Printable · GCSE Higher · ages 14-16

Statistics worksheet — GCSE Higher

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

Non-calculator

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Statistics worksheet — GCSE Higher

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

MathsUKwww.geekhero.co.uk

1.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
2.The mean of 5 numbers is 8. Work out the total of the 5 numbers.
(a)40
(b)1.6
(c)13
(d)8
3.A box plot for the ages of 40 members of a gym is drawn from this five-number summary: minimum 15, lower quartile 22, median 29, upper quartile 38, maximum 61. Work out the interquartile range shown by this box plot.
(a)7
(b)9
(c)46
(d)16
4.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
5.The delivery times, in minutes, of 15 parcels are given in order: 5, 8, 10, 12, 14, 15, 17, 19, 21, 23, 25, 27, 29, 31, 34. Work out the interquartile range of these times.
(a)−15
(b)29
(c)15
(d)8
6.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
7.A school has 1,500 pupils. The head teacher takes a random sample of 150 of them from the school register and asks how long they spend on homework. Rory says the sample is too small for the result to mean anything. Is Rory right? Give a reason for your answer.
(a)No, 150 pupils are a tenth of the school, chosen at random
(b)Yes, 150 pupils cannot be picked at random from 1,500
(c)No, a random sample always gives the exact school figure
(d)Yes, only asking all 1,500 pupils could show anything
8.In a histogram of the times, t minutes, taken by some people to complete a task, the class 15 ≤ t < 30 contains 24 people. Work out the frequency density for this class.
(a)1.6
(b)360
(c)0.625
(d)0.8
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.A café in York counts the number of customers in each of the nine hours it is open on one day: 4, 4, 4, 11, 13, 15, 18, 22 and 25. The owner says that a typical hour has about 4 customers, because 4 is the mode. Is the owner right? Give a reason for your answer.
(a)Yes, the mode is the value that occurs most often
(b)Yes, the mode is the best average for a list of numbers
(c)No, the mode here is the lowest value of the nine
(d)No, the mode can only be used when no value repeats
11.A school has 1200 pupils. A teacher wants to take a random sample of 60 of them. Write down which of these methods gives a random sample.
(a)Drawing 60 names at random from a list of all 1200 pupils
(b)Asking the 60 pupils nearest the door at the first break
(c)Asking every pupil in two of the Year 10 classes
(d)Asking the 60 pupils who volunteer to take part
12.Two classes at a school in Coventry sit the same maths test, out of 20 marks. Class A has a mean mark of 14 and a range of 6. Class B has a mean mark of 14 and a range of 14. Write a sentence comparing the two classes, using the mean and the range.
(a)Equal means; Class A is more consistent, smaller range.
(b)Class B did better on average — its range is bigger.
(c)Class A did better on average — its range is smaller.
(d)The classes can't be compared, since the means are equal.
13.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
14.Priya travels to work by one of two routes and records her journey times, in minutes, over several weeks. Route 1 has a median of 34 minutes and an interquartile range of 22 minutes. Route 2 has a median of 41 minutes and an interquartile range of 6 minutes. Priya wants the more reliable route for getting to an important meeting on time. Which route should she choose, and why?
(a)Route 2, because its median is lower
(b)Route 1, because its interquartile range is smaller
(c)Route 2, because its interquartile range is smaller
(d)Route 1, because its median is lower
15.The mean of three numbers is 50. A fourth number, 100, is added to the set. Work out the mean of the four numbers.
(a)62.5
(b)75
(c)37.5
(d)50

Build your own mix at the worksheet builder.