Edexcel IGCSE Maths
Topic questions Statistics Averages & spread
115 questions · 485 marks · about 9.5 hours
Also involves The four operations
The table shows information about the number of cars sold by a garage in each of 30 weeks.
Work out the mean number of cars sold per week.
The table gives information about the distances 100 adults travel to work.
| Distance (dkm) | Frequency |
0  d  5 | 26 |
5  d 10 | 40 |
10 d  15 | 16 |
| 15 d 20 | 10 |
| 20 d 25 | 8 |
Write down the modal class.
Work out an estimate for the mean distance.
The table gives information about the distances 100 adults travel to work.
| Distance (dkm) | Frequency |
| 0 d 5 | 26 |
| 5 d 10 | 40 |
| 10 d 15 | 16 |
15  d  20 | 10 |
| 20 d 25 | 8 |
Write down the modal class.
Work out an estimate for the mean distance.
Here are the numbers of eggs laid by some hens on each of 11 days in June.
9 10 12 15 17 18 19 19 20 25 26
Work out the interquartile range of the numbers of eggs.
Helena recorded the shoe sizes of seven of her friends.
Here are the results.
2 9 10 6 7 9 4
Write down the mode of the shoe sizes.
Work out the median shoe size.
Find the range of the shoe sizes.
Rio has six cards. He writes a number on each card so that
the range of the numbers is 10 the median of the numbers is 7.5 the mode of the numbers is 6
Rio arranges the cards so that the numbers are in order of size.
Three of the numbers are hidden.
Complete the cards above to show the three numbers that are hidden.
The mean of 7 numbers is 60
The mean of 3 of the numbers is 46
Work out the mean of the other 4 numbers.
Rio has six cards. He writes a number on each card so that
the range of the numbers is 10 the median of the numbers is 7.5 the mode of the numbers is 6
Rio arranges the cards so that the numbers are in order of size.
Three of the numbers are hidden.
Complete the cards above to show the three numbers that are hidden.
The frequency table gives information about the times, in minutes, that 60 people took to complete a puzzle.
Complete the cumulative frequency table.
On the grid opposite, draw a cumulative frequency graph for your table.
Use your graph to find an estimate for the median time.
Use your graph to find an estimate for the number of these people who took more than 45 minutes to complete the puzzle.
The table shows some information about the hourly rates of pay of 60 workers.
Write down the modal class.
Work out an estimate for the mean hourly rate of pay of the 60 workers.
The table shows information about the number of school lunches each of 30 students had in one week.
| Number of school lunches | Frequency |
| 0 | 2 |
| 1 | 5 |
| 2 | 11 |
| 3 | 7 |
| 4 | 4 |
| 5 | 1 |
Work out the mean number of school lunches.
The probability that Alex takes a packed lunch to school is 0.79
Work out the probability that Alex does not take a packed lunch to school.
Here are six cards.
Five of the cards have a number written on them.
Work out the number that should be written on the last card so that the mean of the six numbers will be 11
Also involves Forming and solving equations
Here are six cards.
Five of the cards have a number written on them.
Work out the number that should be written on the last card so that the mean of the six numbers will be 11
Here are the numbers of goals scored by a hockey team in its 11 games this season.
0 1 2 2 3 4 4 6 7 9 11
Work out the interquartile range of the numbers of goals.
The table shows information about the number of oranges in each of 30 bags.
Write down the mode of the number of oranges in a bag.
Work out the mean number of oranges in a bag.
Also involves Forming and solving equations
Here is a list of four numbers written in ascending order of size
x x y 15
where x and y are integers.
The numbers have
a median of 12.5 a range of 4
Find the value of x and the value of y
Also involves Percentages
The cumulative frequency graph gives information about the times, in seconds, that 80 adults took to log in to an online bank.
Find an estimate for the median time.
Work out the percentage of these adults that took longer than 50 seconds to log in. Show your working clearly.
The table shows information about the lengths, in minutes, of 50 telephone calls.
| Length of telephone call (m minutes) | Frequency |
0 < m  5 | 8 |
| 5 < m 10 | 2 |
| 10 < m 15 | 6 |
15 < m  20 | 4 |
| 20 < m 25 | 12 |
25 < m  30 | 18 |
Write down the modal class.
Work out an estimate for the total length, in minutes, of these telephone calls.
