Averages and spread

The table shows information about the marks of students in a test.

Tick one box for each statement.

Here are 11 numbers.

2 8 10 12 12 14 19 23 26 31 33

Work out the inter-quartile range.

The table shows information about the marks of students in a test.

Tick one box for each statement.

Ingrid records the number of minutes she uses her mobile phone over four weeks.

140 168 205 192

Work out the range.

Ingrid records the number of minutes for a fifth week. The mean for all five weeks is 178 minutes.

Work out the number of minutes used in the fifth week.

£4.56 is paid using the smallest possible number of coins.

What is the modal value of the coins used? You must show your working.

Here is a list of five numbers.

5 9 4 16 8

An extra number is put into the list. The median of the numbers is now 7

Work out the extra number.

Here are the temperatures in six cities in degrees Celsius.

0 ° C – 3 ° C 0 ° C 1.5 ° C 23 ° C 4 ° C

Write down the outlier.

Rob records the time he takes to drive to work every day for 80 days. The table shows information about the results.

Time, t (minutes)	Frequency
20 t 25	16
25 t 30	32
30 t 40	24
40 t 60	8
	Total = 80

Last year, the mean time Rob took to drive to work was 25 minutes.

Estimate the percentage increase in the mean driving time for these 80 days.

Each number in a list is increased by 10

Tick one box for each statement.

Each number in a list is increased by 10

Tick one box for each statement.

Here are five numbers.

14.2 15.1 16.5 16.7 18.0

Work out the range.

Work out the mean.

Here is a grouped frequency table.

Work out an estimate of the mean value.

Two types of battery, P and Q, were tested. 100 of each type were put into clocks. The number of days each battery lasted was recorded.

The frequency table represents the results for type P.

On the grid, draw a cumulative frequency diagram to represent the data.

For type Q, the median was 126 days the interquartile range was 57 days.

Compare the number of days that types P and Q lasted. Make one statement about the average and one statement about the spread.

Use statistical measures to support your statements.

Here are some numbers.

12 8 6 11 2 7 7 18 10

Work out the median.

Alina and Sue play netball. The number of goals they scored in 8 games is shown.

Complete this table.

Which player scored the more consistent number of goals? Tick a box.

Give a reason for your answer.

The table shows information about the ages of members of two clubs.

Compare the average age and consistency of ages for the members of the two clubs.

Four numbers have a mean of 10

Three of the numbers are 5 8 9

Work out the other number.

Liam takes part in long jump competitions. Here is some information about 40 of his jumps.

Work out an estimate of the mean distance of these 40 jumps. Give your answer as a decimal.

Here is some information about the lengths, in cm, of leaves.

• Shortest length = 2.4

• Longest length = 9

• Upper quartile = 7

• Median length = 6

• Interquartile range = 3

Draw a box plot to show this information.

Four people are taking part in a television talent show.

Here are Amy’s marks from the 6 judges.

The pie chart represents the phone vote.

Amy’s total score is found by

4 × the mean of her marks

her percentage of the phone vote

Work out Amy’s total score.

Four people are taking part in a television talent show.

Here are Amy’s marks from the 6 judges.

The pie chart represents the phone vote.

Amy’s total score is found by

4 × the mean of her marks

her percentage of the phone vote

Work out Amy’s total score.

Complete the list of six numbers so that the mode is 9 the median is 13 the range is 11

A race was run in 2019 and in 2020 The box plot shows information about the finishing times in 2019

In 2019, what was the fastest time?

The table shows information about the finishing times in 2020

Use the data to comment on each of the following statements.

On average, times were faster in 2019 than in 2020

Times were equally consistent in 2019 and 2020

Here are the salaries, in £, of the 6 workers in a company.

18 300 20 700 21 500 21 500 21 500 99 000

Work out the mean salary.

Why is the mean not the best average to represent the salaries?

Here is some information about the members of a basketball club.

Work out the mean height of all 50 members of the club. Give your answer as a decimal.

Which of these is an estimate? Tick one box.

Here is some data about people visiting a gym one week.

Compare the data for the members with the data for the guests. Make three comparisons.

Sunita is x years old. Beth is one year younger than Sunita. Joel is double Sunita’s age. The mean of their ages is 5 How old is Joel ?

Sunita is x years old. Beth is one year younger than Sunita. Joel is double Sunita’s age. The mean of their ages is 5 How old is Joel ?

Here is a list of 11 whole numbers in numerical order. The lower quartile, median, upper quartile and highest value are missing.

• median = 2 × lower quartile

• upper quartile = 2.5 × lower quartile

• range = 2 × interquartile range

Complete the list.

