Cambridge IGCSE Statistics: Frequency Distributions — Practice Questions (0479)

These are original questions written for Marlbridge, in the style and at the standard of the examination. They are not reproduced past-paper questions — Cambridge International holds copyright in its own papers. Use these alongside the official past papers available free from your board.

Related: Frequency Distributions study guide and revision notes

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Section A

1. State one advantage and one disadvantage of grouping a large data set into class intervals. [2]

2. For continuous data, which of class limits, class boundaries, class midpoints and class widths are required? [1]

3. State the formula for frequency density. [1]

Section B

4. A class interval for continuous data is given as “10 ≤ height < 20” with a frequency of 8.

(a) State the class width and the class midpoint. [2] (b) A histogram is drawn for a distribution where this class has unequal width compared with neighbouring classes. Calculate the frequency density for this class. [2]

5. A cumulative frequency table shows that 12 values fall below 20, and 30 values fall below 30.

(a) Calculate the ordinary (non-cumulative) frequency for the class interval “20 – under 30.” [2] (b) Explain the method used to recover an ordinary frequency distribution from a cumulative one in general terms. [2]

6. Two frequency distributions with equal class widths need to be compared on the same axes.

(a) Identify the most suitable diagram for this comparison, and explain why it is more suitable than a histogram for this purpose. [3] (b) State what is plotted on the horizontal axis when constructing this diagram. [1]

7. A student mistakenly reads a cumulative frequency curve to find “the number of values below 25” by reading a value from the horizontal axis at cumulative frequency 25, instead of reading the cumulative frequency at height 25 on the horizontal axis.

(a) Identify the error the student has made. [2] (b) Describe the correct method for finding the number of values below 25 using the curve. [2]

8. A data set records the number of pets owned by each student in a class (discrete data), grouped into the class “0–2 pets.”

(a) State the class limits for this class interval. [1] (b) Explain why this class would not use “class boundaries” in the same way continuous data does. [2]

9. A histogram has two classes of unequal width: Class A has width 5 and frequency 20; Class B has width 10 and frequency 30. Calculate the frequency density for each class, and state which class would be drawn with the taller bar. [4]

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Answers

1. Advantage: grouping makes a large data set easier to summarise and display [1]. Disadvantage: grouping loses precision, since the exact original values can no longer be identified once combined into class intervals [1].

2. Class boundaries, class midpoints and class widths (class limits are not required for continuous data) [1].

3. Frequency density = frequency ÷ class width [1].

4. (a) Class width = 20 − 10 = 10. Class midpoint = (10 + 20) ÷ 2 = 15 [2]. (b) Frequency density = frequency ÷ class width = 8 ÷ 10 = 0.8 [2].

5. (a) 30 − 12 = 18 [2]. (b) Subtract each cumulative total from the cumulative total of the next class up, working through the table in order; the difference between two consecutive cumulative frequencies gives the ordinary frequency for the class interval between them [2].

6. (a) A frequency polygon [1]. It is more suitable than a histogram for comparing two distributions on the same axes because two polygons (line graphs) can be overlaid clearly on the same set of axes, whereas two sets of histogram bars would overlap and obscure each other, making comparison much harder to read [1–2]. (b) The midpoint of each class interval [1].

7. (a) The student has read the curve from the wrong axis — the question asks for a count (a cumulative frequency value), which should be read from the vertical axis, not treated as if 25 were itself a cumulative frequency to look up on the horizontal axis [2]. (b) Locate 25 on the horizontal axis (the variable being measured), draw a vertical line up to the curve, then draw a horizontal line across to the vertical axis to read off the corresponding cumulative frequency, which gives the number of values below 25 [2].

8. (a) The class limits are 0 and 2 [1]. (b) Discrete data can only take specific values with genuine gaps between them (a student cannot own 1.5 pets), so class limits are meaningful and sufficient on their own; class boundaries are instead needed for continuous data, where there are no natural gaps between classes and a boundary is needed to define exactly where one class ends and the next begins [2].

9. Class A: frequency density = 20 ÷ 5 = 4. Class B: frequency density = 30 ÷ 10 = 3 [2–3]. Since a histogram’s bar height represents frequency density (not raw frequency) when class widths are unequal, Class A would be drawn with the taller bar, despite having a lower raw frequency than Class B [1–2].

A note on exam technique for this topic

Question 7 illustrates the single most common error the study guide flags for this topic: confusing which axis to read a value from on a cumulative frequency curve. Before answering any question based on a cumulative frequency graph, check explicitly whether the question is asking for a value (read from the horizontal axis) or a cumulative frequency (read from the vertical axis) — this one habit prevents the majority of marks lost on this sub-topic.