Assessment · Averages & Range

20 marks

Answer all questions. Show all your working; you get marks for method. Work on your own.Name: __________ Class: ______ Date: ______

Here are the test score for 9 pupils:

2, 2, 3, 2, 10, 4, 8, 5, 8

Write down the median.

Answer: (1 mark)

Here are the shoe size for 7 people:

5, 10, 11, 8, 3, 2, 3

Write down the mode.

Answer: (1 mark)

Here is the test score for 5 pupils.
Work out the mean.

8, 14, 9, 13, 17

Answer: (2 marks)

Here are the test score for 9 pupils.
Work out the median.

3, 4, 10, 5, 6, 3, 8, 4, 6

Answer: (1 mark)

The frequency table shows the number of siblings of some children.

Number of siblings	Frequency
2	6
3	7
4	2
5	2
6	3

Write down the modal number of siblings.

Answer: (1 mark)

Here are the number of siblings for 7 children:

2, 12, 4, 6, 2, 3, 9

Write down the median.

Answer: (1 mark)

Here are the goals scored for 9 matches:

5, 4, 3, 10, 3, 8, 7, 11, 9

Write down the mode.

Answer: (1 mark)

Here is the number of siblings for 8 children.
Work out the mean.

18, 4, 5, 8, 19, 4, 4, 10

Answer: (2 marks)

Here are the cars sold per day for 7 days.
Work out the median.

4, 8, 5, 10, 1, 3, 6

Answer: (1 mark)

The frequency table shows the cars sold per day of some days.

Cars sold per day	Frequency
1	5
2	8
3	2
4	4

Write down the modal cars sold per day.

Answer: (1 mark)

Here are the shoe size for 7 people:

2, 10, 2, 7, 8, 2, 5

Write down the median.

Answer: (1 mark)

Here are the number of pets for 8 students:

10, 9, 3, 2, 2, 11, 7, 12

Write down the mode.

Answer: (1 mark)

Here is the test score for 6 pupils.
Work out the mean.

4, 9, 2, 16, 1, 1

Answer: (2 marks)

Here are the number of pets for 7 students.
Work out the median.

8, 1, 6, 11, 12, 9, 7

Answer: (1 mark)

The frequency table shows the goals scored of some matches.

Goals scored	Frequency
1	6
2	8
3	3
4	1

Write down the modal goals scored.

Answer: (1 mark)

Here are the shoe size for 7 people:

3, 8, 12, 2, 9, 6, 3

Write down the median.

Answer: (1 mark)

The frequency table shows the cars sold per day of some days.
Calculate the mean cars sold per day.
Give your answer to 1 decimal place.

Cars sold per day	Frequency
1	4
2	2
3	2
4	2

Answer: (3 marks)

The frequency table shows the goals scored of 29 matches.
Find the median goals scored.

Goals scored	Frequency
2	5
3	8
4	8
5	4
6	4

Answer: (2 marks)

The mean of these 5 numbers is $14$.
One value is missing (shown as $?$).
Work out the missing value.

16, 16, 3, 18, ?

Answer: (3 marks)

The frequency table shows the shoe size of some people.
Calculate the mean shoe size.
Give your answer to 1 decimal place.

Shoe size	Frequency
0	1
1	3
2	3
3	8

Answer: (3 marks)

The frequency table shows the test score of 25 pupils.
Find the median test score.

Test score (marks)	Frequency
2	9
3	3
4	6
5	7

Answer: (2 marks)

The mean of these 5 numbers is $9$.
One value is missing (shown as $?$).
Work out the missing value.

2, 3, 7, 16, ?

Answer: (3 marks)

The frequency table shows the goals scored of some matches.
Calculate the mean goals scored.
Give your answer to 1 decimal place.

Goals scored	Frequency
1	7
2	1
3	6
4	2
5	9

Answer: (3 marks)

The frequency table shows the number of siblings of 31 children.
Find the median number of siblings.

Number of siblings	Frequency
1	6
2	7
3	6
4	3
5	9

Answer: (2 marks)

The mean of these 5 numbers is $7$.
One value is missing (shown as $?$).
Work out the missing value.