A company has 123 employees. Information about their hourly rates of pay is shown in the table.

Hourly rate, £p	Number of employees
10 p 14	66
14 p 20	32
20 p 40	15
40 p 100	10
	Total = 123

The owner of the company uses the data to make two statements.

Statement A “Over 30% of employees have an hourly rate that is more than £17”

Statement B “The average hourly rate of pay is more than £20”

Show working that supports Statement A.

Why might Statement A not be true?

Work out an estimate of the mean to support Statement B.

Why is the mean not the best average to represent the data?

Here is a list of numbers. 10 8 2 11 12 15 4 4

Write down the mode.

Work out the median.

Work out the range.

180 runners started a marathon. Some of the runners did not complete it.

The histogram represents the times of the runners who did complete the marathon.

How many runners did not complete the marathon?

The table shows information about the runners who did not complete the marathon.

Draw a box plot to represent the information.

Here is some information about the time spent on social media by 40 women and 40 men last week.

Time spent, t (hours)	Number of women	Number of men
2 t 5	12	10
5 t 8	11	17
8 t 11	14	9
11 t 14	2	4
14 t 17	1	0

Tick one box for each statement.

Here is some information about the time spent on social media by 40 women and 40 men last week.

Time spent, t (hours)	Number of women	Number of men
2 t 5	12	10
5 t 8	11	17
8 t 11	14	9
11 t 14	2	4
14 t 17	1	0

Tick one box for each statement.

The table shows information about the heights of 60 athletes.

Height, h (cm)	Frequency
150 h 160	4
160 h 170	12
170 h 180	35
180 h 190	7
190 h 200	2

Complete the cumulative frequency table.

Height, h (cm)	Cumulative frequency
h 150	0
h 160	4
h 170	16
h 180
h 190
h 200

Circle the class interval that contains the lower quartile.

Draw a cumulative frequency diagram to represent the data.

Estimate the number of the athletes whose height is more than 176 cm

A basketball team plays 19 home games and 19 away games. The box plot shows information about the points the team scored in home games.

Here are the points the team scored in the 19 away games.

85 89 93 95 96 96 98 98 98 99

100 103 105 107 109 110 114 119 126

On the grid, draw a box plot for the away games.

On average, did the team score more points in home games or away games? Use one statistical measure to support your decision.

Was the number of points scored more consistent in home games or away games? Use one statistical measure to support your decision.

61 students recorded how many hours they spent revising for a test. The histogram represents the results.

Work out an estimate of the mean time the 61 students spent revising. You may use the table to help you.

Give a reason why the answer to part (a) is an estimate.

40 students were asked the number of visits they made to a gym one week. The chart shows information about the results.

Write down the modal number of visits.

Work out the mean number of visits. Give your answer as a decimal.

One of the 40 students is chosen at random. Work out the probability that the student visited the gym at least once.

Here is some information about the members of clubs A and B.

Give your answer as a decimal.

Here is some information about the members of clubs A and B.

Give your answer as a decimal.

For a set of five numbers, the mode is 8 the median is 12 Work out one possible set of five numbers.

Here are the heights, in centimetres, of some children. 98 103 91 85 159 102 91 Which height is an outlier?

A school play takes place each day from Monday to Friday. Here are the attendances on four of the days.

For all five days, the mean attendance is 90 Work out the attendance on Friday.

A school play takes place each day from Monday to Friday. Here are the attendances on four of the days.

For all five days, the mean attendance is 90 Work out the attendance on Friday.

Students in two classes, A and B, raised money for charity. The box plot for class A is shown on the grid.

For class B,

• the lowest amount was £3 and the highest amount was £26

• the lower quartile was £11

• the median was £2 greater than the class A median

• the interquartile range was 1 times greater than the class A interquartile range.

Draw the box plot for class B on the grid.

A company sells bags of toffees and bags of mints.

Here are the numbers of sweets in 11 bags of toffees. 55 50 49 51 55 47 54 50 49 55 57

Here are the numbers of sweets in 10 bags of mints. 46 47 47 48 48 50 53 54 54 54

The company claims that the average number of sweets per bag is at least 50 Using medians, is the company’s claim correct for each type of sweet? You must work out the median for toffees and the median for mints.

Tick a box for toffees.

Tick a box for mints.

7 102 boys and 85 girls took a test. The table shows information about the mean marks.

The pass mark for the test was 70 Was the mean mark for all of these students greater than the pass mark? You must show your working.

Six positive numbers have a mean of 10 a range of 19 Four of the numbers are 12 7 15 3 Work out the other two numbers.

