Averages and spread

What is the mode of the nine numbers below?

3 8 9 3 7 2 7 9 3

What is the median of the seven numbers below?

8 3 4 9 2 8 1

Work out the mean of the four numbers below.

3 12 10 7

A fifth number is added to the list below.

13 18 4 17

When the fifth number is added to the list, the range increases by 3.

Write down the two possible values for the fifth number.

You must show all your working.

The two possible values are_{…........ ……….} and_{…........ ……….}

The mean of five whole numbers is 20.

The mean of three of these numbers is 22. The other two numbers have a difference of 6.

Find the other two numbers.

1 day and 14 hours 2 days and 3 hours 73 hours

Calculate the mean of the three lengths of times.

Give your answer in days and hours.

The mean =_{……………........ ………} days and_{……………........ ………} hours

The mean of five whole numbers is 20.

The mean of three of these numbers is 22. The other two numbers have a difference of 6.

Find the other two numbers.

Tomos wants to find the median of the numbers below.

7 1 20 14 11

He writes the answer 20.

Explain why Tomos’s answer is incorrect.

Ted writes down five numbers:

59 89 77 31 83

Calculate the mean of Ted’s numbers.

Every number in Ted’s list is decreased by 3.

What is the mean of the numbers in his new list?

Find five numbers so that: 12. • their mean is 4·5 • their mode is 3·5.

Write your five numbers in the boxes below.

The five numbers are

Find five numbers so that: 3. • their mean is 4·5 • their mode is 3·5.

Write your five numbers in the boxes below.

The five numbers are

Ifan has chosen four odd numbers.

Some of the numbers are the same and some of them are different. Ifan’s numbers are all less than 10.

Both the mode and the mean of Ifan’s numbers are 7.

What numbers has Ifan chosen?

Jemma is asked to work out the following calculation.

10 + 4 × 9

Jemma’s method is 14 x 9 = 126

Explain why Jemma’s method is wrong.

Sion is asked to answer the following question.

How many halves are there in 20?

Sion’s method is 20 ÷ 2 = 10

Explain why Sion’s method is wrong.

Rebecca is asked to find the range of the numbers below.

7 1 20 14 11

Rebecca’s method is 11 − 7 = 4

Explain why Rebecca’s method is wrong.

Stef knows what of Paulo’s number is. Using this information, explain how Stef can work out of Paulo’s number.

a and b are two numbers, where b > a.

The mean of the two numbers is equal to the range of the two numbers.

Show that 3a = b.

a and b are two numbers, where b > a.

The mean of the two numbers is equal to the range of the two numbers.

Show that 3a = b.

The mean of four numbers is 9.

What is the total of the four numbers?

Find a set of four numbers such that: • their mean is 9 • their mode is 11.

Write your four numbers in the boxes below.

Arwel writes a list of six numbers:

3 3 4 4 5 6

Arwel adds another number to his list. The mode of his seven numbers is an odd number.

What number does Arwel add to his list?

The number that Arwel adds to his list is_{………........ …………..}

Ffion writes a list of seven numbers:

3 8 4 1 2 8 9

What is the median of Ffion’s seven numbers?

The median of Ffion’s seven numbers is_{………........ …………..}

Marc writes down two numbers:

2 7

Marc adds another number to his list. The mean of his three numbers is 5.

What number does Marc add to his list?

You must show all your working.

The number that Marc adds to his list is_{………........ …………..}

The mean of four numbers is 9.

What is the total of the four numbers?

Find a set of four numbers such that: • their mean is 9 • their mode is 11.

Write your four numbers in the boxes below.

The grouped frequency table below shows data for 32 values of t. One of the frequencies in the table is represented by a.

t	Frequency
20 t 30	2
30 t 40	8
40 t 50	4
50 t 60	a
60 t 70	3
70 t 80	5

Find the estimated mean value of t for the 32 values.

The grouped frequency table below shows data for 32 values of t. One of the frequencies in the table is represented by a.

t	Frequency
20 t 30	2
30 t 40	8
40 t 50	4
50 t 60	a
60 t 70	3
70 t 80	5

Find the estimated mean value of t for the 32 values.

The mean of four numbers is 7.

What is the total of the four numbers?

Find a set of four numbers such that:

• their mean is 7 • their range is 6.

Write your four numbers in the boxes below.

The mean of four numbers is 7.

What is the total of the four numbers?

Find a set of four numbers such that:

• their mean is 7 • their range is 6.

Write your four numbers in the boxes below.

Here is a list of eight numbers.

7 4 9 5 4 5 3 4

What is the range of these eight numbers?

What is the mode of the eight numbers listed above?

Circle the correct answer.

3 4 5 7 9

There are five numbers in a list. The mean of the five numbers is 7. Another number is added to the list. The mean of these six numbers is 8∙5.

Find the value of the sixth number.

You must show all your working.

The 22 pupils in a class were asked, “What is your favourite pet?” The pets chosen by the pupils were dog, cat, rabbit and hamster. Some of the results are shown in the bar chart below.

9 pupils in the class chose either rabbit or hamster. The modal pet is rabbit.

Complete the bar chart by drawing the two missing bars.

Frequency

One of these pupils is chosen at random.

What is the probability that this pupil’s favourite pet is a cat?

There are five numbers in a list. The mean of the five numbers is 7. Another number is added to the list. The mean of these six numbers is 8∙5.

Find the value of the sixth number.

You must show all your working.

Write down four whole numbers so that: • they are all between 1 and 15 inclusive • they have a mode of 7 • they have a median value of 8·5 • their mean is 9.

Write your numbers in the boxes below.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

Geraint writes down three different even numbers.

The range of his numbers is 4.

Which three different even numbers did Geraint write down?

