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Quiz Chapter 8: Measures of Dispersion for Ungrouped Data

10 questions · Form 4 Mathematics Bab 8: Measures of Dispersion for Ungrouped Data

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Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. What happens to the standard deviation of a dataset if every data value is multiplied by 3?

  1. A. It remains unchanged
  2. B. It increases by 3
  3. C. It is multiplied by 3
  4. D. It is multiplied by 9
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Answer: C

Multiplying all data values by a constant k scales the standard deviation by |k|. Hence, it is multiplied by 3.

2. Which display technique shows frequency using individual stacked dots above a number line?

  1. A. Histograms
  2. B. Stem-and-leaf plot
  3. C. Dot plot
  4. D. Scatter plot
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Answer: C

A dot plot displays data points as dots placed above a number line.

3. If a constant 5 is ADDED to every value in a dataset, what happens to the standard deviation?

  1. A. It increases by 5
  2. B. It increases by 25
  3. C. It remains unchanged
  4. D. It is multiplied by 5
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Answer: C

Adding or subtracting a constant to all data values shifts the distribution without altering its spread or standard deviation.

4. For the dataset: 2, 4, 6, 8, 10, 12, 14, what is the third quartile (Q₃)?

  1. A. 8
  2. B. 10
  3. C. 12
  4. D. 14
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Answer: C

Upper half of dataset is 10, 12, 14. The middle value of the upper half (Q₃) is 12.

5. Which measure of dispersion is calculated as the square root of variance?

  1. A. Interquartile Range
  2. B. Range
  3. C. Standard Deviation
  4. D. Mean Absolute Deviation
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Answer: C

By definition, Standard Deviation = √Variance.

6. What components make up the 5-number summary used to construct a box plot?

  1. A. Mean, Median, Mode, Variance, Standard Deviation
  2. B. Minimum, Q₁, Median, Q₃, Maximum
  3. C. Minimum, Mean, Median, Mode, Maximum
  4. D. Q₁, Q₂, Q₃, Range, IQR
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Answer: B

A standard box plot is constructed using the 5-number summary: Minimum, Q₁, Median (Q₂), Q₃, and Maximum.

7. Calculate the variance of the numbers: 2, 4, 6.

  1. A. 2.67
  2. B. 4.00
  3. C. 8.00
  4. D. 1.63
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Answer: A

Mean = 4. Squared deviations: (2-4)² + (4-4)² + (6-4)² = 4 + 0 + 4 = 8. Variance = 83 ≈ 2.67.

8. Find the interquartile range for the data: 10, 12, 15, 18, 22, 25, 30.

  1. A. 13
  2. B. 15
  3. C. 18
  4. D. 20
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Answer: A

N = 7. Median (Q₂) = 18. Lower half = {10, 12, 15} → Q₁ = 12. Upper half = {22, 25, 30} → Q₃ = 25. IQR = 25 - 12 = 13.

9. What formula defines the upper boundary for identifying outliers in a dataset?

  1. A. Q₃ + 1.5 × (Q₃ - Q₁)
  2. B. Q₁ - 1.5 × (Q₃ - Q₁)
  3. C. Q₃ + 2.0 × Range
  4. D. Mean + 1.5 × Standard Deviation
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Answer: A

By definition, an upper outlier lies beyond Q₃ + 1.5 × IQR, where IQR = Q₃ - Q₁.

10. Two classes take the same test. Class A has a standard deviation of 4.2 and Class B has a standard deviation of 8.5. Which statement is true?

  1. A. Class B performed more consistently than Class A
  2. B. Class A performed more consistently than Class B
  3. C. Class A has a higher mean than Class B
  4. D. Class B has a higher mean than Class A
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Answer: B

A smaller standard deviation indicates less spread and greater consistency in performance.

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