Worksheet Chapter 8: Measures of Dispersion for Ungrouped Data

1. True or False: An extreme outlier significantly affects the interquartile range more than it affects the standard deviation.

2. Two archers, Ahmad and Chong, recorded their scores over 8 rounds of shooting:
- Ahmad: Mean = 82, Standard Deviation = 3.4
- Chong: Mean = 82, Standard Deviation = 6.8
(a) Which archer showed more consistent performance? Explain your answer.
(b) If Chong wants to match Ahmad's consistency, what should Chong aim to change about his score distribution?

3. Which of the following statistics is used to construct the box plot?

4. Given a sample dataset: 3, 5, 7, 9, 11.
(a) Calculate the mean, x̄.
(b) Calculate the variance, σ².
(c) Calculate the standard deviation, σ.

5. The data below represents the daily sales (in RM) of a small kiosk over 9 days:
120, 135, 140, 142, 150, 155, 158, 165, 310
(a) Calculate the median and interquartile range.
(b) Determine whether RM 310 is an outlier using the boundary formula: Q₃ + 1.5(Q₃ - Q₁).
(c) State which measure of dispersion (Standard Deviation or Interquartile Range) is more appropriate to summarize this data set, and explain why.

6. A student obtained the following scores in 6 monthly quizzes: 14, 18, 12, 20, 16, 10. Calculate the range of the quiz scores.

7. A set of 10 numbers has a mean of 12 and a standard deviation of 3.
(a) If each number in the set is multiplied by 2, state the new mean and new standard deviation.
(b) If 4 is subsequently subtracted from each new number obtained in (a), state the final mean and final standard deviation.

8. Fill in the blank: The difference between the third quartile and the first quartile is called the ________.

9. True or False: Adding a constant value to each data point in a set increases its standard deviation by that constant.

10. Consider the set of data: 4, 7, 10, 11, 13, 16, 18, 21.
(a) Find the median.
(b) Find the first quartile (Q₁) and third quartile (Q₃).
(c) Calculate the interquartile range.