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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. 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).

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. Find the interquartile range for a dataset with Q₁ = 15 and Q₃ = 38.

  1. A. 23
  2. B. 53
  3. C. 26.5
  4. D. 15
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Answer: A

Interquartile Range = Q₃ - Q₁ = 38 - 15 = 23.

8. In a box plot, what value is represented by the line drawn inside the box?

  1. A. Mean
  2. B. Mode
  3. C. Median (Q₂)
  4. D. Range
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Answer: C

The line inside the box of a box plot marks the second quartile, which is the median.

9. For the dataset: 2, 4, 6, 8, 10, 12, 14, what is the first quartile (Q₁)?

  1. A. 4
  2. B. 6
  3. C. 8
  4. D. 10
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Answer: A

Lower half of dataset is 2, 4, 6. The middle value of the lower half (Q₁) is 4.

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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