Numeracy Sample Questions

8/8/2019 Numeracy Sample Questions

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Numeracy sample questions

These questions can be used to familiarise yourself with the content of the test before you attemptthem under test conditions. There are three sets of mental arithmetic questions with answers andtwo sets of other sample questions.

Mental arithmetic questions (set 1)

No. Question

1 Twenty percent of the pupils in a school with three hundred and fifteen pupils have freeschool meals.

How many pupils is this?

2 The entrance fee for an exhibition is three pounds seventy five.

What will be the total entrance fee for a school party of 50 pupils?

3 In a year group of one hundred and eighty pupils, five percent achieved below level 3 inEnglish Key Stage 4.

How many pupils achieved level 3 or above?

4 A test had forty questions, each worth one mark. If the pass mark is sixty percent, what wasthe minimum number of questions that must be answered correctly in order to pass the test?

5 One gallon is approximately four point five litres. About how many litres is two hundredgallons?

6 Two-fifths of a class of twenty-five pupils were girls.

What percentage were boys?

7 A school had twelve hundred pupils on roll. In the first two weeks of term, ninety percent ofthe pupils used the school library.

How many pupils did not use the school library in the first two weeks of term?

8 Three-eighths of a year group of three hundred and sixty pupils were boys.

How many of the group were girls?

9 In a class of twenty four pupils three eighths are involved in a school concert.

How many pupils are not involved in the school concert?

10 The science department in a school has an annual allowance of six hundred reams of paper.Three hundred and ten reams are used by December and a further one hundred and sixty

reams by March.


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How many reams are left?

11 It is possible to seat forty people in a row across the hall. How many rows are needed toseat four hundred and thirty two people?

12 All 300 Year 11 pupils in a school took GCSE English. The number of pupils gaining grade Cor above increased from 85% in the mock exam to 93% in the actual exam.

How many more pupils gained grade C or above in the actual exam than in the mock exam?


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Twelve mental arithmetic questions (set 3)

No. Question

1 In a class of thirty pupils, seventy per cent achieved grade C and above and twenty per centachieved grades D to G.

How many pupils did not achieve a grade?

2 A teacher had a budget of one hundred and twenty pounds. Half of the budget was spent interm one and thirty six pounds spent in term two.

What proportion of the budget remained at the end of term two? Give your answer as afraction in its lowest terms.

3 A class of twenty four pupils had access to eight computers. Each pupil needed fifteenminutes computer time.

How much time needed to be booked per computer?

4 A school day finished at fifteen thirty. The two afternoon lessons were fifty five minutes each,with a fifteen minute break between lessons. What time did the first afternoon lesson begin?

5 A school play cost one hundred and sixty pounds to produce. Eighty parents paid twopounds fifty each to attend the one performance.

How much profit did the school make?

6 In Class A twenty one out of twenty eight pupils passed a test. In Class B, eighty seven percent of pupils passed the same test.

What was the difference between the two classes in the percentage of pupils passing the

test?

7 A careers teacher gave a talk to four classes each of twenty six pupils and three classeseach of twenty eight pupils.

How many pupils attended the talk?

8 What is one point two minus zero point eight five? Give your answer as a decimal.

9 A class of twenty seven pupils sat an end of Key Stage two test. Eighteen pupils achievedLevel three and above.

What proportion of the class did not achieve Level 3 and above? Give your answer as afraction in its lowest terms.

10 The entrance fee to a French museum is eight euros. The exchange rate is 1.6 euros to thepound.

How much was the entrance fee in pounds?

11 In a class of thirty pupils, three fifths were boys. How many were girls?

12 A pupil scored thirty five out of seventy in one test and forty two out of seventy in a secondtest.

What was the increase in the pupil's percentage score in the second test compared with thepercentage score in the first test?