Also involves Forming and solving equations
The mean number of goals scored by a hockey team in 8 matches is 6 The team plays 2 more matches and scores k goals in each match. The mean number of goals scored by the hockey team in the 10 matches is 7
Work out the value of k
The table shows information about the lengths, in minutes, of 50 telephone calls.
| Length of telephone call (m minutes) | Frequency |
| 0 < m 5 | 8 |
| 5 < m 10 | 2 |
| 10 < m 15 | 6 |
| 15 < m 20 | 4 |
| 20 < m 25 | 12 |
| 25 < m 30 | 18 |
Write down the modal class.
Work out an estimate for the total length, in minutes, of these telephone calls.
Also involves Forming and solving equations
The mean number of goals scored by a hockey team in 8 matches is 6 The team plays 2 more matches and scores k goals in each match. The mean number of goals scored by the hockey team in the 10 matches is 7
Work out the value of k
Robert asked 11 people how many meetings they attended last week.
Here are the results in numerical order.
1 2 4 6 6 8 11 12 13 14 17
Find the interquartile range of the number of meetings.
The table shows how many cousins each of 30 students in Class A has.
| Number of cousins | Frequency |
| 0 | 3 |
| 1 | 7 |
| 2 | 6 |
| 3 | 11 |
| 4 | 1 |
| 5 | 2 |
Work out the range of the number of cousins.
Write down the mode of the number of cousins.
Work out the mean of the number of cousins.
Also involves Forming and solving equations
Pam plays netball for her school team.
Here are the numbers of goals she scored in the last 8 games. The numbers of goals are written in order of size.
1 1 2 2 3 6 x 14
Find the range of the number of goals Pam scored.
Find the median number of goals Pam scored.
The mean number of goals Pam scored in the 8 games is 5
Work out the value of x
The table gives information about the number of minutes that Abby spent walking each day in September.
| Number of minutes (M) | Frequency |
0 M  30 | 5 |
30 M  60 | 6 |
| 60 M 90 | 8 |
90  M 120 | 9 |
120  M 150 | 2 |
Work out an estimate for the total number of minutes that Abby spent walking in September.
The table gives information about the number of minutes that Abby spent walking each day in September.
| Number of minutes (M) | Frequency |
| 0 M 30 | 5 |
| 30 M 60 | 6 |
60  M 90 | 8 |
| 90 M 120 | 9 |
| 120 M 150 | 2 |
Work out an estimate for the total number of minutes that Abby spent walking in September.
Here are the test marks of 15 students.
7 10 14 15 16 17 18 19 20 20 23 25 30 39 40
Find the interquartile range of these marks.
The cumulative frequency graph shows information about the heights, in centimetres, of 50 plants in a flowerbed.
Use the graph to find an estimate for the median height of these plants.
Use the graph to find the frequency for the class interval 30 Height ≤ 40
Use the graph to find an estimate for the number of plants with a height greater than 35 centimetres.
The table gives information about the times taken by 80 people to run a race.
| Time taken (t minutes) | Frequency |
| 50 t 60 | 15 |
| 60 t 70 | 16 |
| 70 t 80 | 21 |
| 80 t 90 | 14 |
90  t  100 | 8 |
| 100 t 110 | 6 |
Complete the cumulative frequency table.
On the grid below, draw a cumulative frequency graph for your table.
Time taken (minutes)
Use your graph to find an estimate for the median time taken.
Use your graph to find an estimate for the interquartile range of the times taken.
Also involves Linear equations · Forming and solving equations
Team A and Team B take part in a quiz league.
After 11 rounds, Team A has a mean score per round of 17 After 9 rounds, Team B has a mean score per round of 18
Both teams take part in a further round. After this round, both teams have a mean score per round of 18.5
In the further round, Team A scored more points than Team B.
How many more?
Also involves Forming and solving equations
Team A and Team B take part in a quiz league.
After 11 rounds, Team A has a mean score per round of 17 After 9 rounds, Team B has a mean score per round of 18
Both teams take part in a further round. After this round, both teams have a mean score per round of 18.5
In the further round, Team A scored more points than Team B.
How many more?
The table shows information about the frame size, in cm, of 60 bicycles sold in a shop.
| Frame size (Scm) | Frequency |
| 30 S 36 | 4 |
| 36 S 42 | 14 |
| 42 S 48 | 18 |
| 48 S 54 | 19 |
| 54 S 60 | 5 |
Write down the modal class.
Work out an estimate for the mean frame size.
80 students entered a dancing competition.
