Printable · GCSE Foundation · ages 14-16

Statistics worksheet — GCSE Foundation

Fifteen questions across the statistics statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

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Statistics worksheet — GCSE Foundation

Maths · GCSE Foundation · Statistics · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.A school has 1,000 pupils. A student wants to estimate how many of them walk to school, so she asks 8 pupils in her own class. She says her sample is large enough to give a reliable estimate for the whole school. Is she right? Give a reason for your answer.
(a)Yes — any sample size is equally reliable.
(b)No — because the sample was not taken online.
(c)No — 8 from one class is too small to represent the school.
(d)Yes — because 8 is more than half of her class.
2.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
3.A sports shop in Cardiff sold 40 pairs of football boots last month: 4 pairs of size 6, 5 pairs of size 7, 8 pairs of size 8, 13 pairs of size 9 and 10 pairs of size 10. The manager will order 40 pairs for next month and wants as many pairs as possible to be in a size customers will buy. Work out the mean size and the modal size, and write down which of the two he should use.
(a)The modal size, 9, bought by more customers than any other
(b)The range of the sizes, 4, which covers every size sold
(c)The mean size, 8, the average of the five sizes on sale
(d)The mean size, 8.5, which takes account of all 40 pairs
4.A council in Leeds wants to know what local people think about letting shops stay open later in the evening. It rings landline telephone numbers between 10 am and 2 pm on a Tuesday. Write down which group is most likely to be under-represented in the sample, and give a reason for your answer.
(a)Children, as most of them are at home at that time
(b)Unemployed people, as most of them are out at that time
(c)Retired people, as most of them are at work then
(d)Full-time workers, as most are at work at that time
5.Isla wants to find out the favourite television programme of the pupils at her school. She asks only her own close group of friends. Write down what is wrong with her sample.
(a)It is fine, as everyone she asked goes to her school
(b)It is too small, though it was picked at random
(c)It is not representative, as she picked her own friends
(d)It is too large, so she gets more replies than she needs
6.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
7.On a scatter graph of the arm span and the height of some pupils, the points rise from left to right. Write down the type of correlation this shows.
(a)Negative correlation
(b)Positive correlation
(c)No correlation
(d)Direct proportion
8.A gardener plants 600 daffodil bulbs. In March she digs up 20 of them, chosen at random, and finds that 17 have flowered. Write down what she can conclude about the 600 bulbs.
(a)Exactly 510 of the 600 bulbs have flowered
(b)Exactly 17 of the 600 bulbs have flowered
(c)About 20 of the 600 bulbs are likely to have flowered
(d)About 510 of the 600 bulbs are likely to have flowered
9.A two-way table records whether each of the 30 pupils in a class passed maths and whether they passed science. 18 pupils passed maths, 12 pupils passed science and 8 pupils passed both. Work out how many pupils passed at least one of the two subjects.
(a)22
(b)14
(c)18
(d)30
10.The number of pets owned by each of 19 pupils in a class is recorded: 0 pets — 7 pupils, 1 pet — 3 pupils, 2 pets — 4 pupils, 3 pets — 5 pupils. Work out the median number of pets.
(a)0
(b)1
(c)3
(d)19
11.The mean of 5 numbers is 8. Work out the total of the 5 numbers.
(a)40
(b)1.6
(c)13
(d)8
12.The rainfall, in millimetres, was recorded in Cambridge on six days: 12, 5, 9, 15, 3 and 11. Work out the range of the rainfall.
(a)12 mm
(b)3 mm
(c)15 mm
(d)10 mm
13.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
14.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.
15.Two classes sat the same test. The 30 pupils in Class A had a mean mark of 72. The 20 pupils in Class B had a mean mark of 82. Work out the mean mark of all 50 pupils.
(a)3800 marks
(b)78 marks
(c)76 marks
(d)77 marks

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