Averages and Data Handling: Practice Set 3 - Worksheets, Questions and Revision

24 original exam-style questions - 9 pages of questions with a full mark scheme - free printable PDF.

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11+ · GL ASSESSMENT

EP.M51 Averages and Data Handling: Practice Set 3

Calculators not allowed · about 50 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Here are the ages, in years, of 7 cousins at a family party: 9, 12, 9, 15, 9, 11, 12.
What is the mode of these ages?
A) 9 B) 11 C) 12 D) 15
(Total for Question 1 is 1 mark)
2
In a PE lesson, five pupils recorded their long jump distances, in centimetres: 142, 118, 156, 131, 127.
What is the range of these distances?
A) 24 cm B) 29 cm C) 38 cm D) 45 cm
(Total for Question 2 is 1 mark)
3
Seven pupils threw a bean bag in a PE lesson. Here are the distances they threw it, in metres: 2.5, 4.0, 1.5, 5.5, 3.0, 1.0, 4.5.
Find the median distance thrown.
(Total for Question 3 is 2 marks)
4
Tariq, Freya, Ade and Olamide collected conkers in the park. The numbers they collected were: 9, 15, 6, 18.
Work out the mean number of conkers collected.
(Total for Question 4 is 2 marks)
5
During a class nature walk, pupils kept a pictogram of how many birds they spotted each day. Key: one full bird symbol = 4 birds, and a half symbol = 2 birds. The pictogram showed: Monday 3 symbols and a half, Tuesday 2 symbols, Wednesday 4 symbols and a half, Thursday 1 symbol and a half.
Figure (to be drawn): Pictogram of birds spotted per day (data given in the question)
(a)How many birds were spotted on Monday?(1)
(b)How many more birds were spotted on Wednesday than on Thursday?(2)
(c)Which day had the fewest birds spotted?
A) Monday B) Tuesday C) Wednesday D) Thursday(1)
(Total for Question 5 is 4 marks)
6
The table shows the number of hours of screen time (TV, tablet or phone) that each pupil in a class of 25 had yesterday. Hours of screen time (x): 0, 1, 2, 3, 4. Number of pupils (f): 4, 8, 7, 4, 2.
Figure (to be drawn): Frequency table (data given in the question)
(a)What is the modal number of hours of screen time?(1)
(b)How many pupils had exactly 2 hours of screen time?(1)
(c)How many pupils had 2 hours or more of screen time?(2)
(Total for Question 6 is 4 marks)
7
The bar chart shows the number of tickets sold for different stalls at a school summer fair: Bouncy castle 35, Face painting 28, Coconut shy 42, Tombola 15, Raffle 20.
Figure (to be drawn): Bar chart of tickets sold per stall (data given in the question)
(a)How many tickets were sold for face painting?(1)
(b)How many more tickets were sold for the coconut shy than for the tombola?(2)
(c)Work out the total number of tickets sold across all five stalls.(2)
(Total for Question 7 is 5 marks)
8
A box contains 7 green counters, 5 yellow counters and 3 pink counters. Callum takes one counter from the box without looking.
What is the probability that he takes a yellow counter?
A) 1/5 B) 1/3 C) 5/8 D) 3/5
(Total for Question 8 is 1 mark)
9
A fair six-sided dice is rolled once.
What is the probability of rolling a number greater than 4?
A) 1/6 B) 1/3 C) 1/2 D) 2/3
(Total for Question 9 is 1 mark)
10
Here is part of a bus timetable for the number 24 bus, which runs from Hawksmoor to Fenbridge, calling at Thorncliffe. Hawksmoor departs: 08:15, 08:45, 09:20, 10:05. Thorncliffe: 08:27, 08:57, 09:32, 10:17. Fenbridge arrives: 08:50, 09:20, 09:55, 10:40.
Figure (to be drawn): Bus timetable (times given in the question)
(a)How long does the 08:15 bus from Hawksmoor take to reach Fenbridge?(2)
(b)Nia arrives at Thorncliffe at 09:10. What is the earliest bus she can catch, and at what time does it leave?(1)
(c)How many minutes does Nia have to wait at Thorncliffe for this bus?(2)
(Total for Question 10 is 5 marks)
11
The line graph shows the height of the tide, in metres, at Bramsea Harbour, recorded every 2 hours during one day: 06:00 1.5 m, 08:00 2.5 m, 10:00 4.0 m, 12:00 4.5 m, 14:00 3.5 m, 16:00 2.0 m, 18:00 1.0 m.
Figure (to be drawn): Line graph of tide height over time (data given in the question)
(a)What was the height of the tide at 12:00?(1)
(b)Work out the difference in tide height between 06:00 and 12:00.(2)
(c)Between which two consecutive readings shown did the tide fall the most?(1)
(Total for Question 11 is 4 marks)
12
60 pupils were asked to choose their favourite ice lolly from three flavours, or to say 'none of these'. The table shows some of the results. Flavour: Strawberry, Orange, Blackcurrant, None of these. Number of pupils: 22, 15, 14, ?.
Work out how many pupils chose 'none of these'.
Figure (to be drawn): Table with one missing frequency (data given in the question)
(Total for Question 12 is 3 marks)
13
