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Averages, spread and comparing distributions worksheet — GCSE Higher

Fifteen questions on "averages, spread and comparing distributions" — DfE statement S4. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Averages, spread and comparing distributions worksheet — GCSE Higher

Maths · GCSE Higher · S4 · Averages, spread and comparing distributions · 15 questions

MathsUKwww.geekhero.co.uk

1.The mean of 5 numbers is 8. Work out the total of the 5 numbers.
(a)40
(b)1.6
(c)13
(d)8
2.The marks scored by 11 pupils in a test are given in order: 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42. Work out the lower quartile of these marks.
(a)15
(b)19.5
(c)18
(d)27
3.Priya travels to work by one of two routes and records her journey times, in minutes, over several weeks. Route 1 has a median of 34 minutes and an interquartile range of 22 minutes. Route 2 has a median of 41 minutes and an interquartile range of 6 minutes. Priya wants the more reliable route for getting to an important meeting on time. Which route should she choose, and why?
(a)Route 2, because its median is lower
(b)Route 1, because its interquartile range is smaller
(c)Route 2, because its interquartile range is smaller
(d)Route 1, because its median is lower
4.A box plot for the ages of 40 members of a gym is drawn from this five-number summary: minimum 15, lower quartile 22, median 29, upper quartile 38, maximum 61. Work out the interquartile range shown by this box plot.
(a)7
(b)9
(c)46
(d)16
5.The delivery times, in minutes, of 15 parcels are given in order: 5, 8, 10, 12, 14, 15, 17, 19, 21, 23, 25, 27, 29, 31, 34. Work out the interquartile range of these times.
(a)−15
(b)29
(c)15
(d)8
6.The masses of eight school bags, in kilograms, are 3, 4, 4, 5, 6, 7, 8 and 11. Work out the median mass.
(a)5 kg
(b)5.5 kg
(c)8 kg
(d)4 kg
7.A shop compares customer waiting times, in minutes, at two branches over one week. Branch A had a median of 12 minutes and an interquartile range of 5 minutes. Branch B had a median of 9 minutes and an interquartile range of 11 minutes. Compare the waiting times at the two branches.
(a)Branch A waits longer, and Branch B is more consistent
(b)Branch B waits longer, and Branch B is more consistent
(c)Branch A waits longer, and Branch A is more consistent
(d)Branch B waits longer, and Branch A is more consistent
8.The mean of the four numbers 10, 15, 20 and x is 18. Work out the value of x.
(a)27
(b)72
(c)45
(d)18
9.Two classes sat the same maths test, both marked out of 100. Class A had a mean mark of 70 and a range of 30 marks. Class B had a mean mark of 70 and a range of 10 marks. Compare the marks of the two classes.
(a)The means are equal, and Class B's marks are the more consistent because its range is smaller.
(b)Class A's mean mark is higher, and Class A's marks are also the more consistent.
(c)The means are equal, and Class A's marks are the more consistent because its range is larger.
(d)Class B's mean mark is higher, and its smaller range makes its marks the more consistent.
10.Grace asked 12 children how many brothers and sisters they have. Her results, in order, were 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 6. Work out the median number of brothers and sisters.
(a)1.5
(b)1
(c)6
(d)2
11.Work out the median of these six numbers: 13, 21, 22, 36, 37, 47
(a)22
(b)36
(c)34
(d)29
12.Box plots summarise house prices, in thousands of pounds, in two towns. Town A: minimum 120, lower quartile 180, median 220, upper quartile 310, maximum 520. Town B: minimum 95, lower quartile 175, median 235, upper quartile 260, maximum 340. A buyer wants the town where house prices are typically higher but more consistent. Which statement is correct?
(a)Town A — higher median and smaller IQR
(b)Town B — higher median and smaller IQR
(c)Town B — higher median and larger IQR
(d)Town A — higher median and larger IQR
13.In a spelling test the 20 pupils in Group A had a mean mark of 80, and the 30 pupils in Group B had a mean mark of 70. Work out the mean mark of all 50 pupils.
(a)75 marks
(b)74 marks
(c)76 marks
(d)150 marks
14.Box plots summarise the test scores of two classes. Class X: minimum 20, lower quartile 45, median 60, upper quartile 70, maximum 95. Class Y: minimum 35, lower quartile 50, median 58, upper quartile 65, maximum 80. Which statement about the two classes is correct?
(a)Class X has the higher median and the narrower spread
(b)Class Y has the higher median and the wider spread
(c)Class X has the higher median and the wider spread
(d)Class Y has the higher median and the narrower spread
15.The mean mass of four parcels is 17 kg. Three of the parcels have masses 12 kg, 16 kg and 18 kg. Work out the mass of the fourth parcel.
(a)17 kg
(b)68 kg
(c)22 kg
(d)5 kg

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