The table gives information about the length of time, in minutes, for which each student spent dancing.
| Time (m) | Frequency |
0 m  12 | 11 |
12  m 24 | 25 |
| 24 m 36 | 23 |
| 36 m 48 | 15 |
| 48 m 60 | 6 |
Work out an estimate for the mean length of time the students spent dancing.
Also involves Forming and solving equations
Here is a list of six numbers written in order of size.
x 5 y z 10 12
qhe=numbers=h~$ve= a range of 9 a median of 8 a mode of 10
Find the value of x, the value of y and the value of z
1 80 students entered a dancing competition.
The table gives information about the length of time, in minutes, for which each student spent dancing.
| Time (m) | Frequency |
| 0 m 12 | 11 |
| 12 m 24 | 25 |
| 24 m 36 | 23 |
| 36 m 48 | 15 |
| 48 m 60 | 6 |
Work out an estimate for the mean length of time the students spent dancing.
The table shows information about the frame size, in cm, of 60 bicycles sold in a shop.
| Frame size (Scm) | Frequency |
30 S  36 | 4 |
36  S 42 | 14 |
| 42 S 48 | 18 |
| 48 S 54 | 19 |
| 54 S 60 | 5 |
Write down the modal class.
Work out an estimate for the mean frame size.
Also involves Forming and solving equations
Here is a list of six numbers written in order of size.
x 5 y z 10 12
qhe=numbers=h~$ve= a range of 9 a median of 8 a mode of 10
Find the value of x, the value of y and the value of z
The table shows information about the times, in minutes, that 80 patients had to wait to see a doctor.
| Time (W minutes) | Frequency |
| 0 W 10 | 7 |
| 10 W 20 | 10 |
| 20 W 30 | 15 |
| 30 W 40 | 32 |
| 40 W 50 | 16 |
Complete the cumulative frequency table below.
On the grid opposite, draw a cumulative frequency graph for your table.
Use your graph to find an estimate for the median.
Use your graph to find an estimate for the interquartile range.
The frequency table shows information about the number of cookies made by each of the 21 people in a cookery class.
| Number of cookies made | Frequency |
| 10 | 1 |
| 11 | 7 |
| 12 | 2 |
| 13 | 5 |
| 14 | 4 |
| 15 | 2 |
Write down the mode of the number of cookies made.
Find the median number of cookies made.
Find the total number of cookies made by the 21 people in the cookery class.
60 students sat a Mathematics exam.
The mean mark for the 32 students in Class A was 55 The mean mark for the 28 students in Class B was 52
Find the mean mark for all 60 students.
8 60 students sat a Mathematics exam.
The mean mark for the 32 students in Class A was 55 The mean mark for the 28 students in Class B was 52
Find the mean mark for all 60 students.
The cumulative frequency graph gives information about the time, in minutes, each of 60 people took to shop in a market.
Use the graph to find an estimate for the median time people took to shop in the market.
Use the graph to find an estimate for the number of people who took longer than 55 minutes to shop in the market.
Use the graph to complete the frequency table to give information about the time, in minutes, each of the 60 people took to shop in the market.
| Time taken to shop in the market (m minutes) | Frequency |
| 0 m 10 | 3 |
| 10 m 20 | 5 |
| 20 m 30 | |
| 30 m 40 | |
| 40 m 50 | |
| 50 m 60 | |
| 60 m 70 |
Here is a list giving the numbers of runs scored last week by the eleven members of cricket team A.
2 3 4 6 21 26 27 32 34 61 72
The interquartile range of the numbers of runs scored last week by the eleven members of cricket team B was 42
Using a suitable calculation, write down one comparison between the numbers of runs scored by the members of cricket team A and the members of cricket team B. Show your working clearly.
Here are the numbers of aces that Rutger served in each of 11 tennis matches.
1 1 2 4 6 8 8 9 11 12 15
Find the interquartile range of the numbers of aces. Show your working clearly.
Kim also plays in 11 tennis matches.
For Kim the median number of aces is 11 the interquartile range of the numbers of aces is 5
State, giving a reason, whether Rutger or Kim
served more aces on average,
was more consistent with the number of aces served.
The table gives information about the number of gold stars won by each of 25 students in class 7T last week.
| Number of gold stars | Number of students |
| 0 | 6 |
| 1 | 5 |
| 2 | 4 |
| 3 | 7 |
| 4 | 3 |
Work out the mean number of gold stars won.
A student in class 8R is to be chosen at random.
The probability that this student won at least one gold star last week is 0.39
Work out the probability that this student did not win at least one gold star last week.
