Averages, Ranges & Data Practice Questions

Question 1

5 marks

Here are the ages, in years, of 8 members of a chess club.

$13\quad 21\quad 9\quad 13\quad 26\quad 18\quad 13\quad 22$

(a)

Write down the modal age.

/ 1

(b)

Work out the median age.

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(c)

Work out the range of the ages.

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Question 2

4 marks

Here are the amounts of rainfall, in mm, in a town on each of 7 days.

$3\quad 8\quad 5\quad 11\quad 4\quad 7\quad 4$

(a)

Work out the mean amount of rainfall.

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(b)

Work out the range of the amounts of rainfall.

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Question 3

4 marks

The table shows information about the number of pets owned by each of 30 students.

Number of pets	Frequency
0	4
1	9
2	8
3	6
4	3

(a)

Write down the modal number of pets.

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(b)

Find the median number of pets.

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(c)

Write down the range of the number of pets.

/ 1

Question 4

3 marks

A shop sells T-shirts. Here are the sizes of the 10 T-shirts sold on Monday.

$10\quad 12\quad 14\quad 8\quad 12\quad 16\quad 12\quad 10\quad 14\quad 12$

(a)

Write down the modal size.

/ 1

(b)

Bea says,

"The range of the sizes is 8 to 16"

What is wrong with Bea's statement?

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(c)

The manager wants to order more T-shirts.

Explain why the mode is the most useful average for the manager to use.

/ 1

Question 5

2 marks

The table shows information about the number of points scored by two netball teams in their matches last season.

Team	Mean number of points	Range
Ashford	34	18
Bewley	29	5

Compare the number of points scored by the two teams.

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Question 0

5 marks

The table shows information about the number of goals scored by a football team in each of 40 matches.

Number of goals	Frequency
0	6
1	12
2	11
3	7
4	4

(a)

Work out the mean number of goals scored per match.

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(b)

Find the median number of goals.

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Question 0

5 marks

The table shows information about the time taken by each of 50 students to travel to school one morning.

Time ( $t$ minutes)	Frequency
$0 < t \leqslant 10$	8
$10 < t \leqslant 20$	15
$20 < t \leqslant 30$	14
$30 < t \leqslant 40$	9
$40 < t \leqslant 50$	4

(a)

Write down the modal class.

/ 1

(b)

Write down the class interval that contains the median.

/ 1

(c)

Work out an estimate for the mean time taken.

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Question 0

5 marks

Yusuf plays a game six times.
His mean score for the six games is 14

Here are his scores for five of the games.

$11\quad 18\quad 9\quad 16\quad 13$

(a)

Work out his score for the sixth game.

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(b)

Yusuf plays the game a seventh time.
The mean score for all seven games is 15

Work out his score for the seventh game.

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Question 0

4 marks

There are 12 boys and 18 girls in a drama group.
The mean height of the 12 boys is 1.52 m.
The mean height of the 18 girls is 1.47 m.

(a)

Work out the total height of the 12 boys.

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(b)

Work out the mean height of all 30 members of the drama group.

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Question 0

5 marks

Here are the numbers of days that each of 7 employees was absent from work last year.

$2\quad 4\quad 3\quad 5\quad 4\quad 3\quad 21$

(a)

Write down the value that is an outlier.

/ 1

(b)

Work out the mean number of days absent.

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(c)

Work out the median number of days absent.

/ 1

(d)

Which of the mean or the median better represents the number of days absent for these employees?
Give a reason for your answer.

/ 1

Question 0

3 marks

There are 4000 households in a town.
Saira asks the people in 50 of these households how many people live in their household.
The mean number of people per household for her sample is 2.6

(a)

Use Saira's results to estimate the total number of people living in the town.

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(b)

Give one reason why your estimate in part (a) may not be accurate.

/ 1

Question 0

4 marks

A gym has 800 members.
The owner wants to find out about the ages of the members.
On Monday morning he records the ages, in years, of the first 10 members to arrive.

$58\quad 71\quad 64\quad 55\quad 68\quad 62\quad 70\quad 59\quad 66\quad 57$

(a)

Work out the mean age of the members in this sample.

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(b)

The owner says,

"The mean age of all 800 members of the gym is 63 years."

Explain why the owner may be wrong.

/ 1

(c)

Describe one way the owner could improve his sample.

/ 1

Question 0

5 marks

The table shows information about the number of children in each of the families living in a street.

Number of children	Frequency
0	5
1	8
2	$x$
3	4

The mean number of children per family is exactly 1.5

(a)

Work out the value of $x$ .

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(b)

Hence write down the modal number of children.

/ 1

Question 0

4 marks

There are 25 students in a class.
15 of the students are girls and 10 of the students are boys.

In a test, the mean mark of the 15 girls was 62
The mean mark of all 25 students in the class was 58

Work out the mean mark of the 10 boys.

/ 4

Number

Algebra

Ratio, Proportion & Rates of Change

Geometry & Measures

Probability

Statistics

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