Six positive numbers have a mean of 10 a range of 19 Four of the numbers are 12 7 15 3 Work out the other two numbers.

Here are some numbers.

Circle the range.

5 11 12 13

Eleven people play a game. Here are their scores. 12 9 15 9 18 18 3 14 9 16 20

Write down the mode.

Work out the median.

Alex and Bev sat six tests, each with 50 marks. The table shows their mean percentages after five tests.

After all six tests, their mean percentages were equal. In the sixth test, Alex scored 24 out of 50 Work out Bev’s score, out of 50, in the sixth test.

Alex and Bev sat six tests, each with 50 marks. The table shows their mean percentages after five tests.

After all six tests, their mean percentages were equal. In the sixth test, Alex scored 24 out of 50 Work out Bev’s score, out of 50, in the sixth test.

A record was kept of the number of days that 25 students were absent one term. The chart represents the results.

Work out the mean number of days absent.

One of the students is chosen at random. Work out the probability that the student was absent for less than 4 days.

Here is some information about 26 houses. a, b and c are all different numbers.

The median number of bedrooms is 3.5 Work out a possible set of values for a, b and c.

a =

c =

Here is some information about 26 houses. a, b and c are all different numbers.

The median number of bedrooms is 3.5 Work out a possible set of values for a, b and c.

a =

c =

The number of goals scored by 20 players in a season is shown.

Work out an estimate of the mean number of goals per player. Give your answer as a decimal.

Amari and Ben each play a game.

Here is some information about Amari’s scores. Lowest 12 Highest 20 Lower quartile 13 Upper quartile 19 Median 17 Draw a box plot to represent his scores.

This box plot represents Ben’s scores.

Who had more consistent scores, Amari or Ben? Work out the interquartile ranges to support your answer.

The box plots represent the distances run by the players in a football match.

On average, which team’s players ran further? Tick a box.

Give a reason for your answer.

The players in Team A ran more consistent distances. How do the box plots show this?

Here are eight numbers. 4 10 9 3 4 12 5 14

Work out the range.

Work out the median.

200 people recorded the time they spent on social media one day. The table shows the results.

Work out an estimate of the mean time.

The table shows the number of films watched one week by 30 people.

Write down the modal number of films watched.

Work out the mean number of films watched per person.

Here is some data about the people listening to a radio station one day.

Compare the data for people aged 40 or under with the data for people aged 41 or over. Make three comparisons.

In a sport, injury time is added time played at the end of a match. The table shows the injury time, t (minutes) played in 380 matches.

Injury time, t (minutes)	Frequency
0 t 2	59
2 t 4	158
4 t 6	106
6 t 8	45
8 t 10	12

Circle the two words that describe the data.

continuous discrete grouped ungrouped

Which class interval contains the median? You must show your working.

What percentage of the matches had more than 6 minutes of injury time?

In a sport, injury time is added time played at the end of a match. The table shows the injury time, t (minutes) played in 380 matches.

Injury time, t (minutes)	Frequency
0 t 2	59
2 t 4	158
4 t 6	106
6 t 8	45
8 t 10	12

Circle the two words that describe the data.

continuous discrete grouped ungrouped

Which class interval contains the median? You must show your working.

What percentage of the matches had more than 6 minutes of injury time?

The amounts spent on clothes by 40 boys and 40 girls in one month were recorded. The table shows information about the amounts spent by the boys.

The mean for the girls was £35 Estimate the mean for the girls as a percentage of the mean for the boys.

Here is some information about the times people took to complete a survey.

Fastest time 3 minutes Slowest time 18 minutes Median 11 minutes Lower quartile 7 minutes Interquartile range 8 minutes Ben draws this box plot to show the information.

Make two criticisms of his box plot.

What does the longest bar in a bar chart represent? Circle your answer.

mean median mode range

Kim works at an airport in the UK. She records the number of planes landing between 10 am and 2 pm each day. The table shows the data for the first 10 days in January.

The airport was affected by fog on one of the days. Which day do you think it was? Give a reason for your answer.

Kim uses the data to predict how many planes will land at the airport in a year. In her method, she uses an estimate of 150 planes in each 4-hour period throughout the day assumes the same number of planes each day. Work out her prediction.

In fact, fewer planes land in winter than in summer fewer planes land at night than during the day. What does this tell you about Kim’s prediction? Tick one box.

Give a reason for your answer.

In a survey, queuing times at supermarket checkouts were recorded. One morning, samples of 50 customers were taken at supermarkets A, B, C and D. The box plots represent the results.

