Maths — Extended

Exam Questions

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Averages & Range (Cambridge International IGCSE Mathematics): Exam Questions

Exam code:0580

28 questions · 117 marks · ≈ 2 hours

Guided practice

13 markseasy

(b)

The students in Class A and in Class B take the same examination.

The lowest score in Class A is 39 The range of scores for Class A is 57 The lowest score in Class B is 33 The range of scores for Class B is 60

Find the range of scores for all the students in both classes.

Your answer

How did you do?/ 3

26 markseasy

(b)

Roberto records the value of each of the coins he has at home. The table shows the results.

Value (cents)	1	2	5	10	20	50
Frequency	3	1	3	2	4	2

i) Find the range.

........................................... cents [1]

ii) Find the mode.

........................................... cents [1]

iii) Find the median.

........................................... cents [1]

iv) Work out the total value of Roberto’s coins.

........................................... cents [2]

v) Work out the mean.

........................................... cents [1]

Your answer

How did you do?/ 6

36 markseasy

(a)

The test scores of 14 students are shown below.

21	21	23	26	25	21	22	20	21	23	23	27	24	21

Find the range, mode, median and mean of the test scores.

Range = ....................................................
Mode = ....................................................
Median = ....................................................
Mean = ....................................................

Your answer

How did you do?/ 6

45 markseasy

(b)

A teacher records the number of days each of the 24 students in her class are absent. The frequency table shows the results.

Number of days	0	1	2	3	4	5
Frequency	10	8	3	2	0	1

Find the mode, the median and the mean.

Mode = ...............................................
Median = ...............................................
Mean = ...............................................

Your answer

How did you do?/ 5

53 marksmedium

The table shows the marks scored by 40 students in a test.

Mark	5	6	7	8	9	10
Frequency	8	5	11	7	5	4

Calculate the mean mark.

Your answer

How did you do?/ 3

64 marksmedium

1 mark

(a)

40 people were asked how many times they visited the cinema in one month. The table shows the results.

Number of cinema visits	0	1	2	3	4	5	6	7
Frequency	5	5	6	6	7	3	6	2

Find the mode.

Your answer

3 marks

(a)

Extract:

| Number of cinema visits | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | | Frequency | 5 | 5 | 6 | 6 | 7 | 3 | 6 | 2 |

Calculate the mean.

Your answer

How did you do?/ 4

74 marksmedium

(a)

The heights, $h$ metres, of the 120 boys in an athletics club are recorded. The table shows information about the heights of the boys.

Height ( $h$ metres)	$1.3<h\leq1.4$	$1.4<h\leq1.5$	$1.5<h\leq1.6$	$1.6<h\leq1.7$	$1.7<h\leq1.8$	$1.8<h\leq1.9$
Frequency	7	18	30	24	27	14

Calculate an estimate of the mean height.

............................................. m

Your answer

How did you do?/ 4

84 marksmedium

(a)

The speed, $v$ km/h, of each of 200 cars passing a building is measured. The table shows the results.

Speed ( $v$ km/h)	$0<v\leq20$	$20<v\leq40$	$40<v\leq45$	$45<v\leq50$	$50<v\leq60$	$60<v\leq80$
Frequency	$16$	$34$	$62$	$58$	$26$	$4$

Calculate an estimate of the mean.

........................................ km/h

Your answer

How did you do?/ 4

93 marksmedium

(b)

The table shows the marks scored by some students in a test.

Mark	5	6	7	8	9	10
Frequency	8	2	12	2	0	1

Calculate the mean mark.

Your answer

How did you do?/ 3

104 marksmedium

(a)

The table shows the time, $t$ seconds, taken by each of 120 boys to solve a puzzle.

Time ( $t$ seconds)	$20<t\leq30$	$30<t\leq35$	$35<t\leq40$	$40<t\leq60$	$60<t\leq100$
Frequency	38	27	21	16	18

Calculate an estimate of the mean time.

............................................. s

Your answer

How did you do?/ 4

114 marksmedium

(a)

20 students each record the mass, $p$ grams, of their pencil case. The table below shows the results.

