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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

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

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 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.

2. 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.

3. 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.

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. 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.

6. 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.

7. 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.

8. 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.

9. 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.

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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