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Sample on-screen questions

Sample on-screen question 1



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Twenty one on-screen questions

Question 1

1 A Year 6 teacher compared the results of pupils in a class with national results at Key Stage2.

National results (percentage)

Level

Absent Assessed by teacher 1 and below 2 3 4 5

Boys 3 3 3 2 30 41 18

Girls 2 3 3 2 32 43 15

All pupils 2 3 3 2 31 42 17

Class results (number of pupils)

Absent Level 2 Level 3 Level 4 Level 5 Total

Boys 2 1 7 7 3 20

Girls 0 0 5 7 3 15

Indicate all the true statements:

1 nationally 58% of girls achieved Level 4 or 5

22/3 of the girls in the class achieved Level 4 and above

3 the percentage of boys absent nationally was greater than the percentage of the boys absent inthe class

Question 2

2 A science teacher compared the results of a theory component test and a practical componenttest given to 16 pupils at the end of a module.


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Using the information given, indicate which of the following are true:

a a quarter of the pupils achieved a result of at least 50% in both the practical and theorycomponents

b half of the pupils achieved a result of at least 50% in the practical component

c the two pupils with the lowest marks in the practical component also had the lowest marks inthe theory component

Questions 3 and 4

A group of 10 pupils sat three equally weighted tests during the last term of their course.

Pupil A B C D E F G H I J

Test 1 66 72 46 72 45 69 70 55 46 35

Test 2 52 60 18 46 22 18 30 46 18 30

Test 3 66 70 32 66 30 32 60 56 58 38

Total 184 202 96 184 97 119 160 167 122 103

3 What was the median score in Test 1?

a 72

b 57.0

c 57.6

d 60.5

4 Which test had the largest range of pupil scores?

Question 5

5 In preparation for a staff meeting, a teacher produced a two-way table showing theperformance of pupils in end of Key Stage 2 science tests compared with the teachersassessments.

Teacher assessment level

1 2 3 4 5 6

1 1 1

2 2 1

3 1 7 1

4 10

5 1 1 5

Testlevel

6 1

What percentage of pupils achieved a higher level in the test than in teacher assessment?

Give your answer correct to one decimal place.


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Question 6

6 A teacher helped a group of pupils to develop a rectangular environmental area in a school.

The proportions of the environmental area are shown below.

Not to scale

The pupils built a path around two sides using square paving slabs each measuring 0.5 m x0.5 m. The path was one slab wide.

How many paving slabs were needed to make the path?

Question 7

7 Tables were prepared to show the relationship between GCSE English language grades andGCSE geography and religious education grades.

GCSE Geography

GCSEgrade

A*-A B-C D-E F-G U-X Total

A*-A 10 6 1 17

B-C 3 30 16 2 51

D-E 3 19 7 3 32

F-G

U-X

GCSEEnglish

language

Total 13 39 36 9 3 100


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GCSE Religious education

GCSEgrade

A*-A B-C D-E F-G U-X Total

A*-A 6 5 11

B-C 5 11 1 17

D-E 12 14 1 1 28

F-G 1 1 2 4

U-X

GCSEEnglish

language

Total 11 29 16 3 1 60


1 the grade A* - C pass rate for GCSE religious education was exactly 10% higher than the gradeA* - C pass rate for geography

2of the pupils taking GCSE geography, more than achieved grade C and above in GCSEEnglish language

3 of the pupils taking GCSE religious education,1/3 did not achieve grade C and above in GCSE

religious education

Question 8

8 A sixth form tutor analysed the destinations of 508 pupils leaving a sixth form.

The number of pupils who went into employment was 325 or 64%. Thirty two pupils hadunknown destinations. What percentage of pupils was this? Give your answer to 1 decimalplace.


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Question 9

9 The table shows a schools end of Key Stage 3 test results.

Percentage of pupils in Year 9 at each level

Level: V 3 4 5 6 7 8 Total

English 0 0 0 8 52 22 18 100%

Mathematics 1 0 0 0 29 62 8 100%

Science 1 0 0 4 55 37 3 100%

(v = invalid completion of test paper)

There were 120 pupils in Year 9. How many more pupils achieved Level 7 and above inmathematics than in English?

