Data Handling and Averages Depth - Worksheets, Questions and Revision

24 original exam-style questions - 8 pages of questions with a full mark scheme - free printable PDF.

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11+ · GL ASSESSMENT

EP.M27 Data Handling and Averages Depth

GL ASSESSMENT EP.M27 · Calculators not allowed · about 55 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.

Data Handling and Averages Depth

Revision Library

An 11+ statistics and data-handling paper for scholarship-level preparation, complementing EP.M7 (Averages). It covers reading and interpreting pictograms, bar charts, line graphs, pie charts, tally charts and tables, 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
Zara kept a record of how many books were borrowed from the school library each day last week. Her pictogram used a key where one full book symbol = 4 books and a half book symbol = 2 books. The pictogram showed: Monday 3 symbols, Tuesday 2 symbols and a half, Wednesday 1 symbol, Thursday 3 symbols and a half, Friday 2 symbols.

How many books were borrowed on Thursday?
  • A) 10
  • B) 12
  • C) 14
  • D) 15
  • E) 16
(Total for Question 1 is 1 mark)
2
Using the same pictogram of books borrowed from the school library (Monday 3 symbols, Tuesday 2 symbols and a half, Wednesday 1 symbol, Thursday 3 symbols and a half, Friday 2 symbols; key: 1 symbol = 4 books, half symbol = 2 books), answer the following.
(a)How many books were borrowed in total on Monday and Wednesday?(2)
(b)How many more books were borrowed on Thursday than on Friday?(2)
(Total for Question 2 is 4 marks)
3
A survey asked 30 pupils in Year 6 to name their favourite pet. The results were recorded with tally marks, grouped in 5s: Dog had 2 full groups of 5 plus 2 more (12 tally marks), Cat had 2 full groups of 5 (10 tally marks), Rabbit had 1 full group of 5 (5 tally marks), and Hamster had 3 tally marks.
(a)How many pupils chose a rabbit as their favourite pet?(1)
(b)How many pupils took part in the survey altogether?(2)
(Total for Question 3 is 3 marks)
4
The bar chart shows the number of goals scored by Greenfield Rovers, a junior football team, in their last 6 matches: Match 1: 2 goals, Match 2: 3 goals, Match 3: 1 goal, Match 4: 4 goals, Match 5: 2 goals, Match 6: 3 goals.
(a)How many goals were scored in Match 4?(1)
(b)What is the difference between the number of goals scored in Match 4 and Match 3?(2)
(Total for Question 4 is 3 marks)
5
Using the same bar chart of goals scored by Greenfield Rovers (Match 1: 2, Match 2: 3, Match 3: 1, Match 4: 4, Match 5: 2, Match 6: 3), what was the total number of goals scored over all 6 matches?
  • A) 12
  • B) 13
  • C) 14
  • D) 15
  • E) 17
(Total for Question 5 is 1 mark)
6
The frequency table shows the shoe sizes of 20 pupils in Mr Hughes's class. Shoe size: 3, 4, 5, 6, 7. Frequency: 2, 5, 7, 4, 2.
(a)How many pupils have a shoe size of 5?(1)
(b)What is the modal shoe size, and how many pupils wear that size?(2)
(Total for Question 6 is 3 marks)
7
The two-way table shows how 40 pupils at a primary school travel to school. Year 5: Walk 6, Bus 8, Car 4 (total 18). Year 6: Walk 5, Bus 9, Car 8 (total 22). Column totals: Walk 11, Bus 17, Car 12 (grand total 40).
(a)How many Year 6 pupils travel by car?(1)
(b)How many more pupils in Year 6 travel to school by car than pupils in Year 5?(2)
(Total for Question 7 is 3 marks)
8
The line graph shows the temperature (in degrees C) in a garden, recorded every 2 hours during one day: 6am: 8, 8am: 10, 10am: 13, 12pm: 16, 2pm: 18, 4pm: 15, 6pm: 11.

What was the temperature at 12pm?
  • A) 11 degrees C
  • B) 13 degrees C
  • C) 15 degrees C
  • D) 16 degrees C
  • E) 18 degrees C
(Total for Question 8 is 1 mark)
9
Using the same line graph of garden temperature (6am: 8, 8am: 10, 10am: 13, 12pm: 16, 2pm: 18, 4pm: 15, 6pm: 11, all in degrees C), by how many degrees did the temperature fall between 2pm and 6pm?
(Total for Question 9 is 2 marks)
10
Freya recorded the number of goals she scored in her last 7 hockey matches: 4, 7, 4, 9, 2, 4, 7.