Here are five cards.
Each card has a number written on it.
The mean of the five numbers is 12
Work out the value of x
Here is the number of runs scored by a baseball team in each of its 15 games this season.
The number of runs have been arranged in order of size.
0 1 1 3 5 6 7 7 8 9 9 12 12 15 16
Work out the interquartile range of the number of runs.
The table shows information about the number of mobile phones owned by each of 40 families.
| Number of mobile phones | Frequency |
| 0 | 1 |
| 1 | 5 |
| 2 | 12 |
| 3 | 9 |
| 4 | 11 |
| 5 | 2 |
For the information in the table,
write down the mode,
work out the mean.
Also involves Forming and solving equations
Alberto, Bill, Candela and Diana are four friends.
Here is some information about the height of each of these friends.
Alberto’s height is 158 cm. Bill’s height is 175 cm. Candela’s height is greater than Diana’s height.
The median height of these four friends is 160 cm. The range of the heights of these four friends is 21 cm.
Work out Candela’s height and Diana’s height.
Also involves Inequalities
Alberto, Bill, Candela and Diana are four friends.
Here is some information about the height of each of these friends.
Alberto’s height is 158 cm. Bill’s height is 175 cm. Candela’s height is greater than Diana’s height.
The median height of these four friends is 160 cm. The range of the heights of these four friends is 21 cm.
Work out Candela’s height and Diana’s height.
The cumulative frequency table shows information about the ages of 60 people who went to a gym on Saturday.
| Age (a years) | Cumulative frequency |
| 10 a 20 | 13 |
| 10 a 30 | 36 |
| 10 a 40 | 42 |
| 10 a 50 | 47 |
| 10 a 60 | 52 |
| 10 a 70 | 56 |
| 10 a 80 | 60 |
On the grid, draw a cumulative frequency graph for the information in the table.
Use your graph to find an estimate for the median of the ages of these people.
Use your graph to find an estimate for the interquartile range of the ages of these people.
Use your graph to find an estimate for the number of these people who are older than 55 years.
The table shows information about the number of eggs laid by each of 36 hens in one week.
| Number of eggs | Frequency |
| 0 | 5 |
| 1 | 5 |
| 2 | 3 |
| 3 | 10 |
| 4 | 7 |
| 5 | 6 |
Work out the mean number of eggs laid.
Also involves Forming and solving equations
Yusuf sat 8 examinations.
Here are his marks for 5 of the examinations.
68 72 75 77 80
For his results in all 8 examinations
the mode of his marks is 80 the median of his marks is 74 the range of his marks is 16
Find Yusuf’s marks for each of the other 3 examinations.
Also involves Forming and solving equations
Jenny has six cards.
Each card has a whole number written on it so that
t he smallest number is 5 the largest number is 24 the median of the six numbers is 14 the mode of the six numbers is 8
Jenny arranges her cards so that the numbers are in order of size.
For the remaining four cards, write on each dotted line a number that could be on the card.
A basketball team plays 6 games. After playing 5 games, the team has a mean score of 21 points per game. After playing 6 games, the team has a mean score of 23 points per game.
Work out the number of points the team scored in its 6th game.
Jenny has six cards.
Each card has a whole number written on it so that
t he smallest number is 5 the largest number is 24 the median of the six numbers is 14 the mode of the six numbers is 8
Jenny arranges her cards so that the numbers are in order of size.
For the remaining four cards, write on each dotted line a number that could be on the card.
A basketball team plays 6 games. After playing 5 games, the team has a mean score of 21 points per game. After playing 6 games, the team has a mean score of 23 points per game.
Work out the number of points the team scored in its 6th game.
The table gives information about the times, in minutes, taken by 80 customers to do their shopping in a supermarket.
| Time taken (t minutes) | Frequency |
| 0 t 10 | 7 |
| 10 t 20 | 26 |
| 20 t 30 | 24 |
| 30 t 40 | 14 |
| 40 t 50 | 7 |
| 50 t 60 | 2 |
Complete the cumulative frequency table.
On the grid opposite, draw a cumulative frequency graph for your table.
Time taken (minutes)
Use your graph to find an estimate for the median time taken.
One of the 80 customers is chosen at random.
Use your graph to find an estimate for the probability that the time taken by this customer was more than 42 minutes.
Here are the salaries, in thousands of dollars, of seven people.
21 28 29 32 34 34 39
Find the mode of the salaries.
