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.

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Statistics worksheet — GCSE Higher

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

MathsUKwww.geekhero.co.uk

1.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
2.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
3.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.
4.The masses of eight school bags, in kilograms, are 3, 4, 4, 5, 6, 7, 8 and 11. Work out the median mass.
(a)5 kg
(b)5.5 kg
(c)8 kg
(d)4 kg
5.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
6.A garden centre's sales, in thousands of pounds, at the end of each quarter last year were: quarter 1 — 18, quarter 2 — 34, quarter 3 — 30, quarter 4 — 22. Work out the increase in sales from quarter 1 to the quarter with the highest sales.
(a)£16,000
(b)£12,000
(c)£34,000
(d)£16
7.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
8.A council in Leeds wants to know what local people think about letting shops stay open later in the evening. It rings landline telephone numbers between 10 am and 2 pm on a Tuesday. Write down which group is most likely to be under-represented in the sample, and give a reason for your answer.
(a)Children, as most of them are at home at that time
(b)Unemployed people, as most of them are out at that time
(c)Retired people, as most of them are at work then
(d)Full-time workers, as most are at work at that time
9.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
10.A shop compares customer waiting times, in minutes, at two branches over one week. Branch A had a median of 12 minutes and an interquartile range of 5 minutes. Branch B had a median of 9 minutes and an interquartile range of 11 minutes. Compare the waiting times at the two branches.
(a)Branch A waits longer, and Branch B is more consistent
(b)Branch B waits longer, and Branch B is more consistent
(c)Branch A waits longer, and Branch A is more consistent
(d)Branch B waits longer, and Branch A is more consistent
11.A stacked bar for one day at a café in Norwich shows total drink sales of 50 drinks, split into three parts: 22 were tea, 15 were coffee and the rest were hot chocolate. Work out the number of hot chocolates sold.
(a)35
(b)13
(c)28
(d)37
12.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
13.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
14.An estate agent in Leeds lists the prices of the five houses sold on one street last year: £170,000, £150,000, £580,000, £140,000 and £160,000. A newspaper wants to print one figure for a typical price on this street. Work out the mean and the median, and write down which figure the newspaper should print.
(a)The mean, £240,000, as a median ignores three of the prices
(b)The median, £580,000, the middle value of the list given
(c)The median, £160,000, as one very high price lifts the mean
(d)The mean, £155,000, found after the top price is dropped
15.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

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