Data Handling and Averages Depth Set 2 - Worksheets, Questions and Revision

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

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11+ · GL ASSESSMENT

EP.M38 Data Handling and Averages Depth Set 2

GL ASSESSMENT EP.M38 · Calculators not allowed · about 58 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.

Data Handling and Averages Depth Set 2

Revision Library

A second 11+ statistics and data-handling paper for scholarship-level preparation, complementing EP.M7 (Averages) and EP.M27 (Data Handling and Averages Depth). It covers reading and interpreting pictograms, tally charts, bar charts, line graphs, frequency tables, timetables and pie charts, calculating the mean, median, mode and range, and simple probability, including probability from two-way tables. Questions are ramped from straightforward reading-off items to demanding multi-step and reverse-reasoning problems designed to stretch the strongest candidates.

1
A stall at a school fete sold cups of tea. A pictogram recorded the number of cups sold each hour, where one full cup symbol = 8 cups and a half cup symbol = 4 cups. The pictogram showed: 10am 3 symbols, 11am 2 symbols and a half, 12pm 4 symbols, 1pm 1 symbol and a half, 2pm 3 symbols and a half.

How many cups of tea were sold at 1pm?
  • A) 8
  • B) 10
  • C) 12
  • D) 16
  • E) 20
(Total for Question 1 is 1 mark)
2
Using the same pictogram of cups of tea sold (10am 3 symbols, 11am 2 symbols and a half, 12pm 4 symbols, 1pm 1 symbol and a half, 2pm 3 symbols and a half; key: 1 symbol = 8 cups, half symbol = 4 cups), answer the following.
(a)How many cups of tea were sold in total at 10am and 12pm?(2)
(b)How many more cups were sold at 2pm than at 11am?(2)
(Total for Question 2 is 4 marks)
3
A survey asked 35 pupils in Year 5 at Oakfield Primary School to name their favourite ice cream flavour. The results were recorded with tally marks, grouped in 5s: Vanilla had 2 full groups of 5 plus 3 more (13 tally marks), Chocolate had 2 full groups of 5 (10 tally marks), Strawberry had 1 full group of 5 plus 2 more (7 tally marks), and Mint choc chip had 1 full group of 5 (5 tally marks).
(a)How many pupils chose strawberry as their favourite flavour?(1)
(b)How many pupils chose vanilla or chocolate?(2)
(Total for Question 3 is 3 marks)
4
The bar chart shows the number of lengths completed by each swimmer in a training session at a leisure centre: Ffion 6, Daniel 9, Aaliyah 4, Ryan 7, Meera 8, Tomasz 5.

How many lengths did Aaliyah complete?
  • A) 4
  • B) 5
  • C) 6
  • D) 7
  • E) 9
(Total for Question 4 is 1 mark)
5
Using the same bar chart of lengths completed by swimmers (Ffion 6, Daniel 9, Aaliyah 4, Ryan 7, Meera 8, Tomasz 5), answer the following.
(a)How many lengths did Meera complete?(1)
(b)What was the total number of lengths completed by all six swimmers?(2)
(Total for Question 5 is 3 marks)
6
The line graph shows the number of visitors to Riverside Museum, recorded every hour during opening hours: 9am 5, 10am 12, 11am 18, 12pm 25, 1pm 30, 2pm 22, 3pm 14.

How many visitors were recorded at 12pm?
  • A) 18
  • B) 22
  • C) 25
  • D) 30
  • E) 14
(Total for Question 6 is 1 mark)
7
Using the same line graph of visitors to Riverside Museum (9am 5, 10am 12, 11am 18, 12pm 25, 1pm 30, 2pm 22, 3pm 14), by how many did the number of visitors fall between 1pm and 3pm?
(Total for Question 7 is 2 marks)
8
The frequency table shows the number of house points earned in a week by 24 pupils in Miss Farrelly's class. House points: 0, 1, 2, 3, 4. Frequency: 3, 6, 9, 4, 2.
(a)How many pupils earned exactly 2 house points?(1)
(b)How many pupils earned 3 or more house points?(2)
(Total for Question 8 is 3 marks)
9
The table shows the departure and arrival times of buses from Elmswood to Castleford on a Saturday morning: Bus A departs 08:15, arrives 08:55. Bus B departs 08:40, arrives 09:25. Bus C departs 09:05, arrives 09:50. Bus D departs 09:30, arrives 10:05.
(a)How many minutes does the journey on Bus B take?(1)
(b)Nadia arrives at the bus stop at 08:50. Which bus should she catch, and how many minutes will she need to wait?(2)
(Total for Question 9 is 3 marks)
10
Mr Patel, a shopkeeper, recorded the number of emails he received each day for 6 days: 11, 8, 11, 14, 8, 11.

