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.The marks scored by four pupils in a quiz were 8, 8, 8, 8. Work out the mean, the median and the mode of these marks.
(a)mean = 2, median = 8, mode = 8
(b)mean = 8, median = 8, mode = 4
(c)mean = 8, median = 8, mode = 8
(d)mean = 32, median = 8, mode = 8
2.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.
3.A scatter graph shows the midday temperature, x °C, and the number of ice creams sold at a seaside kiosk, y. The line of best fit is y = 3x − 20. Give a reason why the y-intercept of this line of best fit is not a sensible estimate of the number of ice creams sold.
y = 3x − 20
(a)x = 0 gives y = −20: a negative number sold
(b)x = 0 gives y = 3, so 3 ice creams still sell
(c)Sales rise without limit as temperature rises
(d)y = −20 means 20 ice creams were given away
4.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
5.A sector of a pie chart stands for 25% of the data. Work out the angle at the centre of that sector.
(a)45°
(b)25°
(c)90°
(d)14.4°
6.A charity shop in Bath holds 2,000 books. Volunteer A checks a random sample of 50 books and finds 35 paperbacks. Volunteer B checks a different random sample of 50 books and finds 31 paperbacks. Work out the estimate each sample gives for the whole stock, and write down what the shop should do next.
(a)1,400 and 1,240, so combine the samples for one estimate
(b)1,400 and 1,240, so keep 1,400 as the larger estimate
(c)1,400 and 1,240, so one volunteer must have miscounted
(d)1,750 and 1,550, so the larger estimate must be right
7.Write down what a scatter graph is used to show.
(a)The relationship between two variables
(b)How a total is shared between categories
(c)How one quantity changes over time
(d)The frequency of each single value
8.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
9.A table shows the time each of four pupils took to run 100 m: Oliver 12 seconds, Grace 15 seconds, Ethan 10 seconds, Freya 14 seconds. Write down the name of the fastest runner and the time taken.
(a)Oliver, 12 seconds
(b)Ethan, 10 seconds
(c)Grace, 15 seconds
(d)Ethan, 15 seconds
10.A scatter graph of the number of hours, x, that pupils revised against their test score, y, has the line of best fit y = 2.5x + 15. Amelia wants a score of at least 80. Work out the least whole number of hours of revision the line of best fit suggests she needs.
y = 2.5x + 15
(a)26
(b)27
(c)38
(d)32
11.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
12.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
13.A random sample of 50 pupils at a school were asked whether they prefer sport to music. 30 of the 50 pupils said they prefer sport. The school has 500 pupils altogether. Work out an estimate for the number of the 500 pupils who prefer sport.
(a)150 pupils
(b)200 pupils
(c)60 pupils
(d)300 pupils
14.There are 10,000 pupils in a city. A researcher picks a sample of 500 of them by drawing names at random from a list of every pupil in the city. Give the reason why this method gives a representative sample.
(a)Because the pupils most willing to help are chosen
(b)Because the sample must be exactly 5% of the population
(c)Because every pupil has an equal chance of being picked
(d)Because 500 is large enough however they are chosen
15.Four books have 120, 200, 160 and 80 pages. Work out the mean number of pages.
(a)120
(b)560
(c)140
(d)280

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