On average, which supermarket had the lowest queuing times? Give a reason for your answer.

Reason

At which supermarket were the queuing times most consistent? Give a reason for your answer.

Here is some information about 20 trains leaving a station.

Work out an estimate of the mean number of minutes late.

The station manager looks at the information in more detail.

Number of minutes late, t	Number of trains
0 t 2	12
2 t 4	0
4 t 6	7
6 t 8	0
8 t 10	0
10 t 12	1

He works out an estimate of the mean using this information. How does his estimate compare with the answer to part (a)? Tick one box.

Here is some information about 20 trains leaving a station.

Work out an estimate of the mean number of minutes late.

The station manager looks at the information in more detail.

Number of minutes late, t	Number of trains
0 t 2	12
2 t 4	0
4 t 6	7
6 t 8	0
8 t 10	0
10 t 12	1

He works out an estimate of the mean using this information. How does his estimate compare with the answer to part (a)? Tick one box.

A company sells houses. The line graph shows the number sold per week for 30 weeks.

Work out the range of the number of houses sold per week.

Work out the median number of houses sold per week.

The company sells three houses. The prices are £185 000, £239 000 and £136 000 The company earns 2% commission on each house. In total, how much commission does the company earn on these three houses?

Four friends all give each other presents. The total cost of the presents is £83.40 Work out the mean cost of a present.

The mean mass of a squad of 19 hockey players is 82 kg A player of mass 93 kg joins the squad. Work out the mean mass of the squad now.

Here is a list of numbers. 5 6 1 3 5 5 8 4 2 2

Work out the median.

Work out the mean.

Work out the largest number.

Type A batteries and type B batteries were tested. The cumulative frequency diagram shows information about the battery life of type A.

Estimate the interquartile range for type A.

Estimate the number of type A batteries that had a battery life of more than 1600 hours.

The box plot shows information about the battery life of type B.

On average, which type had the greater battery life? Tick a box.

Using data from both diagrams, state how you chose your answer.

The diagram shows the scores given by judges during a television show.

Which score was the mode?

There were 4 judges. Each judge gave one score in each round. How many rounds were there?

In one month, the number of hours of exercise taken by 10 people are 4 7 2 8 6 5 1 82 3 9 Which is the appropriate average to use in this situation? Tick a box.

Give one reason for each of the other two averages as to why they are not appropriate.

Here are five cards.

One of the cards is removed.

The mean of the numbers on the remaining four cards is 6

Which card was removed?

You must show your working.

The table shows information about the distances walked by 120 students on their way to school one week.

Work out an estimate for the mean distance.

The following data comes from a large sample survey of the audience at a concert.

Make three comparisons of males and females at the concert. Use the headings given.

Proportion of the audience

Here is some information about the times taken by 40 people to fill in a form.

Time, t minutes	Number of people
0 < t 5	3
5 < t 10	9
10 < t 15	11
15 < t 20	17

In which class interval is the median? Circle your answer.

Here is some information about the length of time cars stayed in a car park.

Shortest time 30 minutes Lower quartile 2 hours Longest time 12 hours Interquartile range 3 hours Median time 4 hours

Draw a box plot to show this information.

The table shows information about the times for 10 people to complete a task.

Time, t (minutes)	Frequency
0 t 20	1
20 t 40	6
40 t 60	3

These statements are about the mean and range of the actual times. Tick the correct box for each statement.

The table shows information about the times for 10 people to complete a task.

Time, t (minutes)	Frequency
0 t 20	1
20 t 40	6
40 t 60	3

These statements are about the mean and range of the actual times. Tick the correct box for each statement.

Here is a list of numbers. 21 17 23 21 29 32 21 25 36

Work out the median.

Lee sells ice creams. The table shows the midday temperature and his sales for five days.

He draws this scatter graph and line of best fit.

Write down two mistakes he has made.

Lee wants to work out the range of the five temperatures. His calculation is 30 – 20 = 10 Is his method correct? Tick a box.

Give a reason to support your answer.

The table shows Lee’s costs.

Work out his total profit for the five days.

Here is a box plot.

Circle the median value.

28 35 24 22

Here is information about the goals scored in some hockey games. Each game has four quarters.

Which quarter was the mode for away goals? Circle your answer. 1st 2nd 3rd 4th

There were 10 games. Work out the mean number of goals per game.

In total, how many more home goals were scored than away goals?

Rob says, “More home teams must have won because there were more home goals.” Is he correct? Give a reason for your answer.

In a class of 28 students the mean height of the 12 boys is 1.58 metres the mean height of all 28 students is 1.52 metres. Work out the mean height of the girls.