2, 3, 2, 10, ?

Answer: (3 marks)

The frequency table shows the goals scored of some matches.
Calculate the mean goals scored.
Give your answer to 1 decimal place.

Goals scored	Frequency
0	9
1	3
2	4
3	7
4	2

Answer: (3 marks)

A match has these 4 goals scored:

3, 12, 7, 7

One more value is added so that the mean of all $5$ values becomes $9$.
What value must be added?

Answer: (3 marks)

Harun and Femi each recorded the test score for 5 pupils.

Harun: 5, 11, 3, 3, 8
Femi: 11, 12, 15, 10, 2

Work out the mean for Harun.

Answer: (1 mark)

The grouped frequency table shows the distance of 25 throws.
Work out an estimate for the mean distance.
Give your answer to 1 decimal place.

Distance (m)	Frequency
10 < d ≤ 20	7
20 < d ≤ 30	7
30 < d ≤ 40	8
40 < d ≤ 50	3

Answer: (3 marks)

A student has these 5 number of pets:

11, 5, 7, 13, 14

One more value is added so that the mean of all $6$ values becomes $11$.
What value must be added?

Answer: (3 marks)

Leo and Harun each recorded the number of pets for 5 students.

Leo: 7, 10, 1, 6, 1
Harun: 8, 7, 3, 10, 2

Work out the mean for Leo.

Answer: (1 mark)

The grouped frequency table shows the length of 35 leaves.
Work out an estimate for the mean length.
Give your answer to 1 decimal place.

Length (cm)	Frequency
0 < L ≤ 5	11
5 < L ≤ 10	6
10 < L ≤ 15	11
15 < L ≤ 20	7

Answer: (3 marks)

A child has these 5 number of siblings:

12, 15, 4, 13, 14

One more value is added so that the mean of all $6$ values becomes $14$.
What value must be added?

Answer: (3 marks)

Amir and Femi each recorded the number of siblings for 5 children.

Amir: 3, 2, 8, 7, 10
Femi: 8, 11, 13, 15, 8

Work out the mean for Amir.

Answer: (1 mark)

The grouped frequency table shows the distance of 25 throws.
Work out an estimate for the mean distance.
Give your answer to 1 decimal place.

Distance (m)	Frequency
10 < d ≤ 20	2
20 < d ≤ 30	7
30 < d ≤ 40	8
40 < d ≤ 50	8

Answer: (3 marks)

A day has these 4 cars sold per day:

13, 15, 13, 9

One more value is added so that the mean of all $5$ values becomes $13$.
What value must be added?

Answer: (3 marks)

Dev and Isla each recorded the shoe size for 5 people.

Dev: 9, 3, 3, 1, 9
Isla: 9, 8, 9, 4, 10

Work out the mean for Dev.

Answer: (1 mark)

The grouped frequency table shows the height of 28 plants.
Work out an estimate for the mean height.
Give your answer to 1 decimal place.

Height (cm)	Frequency
5 < h ≤ 10	2
10 < h ≤ 15	7
15 < h ≤ 20	8
20 < h ≤ 25	11

Answer: (3 marks)

Mark scheme · Averages & Range

Total: 20 marks

Award the marks shown for each correct step, then add up the total out of 20. A method mark counts even if the final answer is wrong.

Here are the test score for 9 pupils:

2, 2, 3, 2, 10, 4, 8, 5, 8

Write down the median.[1 mark]

Method

Put the values in order: $2, 2, 2, 3, 4, 5, 8, 8, 10$.

The middle value is $4$.

Answer: $4$

Marks

✔1 markmedian = 4

Here are the shoe size for 7 people:

5, 10, 11, 8, 3, 2, 3

Write down the mode.[1 mark]

Method

The mode is the most common value. $3$ appears 2 times.

Answer: $3$

Marks

✔1 markmode = 3

Here is the test score for 5 pupils.
Work out the mean.

8, 14, 9, 13, 17

[2 marks]

Method

Add the values: $8 + 14 + 9 + 13 + 17 = 61$.

