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 · 15 questions

MathsUKwww.geekhero.co.uk

1.The mean of five test scores is 68. Four of the scores are 55, 62, 74 and 80. Work out the fifth score.
(a)1
(b)−69
(c)69
(d)68
2.The numbers 2, 4, 6, 8, 10 and 12 have a mean of 7 and a median of 7. The value 100 is now added to the list. Which measure is changed more by adding 100, and why?
(a)The median, because the median always jumps when the count of values changes from even to odd.
(b)The mean, because adding 100 to the list raises the mean by 100, from 7 up to 107.
(c)The mean, because every value counts towards it, so 100 pulls it from 7 up to about 20.3.
(d)The median, because 100 becomes the largest value, so the middle value moves from 7 to 12.
3.The age, in years, and the score in a reaction test are recorded for eight members of a sports club: (14, 92), (18, 88), (23, 85), (27, 80), (31, 78), (36, 74), (42, 70), (49, 65). The eight pairs are plotted on a scatter graph. Describe the correlation between age and score.
(a)Strong positive correlation
(b)No correlation
(c)Strong negative correlation
(d)Weak negative correlation
4.Priya wants to find out the favourite sport of the 900 pupils at her school. She asks 5 pupils, chosen at random. Give a reason why her sample may not give a reliable result.
(a)5 pupils are far too few to represent 900 pupils
(b)A sample must hold at least half of the population
(c)5 pupils were not chosen at random from the 900
(d)The 5 pupils may each name a different sport
5.A survey of 200 car owners in Bristol records the colour of each car: silver 74, black 52, blue 40 and red 34. Write down which average should be used to describe a typical car in this survey, and give a reason for your answer.
(a)The range, because it uses the most and least common colours
(b)The median, because the colours can be put in order
(c)The mean, because it uses all 200 of the colours
(d)The mode, because colours cannot be added or ordered
6.Five friends have heights, in cm, of 150, 152, 155, 158 and 160. A sixth friend, with a height of 170 cm, joins the group. Write down what happens to the mean and the range of the heights once this sixth friend is included.
(a)The mean stays the same but the range increases.
(b)The mean increases but the range stays the same.
(c)Both the mean and the range decrease.
(d)Both the mean and the range increase.
7.A town council wants to find out about the eating habits of the people who live in the town. It asks only the members of a local sports club. Give a reason why this sample is biased.
(a)The club has more members than the council needs
(b)The members were picked at random, so some will not reply
(c)Club members probably eat differently from most people
(d)Everyone asked lives in the town, so all are covered
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 school posts a questionnaire about school dinners to the families of all 200 pupils. Only 30 families send theirs back, and 27 of those 30 say they are unhappy with school dinners. Give a reason why this result may not represent all 200 families.
(a)Postal surveys always have low response rates.
(b)The 27 unhappy replies show most families are unhappy.
(c)The families who replied were picked at random by the school.
(d)Only families with strong feelings bothered to reply.
10.A timetable shows the departure times of a bus from Leeds to Harrogate: 08:15, 08:50, 09:25, 10:05, 10:40. Chloe arrives at the bus stop at 09:30. Work out how many minutes she has to wait for the next bus.
(a)35 minutes
(b)45 minutes
(c)5 minutes
(d)40 minutes
11.On a scatter graph of the age of a car, in years, and its value, in pounds, the points fall from left to right. Write down the type of correlation shown.
(a)Negative correlation
(b)Positive correlation
(c)Strong causation
(d)No correlation
12.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
13.A sports centre in Newcastle asks 60 members which activity they prefer: swimming 15 members, football 25 members, badminton 12 members and other activities 8 members. Work out the angle at the centre of the pie chart sector that represents badminton.
(a)150°
(b)20°
(c)72°
(d)90°
14.The mean of the numbers x, 20 and 30 is equal to the mean of the numbers 15 and 25. Work out the value of x.
(a)20
(b)−10
(c)10
(d)70
15.A sports club has 300 women members and 200 men members, 500 members in total. The club committee wants to choose a sample of 40 members that is in proportion to the club's membership. Work out how many women should be in the sample.
(a)16
(b)20
(c)30
(d)24

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