Cambridge IGCSE Statistics: Quartiles, percentiles, range and interquartile range (0479) – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions cover Cambridge IGCSE Statistics (0479), syllabus for examination in 2027, Topic 5 outcomes 5.1 to 5.5. Methods are in the study guide and revision notes. See also the course hub, the checklist and the free diagnostics. Quartiles of lists and tables use the halves method. Grouped answers are estimates.

Questions

1. Nine pupils each send this many emails in a day: 8, 15, 3, 11, 19, 6, 13, 10, 16. Find the lower quartile, the upper quartile and the interquartile range. [3]

2. The lengths in centimetres of ten leaves are 41, 38, 45, 52, 36, 47, 40, 44, 49, 43.

(a) Find the range. [1] (b) Find the lower quartile and the upper quartile. [3] (c) Find the interquartile range. [1]

3. The table shows the number of faults found in each of 48 items.

Faults	0	1	2	3	4	5
Frequency	12	11	9	10	4	2

(a) Write down the range. [1] (b) Find the lower quartile. [2] (c) Find the upper quartile. [2] (d) Find the interquartile range. [1]

4. A game is played 35 times. The score each time is recorded.

Score	1	2	3	4	5	6
Frequency	4	7	9	8	5	2

Find the interquartile range. [4]

5. The journey times to school of 100 pupils are summarised. The table gives the number of pupils with a journey time of t minutes or less.

t (up to)	10	20	30	40	50	60
Cumulative frequency	10	35	65	85	95	100

Using linear interpolation, estimate:

(a) the median [2] (b) the lower quartile [2] (c) the upper quartile [2] (d) the interquartile range. [1]

6. Use the data in question 5.

(a) Estimate the percentile corresponding to a journey time of 45 minutes. [2] (b) Estimate how many pupils had a journey time of more than 12 minutes and up to 35 minutes. [3]

7. A cumulative frequency polygon for the heights of 200 plants passes through these points (height in cm, cumulative frequency): (30, 0), (40, 18), (50, 70), (60, 140), (70, 185), (80, 200).

(a) Estimate how many plants are shorter than 55 cm. [2] (b) Estimate how many plants are between 45 cm and 64 cm tall. [3] (c) Estimate the 90th percentile of the heights. [3]

8. Seven whole numbers in ascending order are 4, 7, a, 12, 15, b, 22. The interquartile range is 11 and the sum of the numbers is 88. Find a and b. [5]

9. Scores in a test for two classes:

Class A: 46, 52, 38, 61, 49, 55, 43 Class B: 58, 44, 50, 47, 53, 49, 51, 56

(a) Find the interquartile range for class A. [3] (b) Find the interquartile range for class B. [3] (c) Which class has the smaller spread in the middle half of its scores? [1]

10. A pupil finds the quartiles of 2, 5, 7, 8, 11, 14, 15 and writes: “Lower half is 2, 5, 7, 8 so Q1 = 6. Upper half is 8, 11, 14, 15 so Q3 = 12.5. IQR = 6.5.”

(a) Identify the mistake. [1] (b) Find the correct lower quartile, upper quartile and interquartile range. [3]

11. The time, t minutes, that 80 people spent online one evening:

Time t	0 < t ≤ 20	20 < t ≤ 40	40 < t ≤ 60	60 < t ≤ 90	90 < t ≤ 120	120 < t ≤ 180
Frequency	8	20	24	20	6	2

(a) Write the cumulative frequencies. [1] (b) Estimate the lower quartile. [2] (c) Estimate the upper quartile. [2] (d) Estimate the interquartile range. [1] (e) Estimate the percentile for 100 minutes. [2] (f) Estimate how many people spent between 25 and 75 minutes online. [3]

12. The marks of 200 candidates in an assessment are summarised. The table gives the number scoring up to and including each mark.

Mark (up to)	20	40	50	60	70	80	100
Cumulative frequency	10	44	84	130	164	188	200

The lowest 25% of candidates fail. The top 15% earn a distinction.