Question 10

10 The following table shows a teachers assessment of four pieces of GCSE science practicalwork produced by one pupil.

Planning

P

Observation

O

Analysis

A

Evaluation

E

Spelling,

punctuationand grammar(SPAG)

Assessment 1 6 6 4 2 2




The total score for each assessment is obtained by using the formula:

total score = 2 (P+O+A+E) +SPAGThe pupil's highest score was then submitted to the examination board.

Which score was submitted?

a Assessment 1

b Assessment 2

c Assessment 3

d Assessment 4


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Question 11

11 A pupil achieved the following scores in Tests A, B and C.

Test A B C

Actual mark 68 28 5

The pupils weighted score was calculated using the following formula:( A x 60) ( B x 30)Weighted score

= 100+

80+C

What was the pupil's weighted score?

Give your answer to the nearest whole number.

Question 12

12 As part of a study about the performance of boys, a school calculated the ratios of boys togirls taking GCSE optional subjects.

Number of Year 10 pupils in four subjects

Geography History PE IT

Boys 45 28 24 36

Girls 15 56 16 45


1 the ratio of boys to girls in geography was 3:1 and in PE was 2:3

2 the ratio of boys to girls in geography was 1:3 and in history was 1:2

3 the ratio of boys to girls in history was 1:2 and in IT was 4:5

4 the ratio of boys to girls in PE was 3:2 and in geography was 3:1


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Question 13

13 As a prelude to target setting a headteacher referred to a scatter graph showing comparative

GCSE results for 1996 and 1999 for Schools A to N in the local authority.


1 in both years, the same school had the highest percentage of pupils achieving at least 5 A*-Cgrades at GCSE

2 in both years, the same 5 schools had the five highest percentages of pupils achieving at least 5A*-C grades at GCSE

3 no school had a lower percentage of pupils achieving at least 5 A*-C grades at GCSE in 1999than in 1996

4 the majority of schools had a higher percentage of pupils achieving at least 5 A*-C grades atGCSE in 1999 than in 1996

Question 14

14 At a governors meeting to discuss the following years budget the head teacher presented thefollowing information:

The table shows the pupils numbers for 2002, the expected pupil numbers for 2003 and theAge Weighted Pupil Unit (AWPU).

The AWPU is the amount of money the school receives for each pupil in each year group.

Yeargroup

Pupil numbers in2002

Expected pupilsnumbers in 2003

Age weighted pupil unit(AWPU)

Nursery 27 35 2,083

Reception 27 27 2,406

Year 1 27 27 1,878

Year 2 27 27 1,895

Year 3 27 27 1,900

Year 4 27 27 1,900

Year 5 27 27 1,922


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Year 6 27 27 1,922

The increase in the schools budget due to changes in pupil numbers in the same year group canbe calculated using the following formula:

Increase in schools budget = (expected year group pupil numbers in 2003 year grouppupil numbers in 2002) x AWPU for year group

What would be the increase in the schools budget in 2003?

Question 15 and 16

Questions 15 and 16 refer to the table below.

The following table shows the achievement of pupils in a school compared with the national resultsfor GCSE.

GCSE results 5 or more grades

A*-C

5 or more grades

A*-G

1 or more grades

A*-G

Boys 62 120 122

Girls 74 118 119

Number of pupilsachievingstandardspecified

Total 136 238 241

School 55(56) 96(98) 98(99)Percentageachievingstandardspecified

National 43(43) 88(88) 94(94)

Note: Figures in brackets show the previous years results

The number of pupils in Year 11 in this school were as follows:

Boys 126

Girls 121

Total 247

15 Indicate all the true statements:

1 all pupils in the school achieved at least one GCSE grade A*-G

2 of the boys in the school, 7% more achieved 5 or more grades A*-C than the national averagefor all pupils

3 more boys than girls in the school achieved 5 or more grades A*-G

Answer....................

16 Year 10 contained 130 boys and 126 girls. For the following year, the school's target was toincrease the percentage of pupils achieving 5 or more GCSE grades A*- C by 5 percentagepoints.

How many pupils needed to achieve 5 or more grades A*-C in the following year for the

school to meet its target?