40 pupils in Year 6 were asked to name their favourite type of book. The results are shown in a pie chart: Adventure takes up half of the pie chart, Mystery takes up a quarter, Fantasy takes up an eighth, and Comic takes up an eighth.
Figure (to be drawn): Pie chart of favourite book type (fractions given in the question)
(a)How many pupils chose adventure books?(2)
(b)Two of the genres were each chosen by the same number of pupils. How many pupils chose each of these two genres?
A) 5 B) 10 C) 15 D) 20(1)
(Total for Question 13 is 3 marks)
14
Rhys wants to record how his height changed each year from age 5 to age 11. Which type of graph would be most suitable for displaying this data?
A) Pie chart B) Line graph C) Pictogram D) Tally chart
(Total for Question 14 is 1 mark)
15
The table shows the number of visitors to a village fete during each hour it was open. Time: 10:00-11:00, 11:00-12:00, 12:00-13:00, 13:00-14:00, 14:00-15:00, 15:00-16:00. Number of visitors: 45, 62, 58, 130, 51, 39.
Figure (to be drawn): Table of visitor numbers by hour (data given in the question)
(a)Find the range of the number of visitors.(2)
(b)One of these hourly totals is unusually high compared with the rest. State which hour this is, and suggest one reason why the number of visitors might have been so much higher then.(2)
(c)If the unusually high hour were excluded, what would the range of the remaining data be?
A) 13 B) 23 C) 62 D) 91(1)
(Total for Question 15 is 5 marks)
16
Zainab travels by train from Ashby to Norton, changing trains at Bridgeford. The train from Ashby departs at 09:05 and arrives at Bridgeford at 09:38. The connecting train departs Bridgeford at 09:50 and arrives at Norton at 10:22.
Work out the total time, including the wait at Bridgeford, from Zainab leaving Ashby to arriving at Norton.
(Total for Question 16 is 3 marks)
17
Find the median of this set of numbers: 3, 7, 2, 9, 5, 12.
A) 5 B) 6 C) 7 D) 9
(Total for Question 17 is 1 mark)
18
The table shows the number of correct answers, out of 4, that each pupil in a class of 20 got in a times-tables quiz. Correct answers (x): 0, 1, 2, 3, 4. Number of pupils (f): 3, 4, 6, 4, 3.
Figure (to be drawn): Frequency table (data given in the question)
(a)What is the modal number of correct answers?(1)
(b)Work out the mean number of correct answers per pupil.(3)
(Total for Question 18 is 4 marks)
19
A drawer contains 4 black socks and 6 white socks, all mixed up. Declan takes one sock out at random and does not put it back.
Given that the first sock he took was black, what is the probability that the second sock he takes is also black?
(Total for Question 19 is 2 marks)
20
The stem-and-leaf diagram shows the times, in seconds, taken by a group of pupils to complete an obstacle course. Stem 2: leaves 4, 7, 8. Stem 3: leaves 0, 2, 2, 5, 9. Stem 4: leaves 1, 3, 6. Stem 5: leaves 0, 2. Key: 2 | 4 means 24 seconds.
Figure (to be drawn): Stem-and-leaf diagram (data given in the question)
(a)How many pupils are represented in the diagram?(1)
(b)Find the range of the times.(2)
(Total for Question 20 is 3 marks)
21
The mean height of 8 pupils in a running club is 142 cm. A new pupil joins the club, and the mean height of all 9 pupils becomes 143 cm.
What is the height of the new pupil?
(Total for Question 21 is 4 marks)
22
A school canteen recorded the number of hot lunches and packed lunches eaten by pupils over one week. Monday: hot 62, packed 38. Tuesday: hot 58, packed 42. Wednesday: hot 65, packed 35. Thursday: hot 60, packed 40. Friday: hot 45, packed 55.
On which day was the difference between the number of hot lunches and packed lunches the greatest, and what was that difference?
Figure (to be drawn): Table of hot and packed lunches by day (data given in the question)
(Total for Question 22 is 3 marks)
23
Two weeks of absence data were recorded for a class. Week 1: Monday 4, Tuesday 2, Wednesday 6, Thursday 3, Friday 5. Week 2: Monday 3, Tuesday 5, Wednesday 4, Thursday 6, Friday 2.
What is the difference between the mean number of absences in Week 1 and the mean number of absences in Week 2?
A) 0 B) 1 C) 2 D) 4
(Total for Question 23 is 1 mark)
24
A charity bake sale recorded how much money was raised each day over 6 days: £24, £31, £18, £45, £27, £35.
(a)Calculate the mean amount raised per day.(2)
(b)Find the median amount raised.(2)
(c)On the 7th day, an extra £53 was raised. Without recalculating the mean from scratch, state whether the new mean (over all 7 days) will be higher or lower than the mean found in part (a). Give a reason for your answer.(1)
(Total for Question 24 is 5 marks)
Mark scheme · EP.M51 Averages and Data Handling: Practice Set 3

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24