(a) Estimate the highest mark that fails. [2] (b) Estimate the lowest mark that earns a distinction. [2] (c) Find how many candidates scored between these two marks, as a percentage of all candidates. [2] (d) Estimate the percentile for a mark of 65. [3]

Answers

1. Ordered: 3, 6, 8, 10, 11, 13, 15, 16, 19 [1]. Median 11 is left out. Q1 = (6 + 8)/2 = 7 [1]. Q3 = (15 + 16)/2 = 15.5, so IQR = 15.5 − 7 = 8.5 [1]. [3] Examiner insight: With odd n, leaving out the median and then using the two halves is the standard route. Show the ordered list so a slip can be traced.

2. (a) 52 − 36 = 16 cm [1]. (b) Ordered: 36, 38, 40, 41, 43, 44, 45, 47, 49, 52 [1]. Lower half 36, 38, 40, 41, 43 gives Q1 = 40 [1]. Upper half 44, 45, 47, 49, 52 gives Q3 = 47 [1]. (c) IQR = 47 − 40 = 7 cm [1]. [5] Examiner insight: With n = 10 each half has five values, so the quartile is a single data value. Give the units if the question has them.

3. (a) 5 − 0 = 5 [1]. (b) Cumulative: 12, 23, 32, 42, 46, 48. Each half has 24 values, so Q1 is the mean of the 12th and 13th values [1]. The 12th is 0 and the 13th is 1, so Q1 = 0.5 [1]. (c) Q3 is the mean of the 36th and 37th values [1]. Both lie in the row ending at 42 (positions 33 to 42), so Q3 = 3 [1]. (d) IQR = 3 − 0.5 = 2.5 [1]. [6] Examiner insight: When the two middle positions fall in different rows, the quartile is the mean of two values, so it need not be a possible number of faults. Write both positions.

4. Cumulative: 4, 11, 20, 28, 33, 35 [1]. The median is the 18th value, left out. Each half has 17 values. Q1 is the 9th value: it lies in the row ending at 11, so Q1 = 2 [1]. Q3 is the 18 + 9 = 27th value: it lies in the row ending at 28, so Q3 = 4 [1]. IQR = 4 − 2 = 2 [1]. [4] Examiner insight: Work out the positions before looking at the table, and state which method you use.

5. (a) Position 50, between 35 (t = 20) and 65 (t = 30): 20 + (50 − 35)/(65 − 35) × 10 [1] = 25 minutes [1]. (b) Position 25, between 10 (t = 10) and 35 (t = 20): 10 + (25 − 10)/(35 − 10) × 10 [1] = 16 minutes [1]. (c) Position 75, between 65 (t = 30) and 85 (t = 40): 30 + (75 − 65)/(85 − 65) × 10 [1] = 35 minutes [1]. (d) IQR = 35 − 16 = 19 minutes [1]. [7] Examiner insight: The positions 50, 25 and 75 are cumulative frequencies, not times. Show the pair of points you interpolate between.

6. (a) At t = 45 the cumulative frequency is 85 + (45 − 40)/(50 − 40) × (95 − 85) = 90 [1]. Percentile = 90/100 × 100 = 90th [1]. (b) At 35: 65 + (35 − 30)/(40 − 30) × 20 = 75 [1]. At 12: 10 + (12 − 10)/(20 − 10) × 25 = 15 [1]. Number = 75 − 15 = 60 pupils [1]. [5] Examiner insight: “More than 12 and up to 35” needs two cumulative frequencies and a subtraction. Quoting only the cumulative frequency at 35 answers a different question.

7. (a) Between (50, 70) and (60, 140): 70 + (55 − 50)/(60 − 50) × 70 [1] = 105 plants [1]. (b) At 64: 140 + (64 − 60)/(70 − 60) × 45 = 158 [1]. At 45: 18 + (45 − 40)/(50 − 40) × 52 = 44 [1]. Number = 158 − 44 = 114 plants [1]. (c) Position 0.9 × 200 = 180 [1]. It lies between (60, 140) and (70, 185): 60 + (180 − 140)/(185 − 140) × 10 [1] = 68.9 cm (3 s.f.) [1]. [8] Examiner insight: The 90th percentile is a height, not a count. Check the answer sits inside the class you interpolated in, here 60 to 70 cm.