You must show all your working.

Write down four whole numbers so that: • they are all between 1 and 15 inclusive • they have a mode of 7 • they have a median value of 8·5 • their mean is 9.

Write your numbers in the boxes below.

Which one of these numbers is both a square number and an even number?

Circle the correct answer.

2 9 12 16 17

Write 75% as a fraction in its lowest terms.

Write down the mode of these numbers.

28 31 28 29 31 28 34 24 32

Write down four positive whole numbers in the boxes below so that:

• the range of the numbers is 6, • the mean of the numbers is 5,

• the median of the numbers is 4.

Gwenan writes down four numbers:

64 89 83 26

Calculate the mean of Gwenan’s numbers.

Every number in Gwenan’s list is increased by 1.

What is the mean of her new list of numbers?

Write down four positive whole numbers in the boxes below so that:

• the range of the numbers is 6, • the mean of the numbers is 5,

• the median of the numbers is 4.

Write down three different whole numbers so that:

• the median of the three numbers is 13,

• the range of the three numbers is 5.

The three numbers are, and.

Kate writes down three different even numbers.

The mean of Kate’s numbers is 8. She did not write down the number 8.

What possible even numbers could Kate have written down?

Possible numbers Kate could have written are_{……........ ……},_{……........ ……} and_{……........ ……}

Find four different positive whole numbers so that:

• their mean is 8, • their range is 8, • their median is 8.

Write your four numbers in the boxes below.

Data for different values of t are shown in the table below.

t	Frequency
0 t 5	8
5 t 10	0
10 t 15	7
15 t 20	5

Calculate an estimate for the mean value of t.

Find four different positive whole numbers so that:

• their mean is 8, • their range is 8, • their median is 8.

Write your four numbers in the boxes below.

Data for different values of t are shown in the table below.

t	Frequency
0 t 5	8
5 t 10	0
10 t 15	7
15 t 20	5

Calculate an estimate for the mean value of t.

A biased coin is thrown 100 times. The number of heads thrown is recorded after 20 throws, 40 throws, 60 throws, 80 throws and 100 throws.

Some of the results are recorded in the relative frequency table below.

Complete the table.

The pie chart below shows the favourite sport of 60 people.

Which is the modal sport?

One person is chosen at random.

What is the probability that this person said swimming is their favourite sport?

How many people said tennis is their favourite sport?

Look at the following set of four numbers.

5 8 10 13

Find another set of four numbers so that:

• the range has increased by 2, • the mean remains the same, • the median has decreased by 1.

You may use some of the numbers from the original set, but not exactly the same four

numbers.

My four numbers are

Look at the following set of four numbers.

5 8 10 13

Find another set of four numbers so that:

• the range has increased by 2, • the mean remains the same, • the median has decreased by 1.

You may use some of the numbers from the original set, but not exactly the same four

numbers.

My four numbers are

Jane has a different set of cards. These are Jane’s cards.

Jane chooses a card at random from her set of cards. On the probability scale below, mark the points A and B where:

A is the probability of Jane choosing a number less than 10,

B is the probability of Jane choosing the number 15.

Here are 9 numbers:

27 19 20 32 21 29 20 24 33

Find the mean of these numbers.

Neil says,

“To find the median, you just choose the middle number in the list. The median of these numbers is 21.”

Neil’s median is incorrect.

Explain what is wrong with Neil’s method.

Five numbers are listed below.

3 3 6 13 15

Write down another set of five positive whole numbers such that

• all the numbers are less than 20, • the median of the new set of numbers is greater than the median of the set shown above, • the mean of the new set of numbers is less than the mean of the set shown above, • the range of the new set of numbers is less than the range of the set shown above.

Your set of whole numbers must be written in the boxes.

Space for working:

My five positive whole numbers are

Five numbers are listed below.

3 3 6 13 15

Write down another set of five positive whole numbers such that

• all the numbers are less than 20, • the median of the new set of numbers is greater than the median of the set shown above, • the mean of the new set of numbers is less than the mean of the set shown above, • the range of the new set of numbers is less than the range of the set shown above.

Your set of whole numbers must be written in the boxes.

Space for working:

My five positive whole numbers are

Write a number in each box to make the following calculations correct.

The number 283 is multiplied by 10.

What is the value of the 2 in the answer?

Value of the 2 is_........

The number 6518 is divided by 100.

What is the value of the 6 in the answer?

Value of the 6 is_........

Work out the mean of the following numbers.

7 13 10 4 6

Rhys wrote down four whole numbers.

The mode of the four numbers is 7. The median of the four numbers is 6. The range of the four numbers is 5.

What are the four numbers that Rhys wrote down?

You must show all your working.

Rhys’s numbers are_{…........ …...},_{…........ …...},_{…........ …...} and_{…........ …...}

Calculate the mean of these four time periods.

You must give your answer in hours and minutes.

5 hours 20 minutes 2 hours 44 minutes 6 hours 18 minutes 4 hours 34 minutes

Mean time =_{……........ ….} hours_{……........ ….} minutes

Calculate the mean of these four time periods.

You must give your answer in hours and minutes.

5 hours 20 minutes 2 hours 44 minutes 6 hours 18 minutes 4 hours 34 minutes

Mean time =_{……........ ….} hours_{……........ ….} minutes

A number is to be written on the blank card.

The mode and the median of all seven numbers are both the same.

Find one possible number that can be written on the blank card.

One extra number is added to the following list of three numbers.

6 8 13

The mean of the new list of four numbers is 1 less than the mean of the original three numbers.

What number was added to the list?

Write down three integers, all less than 25, whose

• range is 8, and

• mean is 13.

The three integers are_{……........ …..},_{……........ …..} and_{……........ …..}