Mean $= 61 \div 5 = 12.2$.

Answer: $12.2$

Marks

✔1 marktotal = 61

✔1 markmean = 12.2

Here are the test score for 9 pupils.
Work out the median.

3, 4, 10, 5, 6, 3, 8, 4, 6

[1 mark]

Method

Put the values in order: $3, 3, 4, 4, 5, 6, 6, 8, 10$.

The middle value is the median $= 5$.

Answer: $5$

Marks

✔1 markmedian = 5

The frequency table shows the number of siblings of some children.

Number of siblings	Frequency
2	6
3	7
4	2
5	2
6	3

Write down the modal number of siblings.[1 mark]

Method

The modal value is the one with the highest frequency ($7$), which is $3$.

Answer: $3$

Marks

✔1 markmode = 3

Here are the number of siblings for 7 children:

2, 12, 4, 6, 2, 3, 9

Write down the median.[1 mark]

Method

Put the values in order: $2, 2, 3, 4, 6, 9, 12$.

The middle value is $4$.

Answer: $4$

Marks

✔1 markmedian = 4

Here are the goals scored for 9 matches:

5, 4, 3, 10, 3, 8, 7, 11, 9

Write down the mode.[1 mark]

Method

The mode is the most common value. $3$ appears 2 times.

Answer: $3$

Marks

✔1 markmode = 3

Here is the number of siblings for 8 children.
Work out the mean.

18, 4, 5, 8, 19, 4, 4, 10

[2 marks]

Method

Add the values: $18 + 4 + 5 + 8 + 19 + 4 + 4 + 10 = 72$.

Mean $= 72 \div 8 = 9$.

Answer: $9$

Marks

✔1 marktotal = 72

✔1 markmean = 9

Here are the cars sold per day for 7 days.
Work out the median.

4, 8, 5, 10, 1, 3, 6

[1 mark]

Method

Put the values in order: $1, 3, 4, 5, 6, 8, 10$.

The middle value is the median $= 5$.

Answer: $5$

Marks

✔1 markmedian = 5

The frequency table shows the cars sold per day of some days.

Cars sold per day	Frequency
1	5
2	8
3	2
4	4

Write down the modal cars sold per day.[1 mark]

Method

The modal value is the one with the highest frequency ($8$), which is $2$.

Answer: $2$

Marks

✔1 markmode = 2

Here are the shoe size for 7 people:

2, 10, 2, 7, 8, 2, 5

Write down the median.[1 mark]

Method

Put the values in order: $2, 2, 2, 5, 7, 8, 10$.

The middle value is $5$.

Answer: $5$

Marks

✔1 markmedian = 5

Here are the number of pets for 8 students:

10, 9, 3, 2, 2, 11, 7, 12

Write down the mode.[1 mark]

Method

The mode is the most common value. $2$ appears 2 times.

Answer: $2$

Marks

✔1 markmode = 2

Here is the test score for 6 pupils.
Work out the mean.

4, 9, 2, 16, 1, 1

[2 marks]

Method

Add the values: $4 + 9 + 2 + 16 + 1 + 1 = 33$.

Mean $= 33 \div 6 = 5.5$.

Answer: $5.5$

Marks

✔1 marktotal = 33

✔1 markmean = 5.5

Here are the number of pets for 7 students.
Work out the median.

8, 1, 6, 11, 12, 9, 7

[1 mark]

Method

Put the values in order: $1, 6, 7, 8, 9, 11, 12$.

The middle value is the median $= 8$.

Answer: $8$

Marks

✔1 markmedian = 8

The frequency table shows the goals scored of some matches.

Goals scored	Frequency
1	6
2	8
3	3
4	1

Write down the modal goals scored.[1 mark]

Method

The modal value is the one with the highest frequency ($8$), which is $2$.

Answer: $2$

Marks

✔1 markmode = 2

Here are the shoe size for 7 people:

3, 8, 12, 2, 9, 6, 3

Write down the median.[1 mark]

Method

Put the values in order: $2, 3, 3, 6, 8, 9, 12$.