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Question 17

17 A teacher organised revision classes for pupils achieving grade D and below in mock

examinations and used the following table to assess which pupils might benefit fromattending the classes.

Grade Boys Girls Total

A* 0 2 2

A 2 1 3

B 3 4 7

C 3 3 6

D 3 1 4

E 1 2 3

F 0 1 1

G 1 0 1

What fraction of the class was advised to attend the revision classes?

a 2/3

b1/2

c 1/3

d

5

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Question 18

18 A teacher compared the performances of two classes. The results of the Key Stage 3 Englishtests were used.

Class A

Level Below 4 4 5 6 7 Total

Number of boys 2 4 7 3 1 17

Number of girls 0 2 7 4 2 15

Class B

Level Below 4 4 5 6 7 Total

Number of boys 0 3 8 3 2 16

Number of girls 1 3 7 6 2 19


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What fraction of Class A achieved Level 5 and above? Give your answer in its lowest terms.

Question 19

19 To inform the school improvement plan, teachers in School C compared the points scores ofpupils in their school with the points scores of pupils at other local schools.

School Mean GCE A/AS points score per pupil Year

A

18.4

20.5

20.6

21.2

1996

1997

1998

1999

B

13.8

13.7

13.5

13.6

1996

1997

1998

1999

C

18.1

18.0

17.7

17.5

1996

1997

1998

1999

D

14.0

13.5

13.9

14.1

1996

1997

1998

1999


1 School C had the second highest mean points score per pupil for each of the four years

2 School C had the largest range of mean points scores per pupil

3 School C was the only school to show a decline of mean points scores per pupil every year


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Question 20

20 As part of a review of pupils' performance, a group of teachers was provided with the bar chart

below.

What was the increase in the mean points score from 1998 to 1999 as a percentage of themean points score for 1998? Give your answer to one decimal place.

a 3.2%

b 3.3%

c 4.6%

d 5.9%

Question 21

21 A teacher analysed the results in the table below for a group of Year 9 pupils in order to makean end of Key Stage assessment.

PupilsTest 1

out of 25Test 2

out of 30Test 3

out of 40

A 18 27 33

B 12 20 26

C 21 20 36

D 19 11 29

E 17 17 38

F 14 23 14

What is the difference in the mean percentage scores between Test 1 and Test 3?


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Answer key


No. Answer

1 63

2 187.50

3 171

4 24

5 900

6 60%

7 120

8 225

9 15

10 130

11 11

12 24


No. Answer

1 35

2 28

3 44

4 10:45

5 20

6 35

7 75%

8 6

9 0.065

10 10

11 12

12 21 hours 40 minutes


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No. Answer

1 3

2 1/5

3 45 minutes

4 13.25

5 40

6 12%

7 188

8 0.35

9 1/3

10 5

11 12

12 10

Answers and commentaries to sample on-screen questions 1 - 10


What information do I need?The number of books present in stock.The number of pupils in Year 11.The cost of each book.The discount.

How can I work out the answer?Possible methods are:


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1. Look at the number of copies needed of Book A140 44 = 96Use the on-screen calculator to find the cost before discount96 x 3.95 = 379.20Then take off the 10% discount (37.92)Use the on-screen calculator to find the cost after discount379.20 - 37.92 = 341.28

Follow the same procedure for Books B, C and D.

Book B140 80 = 6060 x 4.75 = 28510% discount is 28.50285.00 - 28.50 = 256.50

Book C140 133 = 77 x 7.95 = 55.65

(no discount as less than 10 copies ordered)

Book D140 30 = 110110 x 5.99 = 658.90You could work out this stage mentally by multiplying 110 by 6 (660) and subtracting110 x 1p (1.10).10% discount is 65.89658.90 - 65.89 = 593.01

To find the total cost, add up the costs of the four titles.341.28 + 256.50 + 55.65 + 593.01 = 1246.44

2. Call up the on-screen calculator.For each book work out:(Total - stock) x cost x 90% (if 10 or more copies are ordered) = the amount paid.For Book A: (140 - 44) x 3.95 x 90 100 (or 0.9) = 341.28Jot down the answer.Repeat for Books B, C and D.Once all are calculated, add together for final total.

