OxfordAQA International GCSE Mathematics: Data types, tables and averages (9260) – 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 test statements S1, S2, S3 and S5 from section 3.4.1 of the OxfordAQA International GCSE Mathematics (9260) specification, Version 5.1. Questions marked “(Extension only)” test quartiles, inter-quartile range and percentiles. The rest is Core content, which can also be assessed on the Extension papers.

Revise first with the study guide or the revision notes. Course links: OxfordAQA IGCSE Mathematics hub and printable checklist. For quartiles and percentiles, positions are found using (fraction) × (n + 1).

Questions

1. State whether each is qualitative, discrete or continuous: (a) a person’s blood group, (b) the number of pages in a book, (c) the mass of a parcel. [3]

2. A clinic records waiting times, in minutes, in these classes: 0 ≤ t < 6, 6 ≤ t < 12, 12 ≤ t < 18, 18 ≤ t < 24.

(a) Which class contains a wait of exactly 12 minutes? [1] (b) Explain why waiting time is continuous data. [1] (c) A mean worked out from this table would only be an estimate. Explain why. [1]

3. A courier charges: up to 0.5 kg, £4.20; over 0.5 kg and up to 1 kg, £5.60; over 1 kg and up to 2 kg, £7.35; over 2 kg and up to 5 kg, £10.90.

(a) Write down the charge for a parcel of exactly 1 kg. [1] (b) Find the total charge for three parcels weighing 0.5 kg, 1.2 kg and 3 kg. [3]

4. A school asked 72 pupils which language they study. Some entries are missing.

	French	Spanish	German	Total
Girls	15		9	40
Boys		13		32
Total	26		17	72

(a) Copy and complete the table. [4] (b) Find the percentage of the German pupils who are boys. Give your answer to 1 decimal place. [2]

5. Fifty cyclists were surveyed. 31 mainly ride to commute and the rest mainly ride for leisure. 22 of the cyclists are under 40. 14 of the under-40s commute. Design and complete a two-way table to show this information. [4]

6. Customers in a cafe over nine days: 38, 45, 27, 45, 52, 31, 45, 57, 29. Find the mean, median, mode and range. [4]

7. (a) The mean of five numbers is 8.4. Four of them are 6, 11, 9 and 7. Find the fifth. [2] (b) In a class of 30, the 14 boys have a mean height of 168 cm and the 16 girls have a mean height of 160.5 cm. Find the mean height of all 30 pupils. [3]

8. Faulty bulbs were counted in 50 boxes.

Faulty bulbs	0	1	2	3	4	5
Boxes	6	12	15	9	5	3

(a) Write down the mode. [1] (b) Find the range. [1] (c) Find the median. [2] (d) Calculate the mean. [2]

9. The distances, d km, that 50 pupils travel to school:

Distance, d	0 ≤ d < 3	3 ≤ d < 6	6 ≤ d < 9	9 ≤ d < 12	12 ≤ d < 15
Pupils	9	17	14	7	3

(a) Write down the modal class. [1] (b) Find the class that contains the median. [2] (c) Calculate an estimate of the mean distance. [3]

10. Five employees earn (£ per month) 1850, 1920, 1980, 2040 and 9750.

(a) Find the mean. [1] (b) Find the median. [1] (c) Which average better represents typical pay? Give a reason. [2]

11. (Extension only) Times, in seconds, for 15 runners: 31, 35, 28, 42, 39, 33, 45, 30, 37, 41, 29, 36, 34, 40, 38.

(a) Work out the median, Q1 and Q3. [3] (b) Find the inter-quartile range. [1] (c) The slowest time of 45 is corrected to 60. State what happens to the range and to the inter-quartile range. [1]

12. (Extension only) (a) Nineteen scores in order: 12, 15, 17, 18, 21, 22, 24, 25, 27, 28, 30, 31, 33, 34, 36, 37, 40, 42, 45. Find the 10th and 90th percentiles. [3] (b) Thirty-nine families were asked how many pets they have.

Pets	0	1	2	3	4	5	6
Families	4	6	8	9	6	4	2

Find the median, the lower quartile, the upper quartile and the inter-quartile range. [5]

Answers

1. (a) Qualitative [1]. (b) Discrete [1]. (c) Continuous [1]. [3] Examiner insight: Give a one-word classification for each part. Reasons are not asked for, but a short reason such as “counted” or “measured” can make your thinking clear.

2. (a) 12 ≤ t < 18 [1], because the lower limit of a class is included. [1] (b) Time is measured and can take any value in a range, not only whole numbers [1]. [1] (c) The exact values are not known, so each is treated as the class midpoint [1]. [1] Examiner insight: A reason needs the idea of measuring for (b) and of unknown exact values for (c). Saying “because it is grouped” with no further explanation gives little.

3. (a) “Up to 0.5 kg” does not apply; 1 kg falls in “over 0.5 kg and up to 1 kg”, so £5.60 [1]. [1] (b) 0.5 kg costs £4.20 [1]. 1.2 kg is over 1 kg, up to 2 kg, so £7.35 [1]. 3 kg is over 2 kg, up to 5 kg, so £10.90. Total = 4.20 + 7.35 + 10.90 = £22.45 [1]. [3] Examiner insight: Boundary values such as exactly 0.5 kg or 1 kg are the usual trap. Write the charge beside each parcel before adding, so a slip in one row is easy to spot.