8. The lower half is 4, 7, a, so Q1 = 7 [1]. The upper half is 15, b, 22, so Q3 = b [1]. IQR: b − 7 = 11, so b = 18 [1]. Sum: 4 + 7 + a + 12 + 15 + 18 + 22 = 78 + a = 88 [1], so a = 10 [1]. [5] Examiner insight: Use the ordering given to identify which values are the quartiles. Check your final answers against the order, here 7 ≤ 10 ≤ 12.

9. (a) Ordered A: 38, 43, 46, 49, 52, 55, 61 [1]. Q1 = 43 and Q3 = 55 [1]. IQR = 55 − 43 = 12 [1]. (b) Ordered B: 44, 47, 49, 50, 51, 53, 56, 58 [1]. Q1 = (47 + 49)/2 = 48 and Q3 = (53 + 56)/2 = 54.5 [1]. IQR = 54.5 − 48 = 6.5 [1]. (c) Class B, since 6.5 is less than 12 [1]. [7] Examiner insight: Quote both IQRs when you compare.

10. (a) The median 8 was included in both halves, but with n = 7 it should be left out [1]. (b) Lower half 2, 5, 7 gives Q1 = 5 [1]. Upper half 11, 14, 15 gives Q3 = 14 [1]. IQR = 14 − 5 = 9 [1]. [4] Examiner insight: A good error-spotting answer names the specific step that went wrong. Redoing the question without naming the error may not answer part (a).

11. (a) 8, 28, 52, 72, 78, 80 [1]. (b) Position 20, between 8 (t = 20) and 28 (t = 40): 20 + (20 − 8)/(28 − 8) × 20 [1] = 32 minutes [1]. (c) Position 60, between 52 (t = 60) and 72 (t = 90): 60 + (60 − 52)/(72 − 52) × 30 [1] = 72 minutes [1]. (d) IQR = 72 − 32 = 40 minutes [1]. (e) At 100: 72 + (100 − 90)/(120 − 90) × 6 = 74 [1]. 74/80 × 100 = 92.5th percentile [1]. (f) At 75: 52 + (75 − 60)/(90 − 60) × 20 = 62 [1]. At 25: 8 + (25 − 20)/(40 − 20) × 20 = 13 [1]. 62 − 13 = 49 people [1]. [11] Examiner insight: The class widths differ, so use the width of the class you are in (20 or 30 here). Label estimates as estimates.

12. (a) 25% of 200 = 50th value, between (40, 44) and (50, 84): 40 + (50 − 44)/(84 − 44) × 10 [1] = 41.5 [1]. (b) Top 15% starts above the 85th percentile, position 170, between (70, 164) and (80, 188): 70 + (170 − 164)/(188 − 164) × 10 [1] = 72.5 [1]. (c) 170 − 50 = 120 candidates [1], so 120/200 × 100 = 60% [1]. (d) At 65: 130 + (65 − 60)/(70 − 60) × (164 − 130) = 147 [1]. 147/200 × 100 [1] = 73.5th percentile [1]. [9] Examiner insight: A percentage-of-all question needs a division by n at the end. Keep the cumulative frequency visible so each step can be credited.

Where marks are usually lost

• Not ordering the data first.
• Including the median in both halves when n is odd.
• Forgetting the mean of two values when a quartile falls between rows.
• Mixing up positions and values: n/4 is a cumulative frequency.
• Using the wrong class width when classes are unequal.
• Not subtracting two cumulative frequencies for a part of the distribution.
• Dividing by the wrong total for a percentile.
• Writing the IQR as an interval instead of one number.
• Giving a grouped answer as exact when it is an estimate.

Next steps

• Review the methods in the revision notes.
• Re-read the worked examples in the study guide.
• Check the course hub and the checklist.
• Take one of our free 10-minute diagnostics.
• Book a free trial class.

Official syllabus

Cambridge IGCSE Statistics 0479 syllabus for examination in 2027 (version 1), Cambridge International Education, part of Cambridge University Press & Assessment. Topic 5, outcomes 5.1 to 5.5.