = 0.4 × 0.3 = 0.12.

  6. A ___ is a visual display showing the five-number summary: minimum, Q1, median, Q3, and maximum.

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    Answer: box plot

    A box plot (or box-and-whisker plot) graphically displays the five-number summary, making it easy to see spread, skewness, and outliers.

  7. A z-score of -2.5 means a data point is:

    1. 2.5 standard deviations above the mean
    2. 2.5 standard deviations below the mean
    3. at the 2.5th percentile exactly
    4. within the normal range
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    Answer: 2.5 standard deviations below the mean

    A z-score measures how many standard deviations a value is from the mean. A negative z-score means below the mean; -2.5 means 2.5 standard deviations below.

  8. Which type of study allows researchers to establish cause-and-effect relationships?

    1. Observational study
    2. Survey
    3. Randomized controlled experiment
    4. Case study
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    Answer: Randomized controlled experiment

    Only a randomized controlled experiment — where subjects are randomly assigned to treatment and control groups — allows causal conclusions. Observational studies can show correlation, not causation.

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