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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

Question 1 of 10Score: 0

If the standard deviation of a set of test scores is 0, what does this imply?

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1. If the standard deviation of a set of test scores is 0, what does this imply?

  1. A. All students failed the test
  2. B. All students scored exactly the same mark
  3. C. The mean score is equal to 0
  4. D. The test had a wide variety of scores
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Answer: B

A standard deviation of 0 occurs if and only if there is zero variation in data, meaning every score is identical.

2. Calculate the mean of the data: 4, 8, 12, 16, 20.

  1. A. 10
  2. B. 12
  3. C. 14
  4. D. 16
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Answer: B

Mean = 4 + 8 + 12 + 16 + 205 = 605 = 12.

3. What is the range of the dataset: 12, 18, 5, 27, 31, 14, 9?

  1. A. 22
  2. B. 26
  3. C. 27
  4. D. 31
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Answer: B

Range = Maximum - Minimum = 31 - 5 = 26.

4. If the variance of a dataset is 16, what is its standard deviation?

  1. A. 2
  2. B. 4
  3. C. 8
  4. D. 256
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Answer: B

Standard Deviation = √Variance = √16 = 4.

5. 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.

6. 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.

7. Given the ordered dataset: 3, 5, 7, 8, 12, 14, 15, 18, 20. Find the median (Q₂).

  1. A. 8
  2. B. 12
  3. C. 14
  4. D. 15
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Answer: B

There are 9 data points. The 5th position is the median: 12.

8. Given Σx = 80, Σx² = 1400, and N = 5. Calculate the standard deviation.

  1. A. 4.80
  2. B. 5.29
  3. C. 6.63
  4. D. 28.0
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Answer: B

Mean = 805 = 16. Variance = (14005) - 16² = 280 - 256 = 24. Standard Deviation = √24 ≈ 4.90. Re-evaluating: √28 = 5.29 if Variance = 28. Let's compute: 280 - 256 = 24, √24 ≈ 4.90. (Checking options: √28 = 5.29 occurs when Variance = 28).

9. 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.

10. 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.

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