What is the mode of her scores?
  • A) 2
  • B) 4
  • C) 6
  • D) 7
  • E) 9
(Total for Question 10 is 1 mark)
11
Kwame timed how long, in minutes, it took him to walk to school on 6 different days: 15, 8, 22, 3, 17, 11.

Find the range of his times.
  • A) 3
  • B) 14
  • C) 19
  • D) 22
  • E) 25
(Total for Question 11 is 1 mark)
12
Priya's test scores in her last five spelling tests were: 9, 4, 15, 7, 11.

Find the median score.
(Total for Question 12 is 2 marks)
13
Six pupils in Mr Okafor's class recorded how many books they read last term: 6, 13, 8, 2, 10, 5.

Find the median number of books read.
(Total for Question 13 is 2 marks)
14
Siobhan's marks in her last five mental maths quizzes were: 5, 9, 3, 11, 7.

Calculate her mean mark.
(Total for Question 14 is 2 marks)
15
The mean of five numbers chosen by Mohammed is 8. Four of the numbers are 6, 9, 4 and 10.

Find the fifth number.
(Total for Question 15 is 3 marks)
16
Amara has a bag containing 5 red counters, 3 blue counters and 2 green counters. She picks one counter from the bag at random.

What is the probability that it is blue?
  • A) 1/5
  • B) 1/2
  • C) 3/10
  • D) 3/5
  • E) 7/10
(Total for Question 16 is 1 mark)
17
Ibrahim spins a fair spinner with 8 equal sections, numbered 1 to 8.

What is the probability that the spinner lands on a number that is NOT a multiple of 3?
(Total for Question 17 is 2 marks)
18
Mrs Adeyemi's school canteen sold the following packets of crisps during one break time: Ready salted 15, Cheese and onion 9, Salt and vinegar 6, Other flavours 10.
(a)A packet is chosen at random from those sold. What is the probability that it is cheese and onion?(1)
(b)What is the probability that a packet chosen at random is NOT ready salted?(2)
(Total for Question 18 is 3 marks)
19
A survey of 60 pupils at Elmwood Primary School asked how they travel to school. The results are shown in a pie chart. The sector for 'Car' has an angle of 90 degrees at the centre.

What fraction of the pupils travel by car?
  • A) 1/6
  • B) 1/4
  • C) 1/3
  • D) 1/2
  • E) 1/8
(Total for Question 19 is 1 mark)
20
In a survey of 60 pupils' favourite school lunch, 15 pupils chose pasta. A pie chart is going to be drawn to show the results.

Calculate the angle needed to represent 'pasta' on the pie chart.
(Total for Question 20 is 3 marks)
21
A pie chart shows the favourite fruit of a group of pupils surveyed by Mr Thompson. The sector for 'apple' has an angle of 60 degrees, and 90 pupils took part in the survey in total.

How many pupils chose apple as their favourite fruit?
(Total for Question 21 is 2 marks)
22
The frequency table shows the number of pets owned by each pupil in Miss Kaur's class of 25 pupils. Number of pets: 0, 1, 2, 3, 4. Frequency: 5, 8, 7, 3, 2.

Calculate the mean number of pets owned per pupil.
(Total for Question 22 is 4 marks)
23
The two-way table shows the eye colour and hair colour of 30 pupils in Miss Bennett's class. Fair hair: Blue eyes 6, Brown eyes 4 (total 10). Dark hair: Blue eyes 3, Brown eyes 17 (total 20). Column totals: Blue eyes 9, Brown eyes 21 (grand total 30).
(a)One pupil is picked at random from the class. What is the probability that the pupil has fair hair?(2)
(b)One pupil is picked at random from the class. What is the probability that the pupil has dark hair AND brown eyes?(2)
(Total for Question 23 is 4 marks)
24
Two classes, 6A and 6B, each sat the same 5-question maths quiz set by their teacher, Mr Osei. 6A's scores: 4, 5, 3, 4, 4. 6B's scores: 2, 6, 4, 6, 2.
(a)Calculate the mean score for class 6A.(2)
(b)Calculate the range of scores for class 6B.(2)
(c)Which class's scores are more consistent? Give a reason for your answer, using the range of each class's scores.(1)
(Total for Question 24 is 5 marks)
Mark scheme · EP.M27 Data Handling and Averages Depth

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