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 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
2.A bar chart is drawn for a set of categorical data. Write down what the height of each bar represents.
(a)The total of all the data
(b)The mean of all the data
(c)The frequency of that category
(d)The number of different categories
3.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
4.A bar chart shows the highest temperature recorded on each of five days. The temperatures were Monday 20 °C, Tuesday 22 °C, Wednesday 18 °C, Thursday 25 °C and Friday 23 °C. Write down the day on which the temperature was highest.
(a)Wednesday
(b)Monday
(c)Thursday
(d)Friday
5.A bar chart shows the number of books borrowed from a school library on each of five days. The bar heights are: Monday 12, Tuesday 18, Wednesday 9, Thursday 15 and Friday 21. Work out the total number of books borrowed over the five days.
(a)66
(b)21
(c)15
(d)75
6.A survey of 25 pupils in Derby records how many siblings each has: 0 siblings — 6 pupils, 1 sibling — 10 pupils, 2 siblings — 6 pupils, 3 siblings — 3 pupils. Calculate the mean number of siblings.
(a)1.24
(b)31
(c)1
(d)6.25
7.The seven members of Team A took 20, 21, 22, 23, 24, 25 and 40 seconds to finish a task. The seven members of Team B took 20, 30, 32, 34, 36, 38 and 40 seconds. Tomás says that because the two teams have the same range, their times are spread out in the same way. Is Tomás right? Give a reason for your answer.
(a)Yes, each team has seven times, so the spreads match
(b)Yes, sets with equal ranges are spread out alike
(c)No, Team B's times have a higher mean than Team A's
(d)No, the range uses only the fastest and slowest time
8.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
9.A sports centre in Ipswich has 2,000 members. It wants to know what its members think of its opening hours, so it asks a random sample of 100 of them. Write down what the population is in this survey.
(a)Everybody who lives in Ipswich.
(b)All 2,000 members of the sports centre.
(c)The members who say they are unhappy with the opening hours.
(d)The 100 members who were asked.
10.A café owner in Brighton records the midday temperature, x °C, and the number of hot chocolates sold, y, on 12 days. The temperatures recorded run from 4 °C to 18 °C, and the line of best fit is y = −3x + 74. The forecast for tomorrow gives a midday temperature of 12 °C. Work out the number the line of best fit predicts, and write down how much confidence the owner can have in it.
y = -3x + 74
(a)38, and completely certain, as the line gives exact sales
(b)110, and fairly confident, as 12 °C is inside the range
(c)38, but little confidence, as 12 °C is outside the range
(d)38, and fairly confident, as 12 °C is inside the range
11.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
12.Write down the statement that correctly describes the difference between correlation and causation.
(a)Causation is a link; correlation is one causing the other
(b)They mean the same, so a correlation proves causation
(c)A scatter graph can show causation but not correlation
(d)Correlation is a link; causation is one causing the other
13.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
14.A study found that people who drink more coffee tend to concentrate better at work. A coffee company says that this shows that drinking coffee improves concentration. Give the reason why this conclusion cannot be drawn.
(a)The conclusion is safe because the correlation is positive
(b)The conclusion is wrong because the correlation is negative
(c)The data show a link only; a third factor may affect both
(d)The two quantities are not linked, so nothing can be said
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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