The following shows the sequence of operations:140 44 = 96. 96 x 3.95 = 379.2. 379.2 x 0.9 = 341.28140 80 = 60. 60 x 4.75 = 285. 285 x 0.9 = 256.5140 133 = 7. 7 x 7.95 = 55.65140 30 = 110. 110 x 5.99 = 658.9. 658.9 x 0.9 = 593.01

341.28 + 256.5 + 55.65 + 593.01 = 1246.44

Common MistakesSubtracting a 10% discount from all the stock.

CommentsThis question involves repeating a number of similar calculations. It may be useful to jot down thecosts for each book as you calculate them, and any other stages you feel necessary.If you use the calculator to work out the cost after discount, it may be helpful to simply multiply thecost before discount by 0.9, rather than working out 10% then subtracting it from the cost beforediscount.

Answer

Type your answer in the box.The answer is 1246.44


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What information do I need?The pupils marks in each of the tests.The maximum marks available for each test (60)

How can I work out the answer?One possible method is:

First work out the value of 5 percentage points on a score of 60 and then compare the numbers.5% of 60 is 5/100 x 60= 1/20 x 60 = 3.

This means that all pupils who achieved at least 3 marks more in Test 2 than in Test 1 scored atleast 5 percentage points more.Look at each pupils results in turn and click on any which have a mark for Test 2 which is 3 ormore marks higher than Test 1.The pupils who achieved 3 marks (5 percentage points) or more higher in Test 2 than in Test 1 areB, E, H and J.

Common mistakesTaking the difference in the actual marks to get the answer.Including pupils whose marks were 3 marks higher in Test 1 than in Test 2, rather than the otherway round.

CommentThis question can be answered by working out the percentage mark for each of the pupils andtests before comparing. This method would take a long time and increases the chances of makingmistakes.

AnswerUsing the mouse, click on the letters of Pupils B, E, H and J in the table. If you change your mind,remove one target before clicking on the next pupil.


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What information do I need?The relevant parts of the table to obtain data to answer each statement, which are:

Statement 1The national percentage of boys achieving Level 2 and above in 1999 and in 2002 nationally.

Statement 2The percentage of boys nationally who achieved Level 2 and above in each of the years 1999 and in2002.

Statement 3The LEA and national results for boys and girls for 2002.


Statement 1The national percentage of boys achieving Level 2 and above in 1999 is 73.9% and in 2002 is 75.4%.

The increase in percentage points is 75.4 - 73.9 = 1.5.This is more than 1.4%.Hence Statement 1 is FALSE.

Statement 2During the 4 year period 1999 and in 2002 the increase in percentage points is:75.4 - 73.9 = 1.5The mean yearly percentage point increase during the 4 years can be achieved by taking this increaseand dividing by 3. You need to divide by 3 (rather than 4) because there were three changes in results:From 73.9 to 73.2;From 73.2 to 75.7;From 75.7 to 75.4

1.5 3 = 0.5


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Hence Statement 2 is TRUE.

Statement 3The LEA data in 2002 compared with the national data is:for boys, 78.0 - 75.4 = 2.6

for girls, 87.4 - 84.8 = 2.6Hence Statement 3 is TRUE.

Common mistakesConfusing a percentage point increase with a percentage increase.Calculating the mean by dividing the 4 years (1999 and in 2002) instead of the 3 yearly changes.

AnswerUsing the mouse, click the boxes where the statements are true.Your answer should look like this:Indicate all the true statements:


What information do I need?The number of pupils with special educational needs in each of the five classes.The number of pupils in each of the five classes.


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Look at the bar chart.

The number of pupils in Class P with SEN is 6.

The number of pupils in Class Q with SEN is 2.The number of pupils in Class R with SEN is 7.The number of pupils in Class S with SEN is 3 .The number of pupils in Class T with SEN is 7.

The total number of pupils with SEN is 6 + 2 + 7 + 3 + 7 = 25.

