Worksheet Chapter 8: Measures of Dispersion for Ungrouped Data

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

2. 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.

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

4. 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.

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

6. 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?

7. 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.

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

9. 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.

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