Worksheet Chapter 7: Measures of Dispersion for Grouped Data

1. From an ogive of N = 160 students, the first quartile Q₁ is read as 42 marks and the third quartile Q₃ is read as 68 marks. Find the interquartile range.

2. The mass (in kg) of 50 packages is recorded: 20-24 (f=6), 25-29 (f=14), 30-34 (f=20), 35-39 (f=10). (a) Identify the modal class. (b) Calculate the mean mass. (c) State whether mass data would be better represented by a histogram or a bar chart.

3. A grouped dataset has ∑f = 40 and ∑fx = 680. Calculate the mean value x̄.

4. True or False: A histogram for grouped data with equal class size has gaps between adjacent rectangular bars.

5. Fill in the blank: The cumulative frequency curve is also commonly known as an __________.

6. Which statistical value represents the 75th percentile of a dataset?

7. For the class interval 35 - 39 (preceded by 30 - 34), calculate (a) the midpoint and (b) the upper boundary.

8. Given ∑f = 25, ∑fx = 200, and ∑fx² = 2050 for a frequency distribution, calculate (a) the variance σ² and (b) the standard deviation σ.

9. The table below shows the distribution of scores: Class Interval: 1-5 (f=3), 6-10 (f=7), 11-15 (f=10). Find the mean x̄.

10. True or False: Standard deviation is calculated by taking the square root of variance.