Printable · GCSE Higher · ages 14-16

Averages, spread and comparing distributions worksheet — GCSE Higher

Fifteen questions on "averages, spread and comparing distributions" — DfE statement S4. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Averages, spread and comparing distributions worksheet — GCSE Higher

Maths · GCSE Higher · S4 · Averages, spread and comparing distributions · 15 questions

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1.The midday temperature in Leeds was recorded on each day of one week: 22 °C, 24 °C, 23 °C, 25 °C, 26 °C, 21 °C, 24 °C. Work out the mean midday temperature, giving your answer to 2 decimal places.
(a)24 °C
(b)5 °C
(c)27.5 °C
(d)23.57 °C
2.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
3.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
4.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.
5.The mean of 5 numbers is 8. Work out the total of the 5 numbers.
(a)40
(b)1.6
(c)13
(d)8
6.The times, in seconds, taken by 11 runners to finish a race are given in order: 40, 42, 45, 47, 50, 52, 55, 58, 60, 63, 65. Work out the upper quartile of these times.
(a)52
(b)60
(c)45
(d)58
7.Box plots summarise house prices, in thousands of pounds, in two towns. Town A: minimum 120, lower quartile 180, median 220, upper quartile 310, maximum 520. Town B: minimum 95, lower quartile 175, median 235, upper quartile 260, maximum 340. A buyer wants the town where house prices are typically higher but more consistent. Which statement is correct?
(a)Town A — higher median and smaller IQR
(b)Town B — higher median and smaller IQR
(c)Town B — higher median and larger IQR
(d)Town A — higher median and larger IQR
8.Work out the median of these six numbers: 13, 21, 22, 36, 37, 47
(a)22
(b)36
(c)34
(d)29
9.Box plots summarise the test scores of two classes. Class X: minimum 20, lower quartile 45, median 60, upper quartile 70, maximum 95. Class Y: minimum 35, lower quartile 50, median 58, upper quartile 65, maximum 80. Which statement about the two classes is correct?
(a)Class X has the higher median and the narrower spread
(b)Class Y has the higher median and the wider spread
(c)Class X has the higher median and the wider spread
(d)Class Y has the higher median and the narrower spread
10.Grace asked 12 children how many brothers and sisters they have. Her results, in order, were 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 6. Work out the median number of brothers and sisters.
(a)1.5
(b)1
(c)6
(d)2
11.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
12.A garden centre records the heights, in cm, of eleven seedlings. In order, the heights are 5, 9, x, 17, 20, 24, 28, 31, 35, 40, 44, where x is unknown. The interquartile range of the eleven heights is 19 cm. Work out the value of x.
(a)−16
(b)54
(c)12
(d)16
13.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
14.A box plot for the amount of pocket money, in pounds, saved by 30 students in a month is based on a lower quartile of £18 and an upper quartile of £42. A value above upper quartile + 1.5 × interquartile range is considered an outlier. Amara saved £80 in the month. Determine whether Amara's saving is an outlier.
(a)No — £80 is below the boundary, £132, adding the quartiles to get the IQR
(b)Yes — £80 is above £66, using the IQR once only
(c)Yes — £80 is above the boundary, £78
(d)Yes — £80 is above the upper quartile, £42
15.In a spelling test the 20 pupils in Group A had a mean mark of 80, and the 30 pupils in Group B had a mean mark of 70. Work out the mean mark of all 50 pupils.
(a)75 marks
(b)74 marks
(c)76 marks
(d)150 marks

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