Mass ( $p$ grams)	$0<p\leq50$	$50<p\leq100$	$100<p\leq125$	$125<p\leq150$	$150<p\leq200$
Frequency	$2$	$5$	$4$	$6$	$3$

Calculate an estimate of the mean mass.

................................................ g

Your answer

How did you do?/ 4

124 marksmedium

(a)

A school nurse records the height, $h$ cm, of each of 180 children. The table shows the information.

Height ( $h$ cm)	$60<h\leq70$	$70<h\leq90$	$90<h\leq100$	$100<h\leq110$	$110<h\leq115$	$115<h\leq125$
Frequency	8	26	35	67	28	16

Calculate an estimate of the mean.

Give your answer correct to 1 decimal place.

.......................................... cm

Your answer

How did you do?/ 4

134 marksmedium

(a)

The table shows the amount of time, T minutes, 120 people each spend in a supermarket one Saturday.

Time (T minutes)	Number of people
$10<T\leq30$	16
$30<T\leq40$	18
$40<T\leq45$	22
$45<T\leq50$	40
$50<T\leq60$	21
$60<T\leq70$	3

Use the midpoints of the intervals to calculate an estimate of the mean.

......................................... min

Your answer

How did you do?/ 4

144 marksmedium

(a)

A factory recycles metal. The mass, $x$ tonnes, of metal is measured each week. The table shows the results for 52 weeks.

Mass ( $x$ tonnes)	$100<x\leq200$	$200<x\leq250$	$250<x\leq300$	$300<x\leq500$
Frequency	8	20	12	12

Calculate an estimate of the mean.

....................................... tonnes

Your answer

How did you do?/ 4

156 marksmedium

1 mark

(a)

The time taken for each of 120 students to complete a cooking challenge is shown in the table.

Time ( $t$ minutes)	$20<t\leq25$	$25<t\leq30$	$30<t\leq35$	$35<t\leq40$	$40<t\leq45$
Frequency	$44$	$32$	$28$	$12$	$4$

Write down the modal time interval.

................... $<t\leq$ ...................

Your answer

1 mark

(a)

Extract:

| Time (t minutes) | 20 < t ≤ 25 | 25 < t ≤ 30 | 30 < t ≤ 35 | 35 < t ≤ 40 | 40 < t ≤ 45 | | Frequency | 44 | 32 | 28 | 12 | 4 |

Write down the interval containing the median time.

................... $<t\leq$ ...................

Your answer

4 marks

(a)

Extract:

The time taken for each of 120 students to complete a cooking challenge is shown in the table.

| Time (t minutes) | 20 < t ≤ 25 | 25 < t ≤ 30 | 30 < t ≤ 35 | 35 < t ≤ 40 | 40 < t ≤ 45 | | Frequency | 44 | 32 | 28 | 12 | 4 |

Calculate an estimate of the mean time.

......................................... min

Your answer

How did you do?/ 6

164 marksmedium

(b)

The information below summarises data regarding the heights of plants, measured in centimetres.

Height, h cm	$0<h\leq10$	$10<h\leq20$	$20<h\leq30$	$30<h\leq50$
Frequency	2	18	62	38

Calculate an estimate of the mean height.

............................................ cm

Your answer

How did you do?/ 4

174 markshard

The height, $h$ cm, of each of 100 students is measured. The table shows the results.

Height ( $h$ cm)	100 < $h$ ⩽ 150	150 < $h$ ⩽ 160	160 < $h$ ⩽ 165	165 < $h$ ⩽ 185
Frequency	7	30	41	22

Calculate an estimate of the mean.

.......................................... cm

Your answer

How did you do?/ 4

184 markshard

(a)

The table shows information about the times, $t$ seconds, taken by each of 100 students to solve a puzzle.

Time ( $t$ s)	$0<t\leq10$	$10<t\leq15$	$15<t\leq20$	$20<t\leq40$	$40<t\leq75$
Frequency	$9$	$18$	$22$	$30$	$21$

Calculate an estimate of the mean time.

............................................... s

Your answer

How did you do?/ 4

194 markshard

The table shows the amount of money, $ x, given to a charity by each of 60 people.