The number of pupils in Class P is 30.The number of pupils in Class Q is 30.The number of pupils in Class R is 30.The number of pupils in Class S is 29.The number of pupils in Class T is 31.

The total number of pupils is 30 + 30 + 30 + 29 + 31 = 150.

The ratio of pupils with SEN to all pupils is 25:150.

25:150 is 1:6 in its simplest form.

Common mistakesMisreading information from the bar chart.Not reducing the ratio to its simplest form.

AnswerType your answer in the answer box provided.

The answer is 1:6



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What information do I need?The two schools which have results for 2002 which are more than 10 percentage points higherthan in 1999.

How can I work out the answer?

One possible method is:

Look at the horizontal axis (1999 results)

for 0-10%School N (9%, 15%) does not achieve a 10 or more percentage points increase.

for 11-20%School K (15%, 23%) does not achieve a 10 or more percentage points increase.

for 21-30%

School M (21%, 17%) does not achieve a 10 or more percentage points increase.School L (23%, 28%) does not achieve a 10 or more percentage points increase.School I (24%, 30%) does not achieve a 10 or more percentage points increase.School J (25%, 27%) does not achieve a 10 or more percentage points increase.School H (28%, 32%) does not achieve a 10 or more percentage points increase.School E (28%, 39%) does achieve a 10 or more percentage points increase.School B (27%, 46%) does achieve a 10 or more percentage points increase.

The two schools are B and E.

Common mistakesSubtracting the y axis (2002) value from the x axis (1999) value.

CommentsThe question asks you to click on the positions of the two schools whose percentage of pupils


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meet the criterion. Once you have found two such schools and checked they meet the criterion youhave answered the question. It is then not essential to look at other schools.There is a quick way of checking to see if a school meets the criterion. For example, locate Csposition on the horizontal axis. You should find it is 34. Add 10 to this value. Then ask yourself thequestion: is it more than 44 on the vertical axis? If the answer is no, it does not meet the criterion.

AnswerUsing the mouse, click the points for Schools B and E on the scattergraph. If you change yourmind, remove one target before clicking on the next school.


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What information do I need?The number of pupils on the Business course in 2001 and 2002.The total number of pupils in 2001 and 2002.


The proportion of Business course pupils for 2001 is21

114

Written as a percentage this is21

114x 100 = 18.4%

The proportion of Business course pupils for 2002 is29

131

Written as a percentage this is

29

131x 100 = 22.1%

So the percentage points increase is 22.1 - 18.4 = 3.7

Common mistakesNot expressing answers correct to one decimal place.Dividing by the wrong totals.

CommentsThe question is only concerned with the two bars for Business course pupils. Check carefully theheights of the bars against the vertical scale.


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AnswerType your answer in the answer box provided.Only type the number 3.7 because percentage points is stated in the question.


What information do I need?From the graph the percentage of pupils who made more than 5 spelling mistakes.The number of pupils in the school.

How can I work out an answer?One possible method is:

Look at the graph line and identify the cumulative frequency (%) for 5 spelling mistakes. The valueis 60%.This means that 60% of pupils in the school made 5 spelling mistakes or less.So 40% of pupils (ie the rest) missed more than 5 spelling mistakes in the standard spelling test.There are 210 pupils in the school.

40% of 210 is 40/100 x 210 =" 8484 pupils made more than 5 spelling mistakes in the test.

Common mistakesMisreading the value from the graph.Using 60% to calculate the number of pupils.Forgetting to calculate the number of pupils.

CommentsCumulative frequency graphs require complex interpretation. For more detail on CumulativeFrequency graphs see the Numeracy Support section.

Answer

Using the mouse, click the circle for the correct statement, B. If you change your mind, removeone answer before reselecting another.Your answer should look like this:


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What information do I need?The relevant parts of the table to obtain data to answer each statement, which are:

Statement 1The proportion of A - C grades for each subject.

Statement 2The median for each subject.

Statement 3The subjects which had achievement at grade A.

How can I work out the answer?

