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.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
2.A Year 10 class has 20 boys with a mean height of 150 cm and 10 girls with a mean height of 168 cm. Work out the mean height of all 30 pupils in the class.
(a)4,680 cm
(b)234 cm
(c)156 cm
(d)159 cm
3.A dual bar chart shows how many boys and how many girls are in a class. The bar for boys stands at 14 and the bar for girls stands at 16. Work out how many pupils are in the class altogether.
(a)32
(b)28
(c)2
(d)30
4.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
5.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
6.Four pairs of variables are listed below. Write down the pair that you would expect to show negative correlation.
(a)Minutes a candle has burned and length remaining
(b)Letters in a pupil's first name and maths score
(c)A football team's shirt colour and matches won
(d)Age of a primary-school pupil and their shoe size
7.A vertical line chart shows the number of goals scored by a football team in each of its 20 matches: 0 goals in 4 matches, 1 goal in 7 matches, 2 goals in 6 matches and 3 goals in 3 matches. Write down the modal number of goals.
(a)7
(b)1
(c)3
(d)2
8.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.
9.A scatter graph shows the number of days, x, that each of 16 tomato plants was watered and its height, y cm. The line of best fit has equation y = 1.5x + 4. Write down what the 1.5 in this equation tells you about the plants.
y = 1.5x + 4
(a)Watering a plant for 1.5 days made it 1 cm taller
(b)On average a plant grew 1.5 cm taller for each extra day
(c)The tallest plant was 1.5 cm taller than the shortest
(d)On average a plant was 1.5 cm tall before any watering
10.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.
11.On a scatter graph the horizontal axis shows height in centimetres and the vertical axis shows mass in kilograms. One point is plotted at (170, 65). Write down the height and the mass of that person.
(a)Height 65 cm, mass 170 kg
(b)Height 170 cm, mass 170 kg
(c)Height 170 cm, mass 65 kg
(d)Height 235 cm, mass 105 kg
12.A scatter graph shows the number of guests, x, at a wedding and the length of buffet table needed, y metres. The line of best fit is y = 0.5x + 2. Write down what the 2 in this equation tells you about the buffet table.
y = 0.5x + 2
(a)At least 2 guests are needed before set-up
(b)At 0 guests, the model predicts 2 m of table
(c)The table is always 2 m, whatever the guests
(d)Each extra guest adds 2 m of table needed
13.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
14.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
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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