The middle value is $6$.

Answer: $6$

Marks

✔1 markmedian = 6

The frequency table shows the cars sold per day of some days.
Calculate the mean cars sold per day.
Give your answer to 1 decimal place.

Cars sold per day	Frequency
1	4
2	2
3	2
4	2

[3 marks]

Method

Multiply each value by its frequency and add: $\sum fx = 1\times4 + 2\times2 + 3\times2 + 4\times2 = 22$.

Total frequency $\sum f = 4 + 2 + 2 + 2 = 10$.

Mean $= 22 \div 10 = 2.2$.

Answer: $2.2$

Marks

✔1 markΣfx = 22

✔1 markΣf = 10

✔1 markmean = 2.2

The frequency table shows the goals scored of 29 matches.
Find the median goals scored.

Goals scored	Frequency
2	5
3	8
4	8
5	4
6	4

[2 marks]

Method

There are $29$ values, so the median is the $\tfrac{29+1}{2} = 15$th value.

Counting up the frequencies, the 15th value is $4$.

Answer: $4$

Marks

✔1 markmedian is the 15th value

✔1 markmedian = 4

The mean of these 5 numbers is $14$.
One value is missing (shown as $?$).
Work out the missing value.

16, 16, 3, 18, ?

[3 marks]

Method

Total of all $5$ values $= 5 \times 14 = 70$.

Total of the known values $= 16 + 16 + 3 + 18 = 53$.

Missing value $= 70 - 53 = 17$.

Answer: $17$

Marks

✔1 marktotal = 5 × 14 = 70

✔1 markknown total = 53

✔1 markmissing = 17

The frequency table shows the shoe size of some people.
Calculate the mean shoe size.
Give your answer to 1 decimal place.

Shoe size	Frequency
0	1
1	3
2	3
3	8

[3 marks]

Method

Multiply each value by its frequency and add: $\sum fx = 0\times1 + 1\times3 + 2\times3 + 3\times8 = 33$.

Total frequency $\sum f = 1 + 3 + 3 + 8 = 15$.

Mean $= 33 \div 15 = 2.2$.

Answer: $2.2$

Marks

✔1 markΣfx = 33

✔1 markΣf = 15

✔1 markmean = 2.2

The frequency table shows the test score of 25 pupils.
Find the median test score.

Test score (marks)	Frequency
2	9
3	3
4	6
5	7

[2 marks]

Method

There are $25$ values, so the median is the $\tfrac{25+1}{2} = 13$th value.

Counting up the frequencies, the 13th value is $4$.

Answer: $4$

Marks

✔1 markmedian is the 13th value

✔1 markmedian = 4

The mean of these 5 numbers is $9$.
One value is missing (shown as $?$).
Work out the missing value.

2, 3, 7, 16, ?

[3 marks]

Method

Total of all $5$ values $= 5 \times 9 = 45$.

Total of the known values $= 2 + 3 + 7 + 16 = 28$.

Missing value $= 45 - 28 = 17$.

Answer: $17$

Marks

✔1 marktotal = 5 × 9 = 45

✔1 markknown total = 28

✔1 markmissing = 17

The frequency table shows the goals scored of some matches.
Calculate the mean goals scored.
Give your answer to 1 decimal place.

Goals scored	Frequency
1	7
2	1
3	6
4	2
5	9

[3 marks]

Method

Multiply each value by its frequency and add: $\sum fx = 1\times7 + 2\times1 + 3\times6 + 4\times2 + 5\times9 = 80$.

Total frequency $\sum f = 7 + 1 + 6 + 2 + 9 = 25$.

Mean $= 80 \div 25 = 3.2$.

Answer: $3.2$

Marks

✔1 markΣfx = 80

✔1 markΣf = 25

✔1 markmean = 3.2

The frequency table shows the number of siblings of 31 children.
Find the median number of siblings.

Number of siblings	Frequency
1	6
2	7
3	6
4	3
5	9

[2 marks]

Method

There are $31$ values, so the median is the $\tfrac{31+1}{2} = 16$th value.

