Averages, Ranges & Data Practice Questions

Question 1

4 marks

Do not use a calculator for this question.

Zara records the number of emails she receives each day for 10 days.

$7,\quad 3,\quad 9,\quad 3,\quad 5,\quad 8,\quad 6,\quad 3,\quad 10,\quad 6$

(a)

Write down the mode of the number of emails.

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(b)

Work out the range of the number of emails.

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(c)

Work out the mean number of emails.

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Question 2

3 marks

Do not use a calculator for this question.

The table shows information about the masses of 60 parcels posted from a shop in one day.

Mass ( $m$ kg)	Frequency
$0 < m \le 2$	5
$2 < m \le 4$	14
$4 < m \le 6$	12
$6 < m \le 8$	22
$8 < m \le 10$	7

(a)

Write down the modal class.

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(b)

Find the class interval that contains the median.

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(c)

Explain why you cannot work out the exact value of the mean mass from this table.

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Question 3

4 marks

Do not use a calculator for this question.

The table shows information about the number of times each of 30 students was late for school last term.

Number of times late	Frequency
0	12
1	5
2	6
3	4
4	3

(a)

Write down the mode.

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(b)

Find the median number of times late.

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(c)

Write down the range.

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Question 0

5 marks

Do not use a calculator for this question.

The table shows information about the number of children in each of 40 families.

Number of children	Frequency
0	6
1	13
2	14
3	5
4	2

(a)

Calculate the mean number of children per family.

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(b)

Find the interquartile range of the number of children.

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Question 0

6 marks

Do not use a calculator for this question.

A supermarket manager records the amount spent by each of 60 customers on Saturday morning.

Amount spent (£ $x$ )	Frequency
$0 < x \le 10$	10
$10 < x \le 20$	20
$20 < x \le 30$	18
$30 < x \le 40$	8
$40 < x \le 50$	4

(a)

Work out an estimate for the mean amount spent by these customers.

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(b)

In total, 1500 customers use the supermarket that day.

Use your answer to part (a) to work out an estimate for the total amount spent by all 1500 customers.

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(c)

Explain why this estimate may not be reliable.

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Question 0

7 marks

Do not use a calculator for this question.

18 students in Year 10 and 12 students in Year 11 each raised money for charity.

The mean amount raised by the 18 Year 10 students was £34.50
The mean amount raised by the 12 Year 11 students was £29.00

(a)

Work out the mean amount raised by all 30 students.

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(b)

Jay says, "The mean for all 30 students must be halfway between £34.50 and £29.00"

Explain why Jay is wrong.

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(c)

One more student then hands in the money she raised.

The mean amount raised by all 31 students is £33.00

Work out the amount of money this student raised.

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Question 0

5 marks

Do not use a calculator for this question.

A small company has 7 employees. Their annual salaries are listed below.

£18 000 £20 000 £22 000 £24 000 £25 000 £26 000 £96 000

(a)

Work out the mean salary.

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(b)

Write down the median salary.

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(c)

The manager wants to advertise a typical salary at the company.

Which average, the mean or the median, better represents these salaries? Give a reason for your answer.

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(d)

The employee earning £96 000 leaves the company.

Describe the effect this has on the range of the salaries.

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Question 0

5 marks

Do not use a calculator for this question.

Two machines fill bags with flour. Each bag should contain 250 g of flour.

A sample of 8 bags from machine A has a mean mass of 250.4 g and a range of 3 g.

The masses, in grams, of a sample of 8 bags from machine B are shown below.

$248,\quad 251,\quad 249,\quad 253,\quad 250,\quad 247,\quad 252,\quad 250$

(a)

Work out the mean mass of the 8 bags from machine B.

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(b)

Work out the range of the masses of the 8 bags from machine B.

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(c)

Compare the masses of the bags filled by machine A with the masses of the bags filled by machine B.

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Question 0

5 marks

Do not use a calculator for this question.

A ranger wants to estimate the number of deer in a forest.

She catches 48 deer, puts a tag on each one and releases them back into the forest.

One week later she catches 60 deer. Of these deer, 8 have a tag.

(a)

Work out an estimate for the total number of deer in the forest.

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(b)

Write down one assumption you have made. Explain how this assumption affects your answer if it is not true.

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(c)

In fact, some of the tags fell off before the second sample was caught.

Explain what effect this has on the ranger's estimate.

/ 1

Question 0

6 marks

Do not use a calculator for this question.

The table shows information about the times taken by 40 workers to travel to work one morning.

Time ( $t$ minutes)	Frequency
$0 < t \le 10$	9
$10 < t \le 20$	$x$
$20 < t \le 30$	14
$30 < t \le 40$	$y$
$40 < t \le 50$	3

An estimate for the mean time taken is 23 minutes.

(a)

Work out the value of $x$ and the value of $y$ .

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(b)

Using your values of $x$ and $y$ , find the class interval that contains the median.

/ 1

Number

Algebra

Ratio, Proportion & Rates of Change

Geometry & Measures

Probability

Statistics

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