Printable · GCSE Foundation · ages 14-16

Averages, spread and comparing distributions worksheet — GCSE Foundation

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 Foundation

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

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1.The mean of three numbers is 50. A fourth number, 100, is added to the set. Work out the mean of the four numbers.
(a)62.5
(b)75
(c)37.5
(d)50
2.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
3.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.
4.A café sold 10 sandwiches on each of four days: 10, 10, 10, 10. Work out the range of the numbers sold.
(a)20
(b)40
(c)10
(d)0
5.The midday temperature in Leeds was recorded on each day of one week: 22 °C, 24 °C, 23 °C, 25 °C, 26 °C, 21 °C, 24 °C. Work out the mean midday temperature, giving your answer to 2 decimal places.
(a)24 °C
(b)5 °C
(c)27.5 °C
(d)23.57 °C
6.Work out the median of these five numbers: 2, 4, 7, 12, 26
(a)24
(b)14
(c)7
(d)10.2
7.Noah wrote down the numbers 9, 3, 7, 1, 5 and said, “The median is 7, because 7 is in the middle of my list.” Is Noah right? Give a reason for your answer.
(a)Yes — the mean of the five numbers is 7, so the median is 7 as well.
(b)No — in order the numbers are 1, 3, 5, 7, 9, so the median is 5.
(c)No — in order the numbers are 1, 3, 5, 7, 9, so the median is 3.
(d)Yes — 7 is the third of the five numbers he wrote, so it is the median.
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.A netball team scored 50, 83 and 68 points in three matches. Work out the mean number of points scored.
(a)68
(b)33
(c)67
(d)100.5
10.Five pupils spent these numbers of minutes on their homework: 50, 65, 55, 90, 60. Work out the median time.
(a)64 minutes
(b)40 minutes
(c)60 minutes
(d)70 minutes
11.Seven pupils were asked how many books they had read last month. Their answers were 3, 5, 5, 7, 8, 5, 3. Write down the mode.
(a)7
(b)8
(c)5
(d)3
12.A shop recorded the number of books it sold on five days: 100, 40, 70, 20, 60. Work out the range of the numbers of books sold.
(a)100
(b)58
(c)80
(d)60
13.Four books have 120, 200, 160 and 80 pages. Work out the mean number of pages.
(a)120
(b)560
(c)140
(d)280
14.Amelia's mean mark over four tests is 29. Her first three marks are 31, 26 and 26. Work out her fourth mark.
(a)116
(b)4
(c)33
(d)29
15.Work out the median of these six numbers: 13, 21, 22, 36, 37, 47
(a)22
(b)36
(c)34
(d)29

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