Counting up the frequencies, the 16th value is $3$.

Answer: $3$

Marks

✔1 markmedian is the 16th value

✔1 markmedian = 3

The mean of these 5 numbers is $7$.
One value is missing (shown as $?$).
Work out the missing value.

2, 3, 2, 10, ?

[3 marks]

Method

Total of all $5$ values $= 5 \times 7 = 35$.

Total of the known values $= 2 + 3 + 2 + 10 = 17$.

Missing value $= 35 - 17 = 18$.

Answer: $18$

Marks

✔1 marktotal = 5 × 7 = 35

✔1 markknown total = 17

✔1 markmissing = 18

The frequency table shows the goals scored of some matches.
Calculate the mean goals scored.
Give your answer to 1 decimal place.

Goals scored	Frequency
0	9
1	3
2	4
3	7
4	2

[3 marks]

Method

Multiply each value by its frequency and add: $\sum fx = 0\times9 + 1\times3 + 2\times4 + 3\times7 + 4\times2 = 40$.

Total frequency $\sum f = 9 + 3 + 4 + 7 + 2 = 25$.

Mean $= 40 \div 25 = 1.6$.

Answer: $1.6$

Marks

✔1 markΣfx = 40

✔1 markΣf = 25

✔1 markmean = 1.6

A match has these 4 goals scored:

3, 12, 7, 7

One more value is added so that the mean of all $5$ values becomes $9$.
What value must be added?[3 marks]

Method

New total needed $= 5 \times 9 = 45$.

Current total $= 3 + 12 + 7 + 7 = 29$.

Value to add $= 45 - 29 = 16$.

Answer: $16$

Marks

✔1 marknew total = 5 × 9

✔1 markcurrent total = 29

✔1 markadd 16

Harun and Femi each recorded the test score for 5 pupils.

Harun: 5, 11, 3, 3, 8
Femi: 11, 12, 15, 10, 2

Work out the mean for Harun.[1 mark]

Method

Mean $= (5 + 11 + 3 + 3 + 8) \div 5 = 30 \div 5 = 6$.

Answer: $6$

Marks

✔1 markHarun mean = 6

The grouped frequency table shows the distance of 25 throws.
Work out an estimate for the mean distance.
Give your answer to 1 decimal place.

Distance (m)	Frequency
10 < d ≤ 20	7
20 < d ≤ 30	7
30 < d ≤ 40	8
40 < d ≤ 50	3

[3 marks]

Method

Use the midpoint of each class: $15,\ 25,\ 35,\ 45$.

Multiply each midpoint by its frequency and add: $\sum fx = 15\times7 + 25\times7 + 35\times8 + 45\times3 = 695$.

Total frequency $\sum f = 7 + 7 + 8 + 3 = 25$. Estimated mean $= 695 \div 25 = 27.8$.

Answer: $27.8$

Marks

✔1 markuse midpoints

✔1 markΣfx = 695, Σf = 25

✔1 markmean ≈ 27.8

A student has these 5 number of pets:

11, 5, 7, 13, 14

One more value is added so that the mean of all $6$ values becomes $11$.
What value must be added?[3 marks]

Method

New total needed $= 6 \times 11 = 66$.

Current total $= 11 + 5 + 7 + 13 + 14 = 50$.

Value to add $= 66 - 50 = 16$.

Answer: $16$

Marks

✔1 marknew total = 6 × 11

✔1 markcurrent total = 50

✔1 markadd 16

Leo and Harun each recorded the number of pets for 5 students.

Leo: 7, 10, 1, 6, 1
Harun: 8, 7, 3, 10, 2

Work out the mean for Leo.[1 mark]

Method

Mean $= (7 + 10 + 1 + 6 + 1) \div 5 = 25 \div 5 = 5$.

Answer: $5$

Marks

✔1 markLeo mean = 5

The grouped frequency table shows the length of 35 leaves.
Work out an estimate for the mean length.
Give your answer to 1 decimal place.