Amount (`$ x`)	$0<x\leq20$	$20<x\leq25$	$25<x\leq35$	$35<x\leq50$	$50<x\leq100$
Frequency	$21$	$16$	$6$	$10$	$7$

Calculate an estimate of the mean.

$................................................

Your answer

How did you do?/ 4

204 markshard

Bob asked each of $40$ friends how many minutes they took to get to work. The table shows some information about his results.

Time taken (m minutes)	Frequency
`0 less than m less-than or slanted equal to 10`	$3$
`10 less than m less-than or slanted equal to 20`	$8$
`20 less than m less-than or slanted equal to 30`	$11$
`30 less than m less-than or slanted equal to 40`	$9$
`40 less than m less-than or slanted equal to 50`	$9$

Work out an estimate for the mean time taken.

Your answer

How did you do?/ 4

214 markshard

Sumeet records the times, in minutes, for 40 runners to finish a half marathon. Information about these times is shown in the table.

Time ( $t$ minutes)	Frequency
`60 less than t less-than or slanted equal to 90`	$10$
`90 less than t less-than or slanted equal to 120`	$14$
`120 less than t less-than or slanted equal to 150`	$9$
`150 less than t less-than or slanted equal to 180`	$5$
`180 less than t less-than or slanted equal to 210`	$2$

Calculate an estimate for the mean time.

Your answer

How did you do?/ 4

224 markshard

(b)

The frequency table shows the times, $t$ minutes, each of 100 children spent exercising in one week.

Time ( $t$ minutes)	$0<t\leq60$	$60<t\leq100$	$100<t\leq160$	$160<t\leq220$	$220<t\leq320$
Frequency	41	24	23	8	4

Calculate an estimate of the mean time.

.......................................... min

Your answer

How did you do?/ 4

234 markshard

(b)

200 students estimate the total area, $Am^{2}$ , of the windows in the classroom. The table shows their results.

Area ( $A$ m²)	$20<A\leq60$	$60<A\leq100$	$100<A\leq150$	$150<A\leq250$
Frequency	32	64	80	24

Calculate an estimate of the mean. You must show all your working.

.......................................... m²

Your answer

How did you do?/ 4

244 markshard

(c)

During one year the midday temperatures, t°C, in Zedford were recorded. The table shows the results.

Temperature (t°C)	$0<t\leq10$	$10<t\leq15$	$15<t\leq20$	$20<t\leq25$	$25<t\leq35$
Number of days	50	85	100	120	10

Calculate an estimate of the mean.

............................................... °C

Your answer

How did you do?/ 4

254 markshard

(a)

100 students were each asked how much money, $ m, they spent in one week. The frequency table shows the results.

Amount $( \$ m )$	$0<m\leq5$	$5<m\leq10$	$10<m\leq20$	$20<m\leq30$	$30<m\leq50$
Frequency	16	38	30	9	7

Calculate an estimate of the mean.

$ .............................................

Your answer

How did you do?/ 4

265 markshard

(c)

The frequency table shows information about the number of books read by some students in a reading marathon.

Number of books read	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
Frequency	$2$	$2$	$16$	$10$	$9$	$4$	$x$	$2$

i) The mean number of books read is 4.28.

Find the value of $x$ .

$x=$ .................................................. [3]

ii) Write down the mode.

(1 mark)

iii) Write down the median.

(1 mark)

Your answer

How did you do?/ 5

274 markshard

(c)

Three sizes of eggs are sold in a shop. The table shows the number of eggs of each size sold in one day.

Size	Small	Medium	Large
Mass ( $m$ grams)	$46<m\leq52$	$52<m\leq62$	$62<m\leq80$
Number of eggs sold	$78$	$180$	$162$

Calculate an estimate of the mean mass.

............................................. g

Your answer

How did you do?/ 4

284 markshard

(a)

The frequency table shows information about the time, $m$ minutes, that each of 160 people spend in a library.

Time ( $m$ minutes)	$0<m\leq10$	$10<m\leq40$	$40<m\leq60$	$60<m\leq90$	$90<m\leq100$	$100<m\leq120$
Frequency	3	39	43	55	11	9

Calculate an estimate of the mean time spent in the library.

......................................... min

Your answer

How did you do?/ 4