Statement 1To test Statement 1 the proportion of A - C grades for systems and control is compared with theproportions for the other 3 subjects to see if it is the highest.The proportion of A - C grades:

Research mechanisms - 25% (upper quartile) Systems and control - more than 25% (upper quartile) but less than 50% (median line)

Food technology - 25% (upper quartile)


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Textiles - 50% (median line)Textiles has the highest proportion of A - C grades.Hence Statement 1 is FALSE.

Statement 2To test Statement 2 the median grade for food technology is compared with the other 3 median

grades to see if it is the lowest.The median grade for each of the 4 technology subjects is represented by the white line in eachboxResearch mechanisms - ESystems & control - DFood technology - DTextiles - CThe lowest median grade is E for research mechanisms, so food technology does not have thelowest median grade.Hence Statement 2 is FALSE.

Statement 3To test Statement 3 each of the 4 box and whisker diagrams is examined to see if their ranges

include a grade A.The range for research mechanisms is G to A. So at least 1 pupil achieved a grade A.The range for systems and control is also G to A. So at least 1 pupil achieved a grade A.The range for food technology is F to B. So no pupil achieved a grade A.The range for textiles is E to A. So at least 1 pupil achieved a grade A.At least 1 grade A was achieved in 3 of the 4 technology subjects.Hence Statement 3 is TRUE.

Common mistakesTrying to obtain from a box and whisker diagram detailed information which is not summarised inthe diagram.

Comments

The box and whisker diagram summarises 4 pieces of information. The grade ranges for thebottom 25%, the middle 50%, the top 25% of pupils and the median grade.

AnswerUsing the mouse, click the boxes where the statements are true.Your answer should look like this:Indicate all the true statements:


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What information do I need?For Pupil A: The modal score.For Pupil B: The range of scores.For Pupil C: The number of tests and Pupil C's score in each test.



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Pupil AThe modal score is the percentage test score that pupil A achieved most often over the eight mentalarithmetic tests. Look at the graph and identify the line representing the scores for Pupil A.The individual scores achieved by Pupil A are: (30, 30, 40, 40, 40, 40, 50, 80). In Tests 3, 4, 5 and 6Pupil A scored 40%. This is the test score that Pupil A scored most often.

The modal score for Pupil A = 40.

Pupil BThe range of scores achieved by Pupil B is the difference between the lowest and the highest scoresthat Pupil B achieved. Look at the graph and identify the line representing the scores for Pupil B.The highest percentage score is 70. The lowest percentage score is 40. The range is the differencebetween these two readings.The range of scores for Pupil B is 70 40 = 30.

Pupil CThe mean score for Pupil C is the sum of the scores achieved divided by the number of tests. Look atthe graph and identify the line representing the scores for pupil C.Add together the individual percentage points scored in the tests.

Total score: 50 + 60 + 50 + 50 + 50 + 40 + 50 + 50 = 400The number of tests is 8.The mean score for pupil C is 400 8 = 50.Notice that the 60 marks and 40 marks give a mean score of 50, so effectively all the scores are 50 andthere is no need to do any calculation.

Common MistakesIdentifying the wrong line graph for the pupil.Reading incorrect values from the graph.

CommentsThis question is testing your knowledge of mean, range, and mode. See the Numeracy Support sectionon Averages for more information.

AnswerUsing the mouse, select the value 40, click on the box and drag the value to the place here box next toPupil A.Select the value 30, click on the box and drag the value to the place here box next to Pupil B.Select the value 50, click on the box and drag the value to the place here box next to Pupil C.When selecting and placing the boxes into the table, watch for the cursor to become a white arrow andbox which tells you the box has parked in the place here space.Your answer should look like the image above:If you have made a mistake then move the box(es) back to their original position(s) and place thecorrect value(s) in the table.


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Twenty one on-screen questions

No. Answer

1 1 and 2

2 B

3 D

4 2

5 12.5%

6 53

7 2 and 3

8 6.3%

9 36

10 D

11 56

12 3 and 4

13 1 and 4

14 16,664

15 3 only

16 154

17 C

18 3/4

19 1 and 3

20 B

21 6%

Numeracy Sample Questions

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