Length (cm)	Frequency
0 < L ≤ 5	11
5 < L ≤ 10	6
10 < L ≤ 15	11
15 < L ≤ 20	7

[3 marks]

Method

Use the midpoint of each class: $2.5,\ 7.5,\ 12.5,\ 17.5$.

Multiply each midpoint by its frequency and add: $\sum fx = 2.5\times11 + 7.5\times6 + 12.5\times11 + 17.5\times7 = 332.5$.

Total frequency $\sum f = 11 + 6 + 11 + 7 = 35$. Estimated mean $= 332.5 \div 35 = 9.5$.

Answer: $9.5$

Marks

✔1 markuse midpoints

✔1 markΣfx = 332.5, Σf = 35

✔1 markmean ≈ 9.5

A child has these 5 number of siblings:

12, 15, 4, 13, 14

One more value is added so that the mean of all $6$ values becomes $14$.
What value must be added?[3 marks]

Method

New total needed $= 6 \times 14 = 84$.

Current total $= 12 + 15 + 4 + 13 + 14 = 58$.

Value to add $= 84 - 58 = 26$.

Answer: $26$

Marks

✔1 marknew total = 6 × 14

✔1 markcurrent total = 58

✔1 markadd 26

Amir and Femi each recorded the number of siblings for 5 children.

Amir: 3, 2, 8, 7, 10
Femi: 8, 11, 13, 15, 8

Work out the mean for Amir.[1 mark]

Method

Mean $= (3 + 2 + 8 + 7 + 10) \div 5 = 30 \div 5 = 6$.

Answer: $6$

Marks

✔1 markAmir mean = 6

The grouped frequency table shows the distance of 25 throws.
Work out an estimate for the mean distance.
Give your answer to 1 decimal place.

Distance (m)	Frequency
10 < d ≤ 20	2
20 < d ≤ 30	7
30 < d ≤ 40	8
40 < d ≤ 50	8

[3 marks]

Method

Use the midpoint of each class: $15,\ 25,\ 35,\ 45$.

Multiply each midpoint by its frequency and add: $\sum fx = 15\times2 + 25\times7 + 35\times8 + 45\times8 = 845$.

Total frequency $\sum f = 2 + 7 + 8 + 8 = 25$. Estimated mean $= 845 \div 25 = 33.8$.

Answer: $33.8$

Marks

✔1 markuse midpoints

✔1 markΣfx = 845, Σf = 25

✔1 markmean ≈ 33.8

A day has these 4 cars sold per day:

13, 15, 13, 9

One more value is added so that the mean of all $5$ values becomes $13$.
What value must be added?[3 marks]

Method

New total needed $= 5 \times 13 = 65$.

Current total $= 13 + 15 + 13 + 9 = 50$.

Value to add $= 65 - 50 = 15$.

Answer: $15$

Marks

✔1 marknew total = 5 × 13

✔1 markcurrent total = 50

✔1 markadd 15

Dev and Isla each recorded the shoe size for 5 people.

Dev: 9, 3, 3, 1, 9
Isla: 9, 8, 9, 4, 10

Work out the mean for Dev.[1 mark]

Method

Mean $= (9 + 3 + 3 + 1 + 9) \div 5 = 25 \div 5 = 5$.

Answer: $5$

Marks

✔1 markDev mean = 5

The grouped frequency table shows the height of 28 plants.
Work out an estimate for the mean height.
Give your answer to 1 decimal place.

Height (cm)	Frequency
5 < h ≤ 10	2
10 < h ≤ 15	7
15 < h ≤ 20	8
20 < h ≤ 25	11

[3 marks]

Method

Use the midpoint of each class: $7.5,\ 12.5,\ 17.5,\ 22.5$.

Multiply each midpoint by its frequency and add: $\sum fx = 7.5\times2 + 12.5\times7 + 17.5\times8 + 22.5\times11 = 490$.

Total frequency $\sum f = 2 + 7 + 8 + 11 = 28$. Estimated mean $= 490 \div 28 = 17.5$.

Answer: $17.5$

Marks

✔1 markuse midpoints

✔1 markΣfx = 490, Σf = 28

✔1 markmean ≈ 17.5