What is the mode of these values?
  • A) 8
  • B) 11
  • C) 14
  • D) 10
  • E) 12
(Total for Question 10 is 1 mark)
11
The lengths of six phone calls made by Priya, in minutes, were: 4, 19, 7, 2, 15, 11.

Find the range of these lengths.
  • A) 2
  • B) 11
  • C) 15
  • D) 17
  • E) 19
(Total for Question 11 is 1 mark)
12
The resting heart rates (in beats per minute) of 7 athletes at a training camp were recorded: 58, 72, 65, 60, 77, 63, 68.

Find the median heart rate.
(Total for Question 12 is 2 marks)
13
Six runners recorded these times, in seconds, for a 100m sprint: 14.2, 13.8, 15.1, 14.6, 13.5, 14.9.

Find the median time.
(Total for Question 13 is 2 marks)
14
The prices of five second-hand books bought by Oliver at a car boot sale were: 2 pounds, 5 pounds, 3 pounds, 6 pounds, 4 pounds.

Calculate the mean price.
(Total for Question 14 is 2 marks)
15
The mean temperature recorded over 6 days in a town was 9 degrees C. On five of the days the temperatures were 7, 11, 6, 12 and 8 degrees C.

Find the temperature on the sixth day.
(Total for Question 15 is 3 marks)
16
A jar contains 6 red sweets, 4 yellow sweets and 5 green sweets. Priya picks one sweet from the jar at random.

What is the probability that it is yellow?
  • A) 2/5
  • B) 1/3
  • C) 4/15
  • D) 11/15
  • E) 4/11
(Total for Question 16 is 1 mark)
17
Kai spins a fair spinner with 10 equal sections, numbered 1 to 10.

What is the probability that the spinner lands on a number that is NOT a factor of 12?
(Total for Question 17 is 2 marks)
18
A cafe in Leeds sold the following number of hot drinks during one morning: Latte 18, Americano 12, Hot chocolate 8, Tea 22.
(a)A drink is chosen at random from those sold. What is the probability that it is an Americano?(1)
(b)What is the probability that a drink chosen at random is NOT a latte?(2)
(Total for Question 18 is 3 marks)
19
A survey of 72 pupils at Millbrook Academy asked about their favourite sport. The results are shown in a pie chart. The sector for 'swimming' has an angle of 45 degrees at the centre.

What fraction of the pupils chose swimming?
  • A) 1/8
  • B) 1/6
  • C) 1/4
  • D) 1/3
  • E) 1/9
(Total for Question 19 is 1 mark)
20
In a survey of the colours of 90 cars parked in a supermarket car park, 21 cars were silver.

Calculate the angle needed to represent 'silver' cars on a pie chart.
(Total for Question 20 is 3 marks)
21
A pie chart shows the favourite school subject of a group of pupils surveyed by Mrs Ibrahim. The sector for 'art' has an angle of 40 degrees, and 15 pupils chose art.

How many pupils took part in the survey in total?
(Total for Question 21 is 2 marks)
22
The frequency table shows the number of goals scored per match by Elmswood Town over a 20-match season. Goals scored: 0, 1, 2, 3, 4, 5. Frequency: 3, 5, 6, 4, 1, 1.

Calculate the mean number of goals scored per match.
(Total for Question 22 is 4 marks)
23
The two-way table shows whether 50 pupils at a secondary school are left-handed or right-handed, split by year group. Year 7: Left-handed 5, Right-handed 20 (total 25). Year 8: Left-handed 4, Right-handed 21 (total 25). Column totals: Left-handed 9, Right-handed 41 (grand total 50).
(a)One pupil is picked at random from the group. What is the probability that the pupil is left-handed?(2)
(b)One pupil is picked at random from the group. What is the probability that the pupil is in Year 7 AND right-handed?(2)
(Total for Question 23 is 4 marks)
24
Two long jump athletes, Chidi and Freya, each recorded their jump distances (in metres) over 5 attempts at a school athletics meet. Chidi's distances: 4.2, 4.6, 4.1, 4.8, 4.3. Freya's distances: 3.9, 5.1, 4.0, 5.0, 3.9.
(a)Calculate the median distance for Chidi.(2)
(b)Calculate the range of distances for Freya.(2)
(c)Which athlete's distances are more consistent? Give a reason for your answer, using the range of each athlete's distances.(1)
(Total for Question 24 is 5 marks)
25
A list of 6 whole numbers has mean 10, median 9.5, mode 8 and range 12.

Find a set of six numbers that satisfies all four conditions.
(Total for Question 25 is 4 marks)
Mark scheme · EP.M38 Data Handling and Averages Depth Set 2

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

Question 25