4. (a) Girls Spanish = 40 − 15 − 9 = 16 [1]. Boys French = 26 − 15 = 11 [1]. Boys German = 32 − 11 − 13 = 8 [1]. Spanish total = 16 + 13 = 29 [1]. [4] (b) 8 ÷ 17 × 100 [1] = 47.1% [1]. [2] Examiner insight: Check the completed table: 26 + 29 + 17 = 72 and 40 + 32 = 72. Part (b) uses the German column total as the denominator, not the number of boys.

5. Table with rows “Under 40” and “40 or over”, columns “Commute” and “Leisure”, and a totals row and column [1]:

	Commute	Leisure	Total
Under 40	14	8	22
40 or over	17	11	28
Total	31	19	50

Under-40 leisure = 22 − 14 = 8 [1]. Over-40 commute = 31 − 14 = 17 [1]. Over-40 leisure = 28 − 17 = 11, with all totals shown [1]. [4] Examiner insight: Your own categories must not overlap and must cover all 50 cyclists. Labelled rows, columns and totals are part of a well-designed table.

6. Sum = 369, so mean = 369 ÷ 9 = 41 [1]. Ordered: 27, 29, 31, 38, 45, 45, 45, 52, 57, so median = 5th value = 45 [1]. Mode = 45 [1]. Range = 57 − 27 = 30 [1]. [4] Examiner insight: Order the list before choosing the median. If the list is not ordered, the middle value of the original list is usually wrong.

7. (a) Total = 5 × 8.4 = 42 [1]. Fifth = 42 − (6 + 11 + 9 + 7) = 42 − 33 = 9 [1]. [2] (b) Total heights = 14 × 168 + 16 × 160.5 = 2352 + 2568 = 4920 [2]. Mean = 4920 ÷ 30 = 164 cm [1]. [3] Examiner insight: Averaging 168 and 160.5 directly gives 164.25, which is not the correct answer because the groups have different sizes. Work from totals.

8. (a) Mode = 2 [1]. [1] (b) Range = 5 − 0 = 5 [1]. [1] (c) Cumulative frequencies: 6, 18, 33, 42, 47, 50. Median is between the 25th and 26th values, both in the group for 2 [1]. Median = 2 [1]. [2] (d) Σfx = 0 + 12 + 30 + 27 + 20 + 15 = 104 [1]. Mean = 104 ÷ 50 = 2.08 [1]. [2] Examiner insight: The mode is the value 2, not its frequency 15. For the mean, divide by the total number of boxes (50), not by 6.

9. (a) 3 ≤ d < 6 [1]. [1] (b) n ÷ 2 = 25. Cumulative frequencies: 9, 26, 40, 47, 50 [1]. The 25th value lies in 3 ≤ d < 6 [1]. [2] (c) Midpoints 1.5, 4.5, 7.5, 10.5, 13.5. Σfx = 13.5 + 76.5 + 105 + 73.5 + 40.5 = 309 [2]. Estimated mean = 309 ÷ 50 = 6.18 km [1]. [3] Examiner insight: Use midpoints, not class limits. Write out every f × midpoint product, so that a slip in one product is easy to find and fix.

10. (a) Total = 17540, so mean = 17540 ÷ 5 = £3508 [1]. [1] (b) Middle value of the ordered list = £1980 [1]. [1] (c) The median [1], because the 9750 pulls the mean above what four of the five employees earn [1]. [2] Examiner insight: A choice of average needs a reason that refers to the data. “The median is better” alone is not enough.

11. (Extension only) (a) Ordered: 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 45. n + 1 = 16 [1]. Median at position 8 = 36 [1]. Q1 at position 4 = 31 and Q3 at position 12 = 40 [1]. [3] (b) IQR = 40 − 31 = 9 [1]. [1] (c) The range rises from 17 to 32, but the IQR stays at 9 [1]. [1] Examiner insight: Show the position as well as the value. If the value is wrong, working that shows the positions is easier to follow.

12. (Extension only) (a) n + 1 = 20 [1]. 10th percentile at position 2 = 15 [1]. 90th percentile at position 18 = 42 [1]. [3] (b) n + 1 = 40 [1]. Cumulative: 4, 10, 18, 27, 33, 37, 39 [1]. Q1 at position 10 = 1 [1]. Median at position 20 = 3, and Q3 at position 30 = 4 [1]. IQR = 4 − 1 = 3 [1]. [5] Examiner insight: Build the cumulative column first, then look up each position. The IQR is a difference of two values, not a position.

Where marks are usually lost

• Using the frequency, not the value, as the mode.
• Dividing Σfx by the number of columns instead of Σf.
• Putting a class limit into Σfx where the midpoint should go.
• Choosing the middle of an unordered list as the median.
• Reading the wrong row at a boundary such as “over 1 kg, up to 2 kg”.
• Averaging two means without allowing for group sizes.
• Giving a choice of average with no reason tied to the data.
• Overlapping or incomplete categories when designing a two-way table.
• Giving the position of a quartile instead of its value (Extension only).

Next steps

• Read the revision notes and the study guide.
• Go to the OxfordAQA IGCSE Mathematics hub or the checklist.
• Try all the free 10-minute diagnostics.
• Book a free trial class.

Official syllabus

Source: OxfordAQA International GCSE Mathematics (9260) specification, Version 5.1, for exams from May/June 2018, published by OxfordAQA. Section 3.4.1, statements S1, S2, S3 and S5.