Find the range of the salaries.
A scientist is investigating the weight of 50 tigers.
Here is some information about these tigers.
| Type of tiger Siberian | Bengal | |
| Number of tigers | 22 | 28 |
| Mean weight of tigers (kg) | 260 |
The mean weight of all 50 tigers is 218 kg
Work out the mean weight of the Bengal tigers.
A scientist is investigating the weight of 50 tigers.
Here is some information about these tigers.
| Type of tiger Siberian | Bengal | |
| Number of tigers | 22 | 28 |
| Mean weight of tigers (kg) | 260 |
The mean weight of all 50 tigers is 218 kg
Work out the mean weight of the Bengal tigers.
The frequency table gives information about the number of points scored by a player.
| Number of points | Frequency |
| 0 | 13 |
| 1 | 17 |
| 2 | 8 |
| 3 | x |
| 4 | 11 |
The mean number of points scored is 2
Work out the value of x
Also involves Conditional probability
A group of 60 students each sat an algebra test and a geometry test. Each test was marked out of 110
The cumulative frequency graph gives information about the marks gained by the 60 students in the algebra test.
Use the graph to find an estimate for the median mark in the algebra test.
Use the graph to find an estimate for the number of students who gained 58 marks or less in the algebra test.
Use the graph to find an estimate for the interquartile range of the marks gained in the algebra test.
The interquartile range of the marks gained in the geometry test is 9
Luis says
“The students’ marks are more spread out in the algebra test than in the geometry test.”
Is Luis correct? Give a reason for your answer.
To be awarded a grade A in the algebra test, a student had to gain a mark greater than 64
Two students are to be selected at random from the 60 students in the group.
Use the graph to find an estimate for the probability that both of these students were awarded a grade A in the algebra test.
Diyar recorded the distance, in kilometres, that he cycled each day for 11 days. Here are his results.
8 10 12 13 5 23 21 7 5 16 14
Find the interquartile range of his results.
The table shows the average number of spectators per match, for each of six Spanish football teams, in one season.
| Team | Average number of spectators per match |
| Real Betis | 46 393 |
| Valencia | 38699 |
| Barcelona | 65731 |
| Athletic Bilbao | 37378 |
| Sevilla | 33069 |
| Real Madrid | 65027 |
Which team had the lowest average number of spectators per match?
Write the number 65 731 correct to the nearest thousand.
Write down the value of the 6 in the number 38 699
In one match, Sevilla played Valencia. In the match, Sevilla had 8 shots on target and Valencia had 12 shots on target.
Write the ratio 8:12 in its simplest form.
In the same match, Valencia had 72% possession of the ball.
Write 72% as a fraction in its simplest form.
Also involves Angle facts
Cate asked the 60 members of a leisure centre how many times they had each visited the leisure centre last week.
The table gives information about her results.
| Number of visits | Frequency |
| 0 | 4 |
| 1 | 12 |
| 2 | 17 |
| 3 | 20 |
| 4 | 7 |
Write down the mode of the number of visits.
Cate is going to draw a pie chart for the information in the table.
Work out the size of the angle in the pie chart for the sector representing 1 visit.
35% of the 60 members are aged 50 or over.
Work out how many of the members are aged 50 or over.
The table gives information about the speeds, in kilometres per hour, of 80 motorbikes as each pass under a bridge.
| Speed (s kilometres per hour) | Frequency |
| 40 s 50 | 10 |
| 50 s 60 | 16 |
| 60 s 70 | 19 |
| 70 s 80 | 23 |
| 80 s 90 | 12 |
Write down the modal class.
Work out an estimate for the mean speed of the motorbikes as they pass under the bridge. Give your answer correct to 3 significant figures.
........ kilometres per hour
The table gives information about the speeds, in kilometres per hour, of 80 motorbikes as each pass under a bridge.
| Speed (s kilometres per hour) | Frequency |
| 40 s 50 | 10 |
| 50 s 60 | 16 |
| 60 s 70 | 19 |
| 70 s 80 | 23 |
| 80 s 90 | 12 |
Write down the modal class.
Work out an estimate for the mean speed of the motorbikes as they pass under the bridge. Give your answer correct to 3 significant figures.
........ kilometres per hour
Also involves Forming and solving equations
Given that a < b < c
the four whole numbers a, a, b and c have
a mode of 7 a median of 8.5 a mean of 9
Work out the value of a, the value of b and the value of c.
Also involves Forming and solving equations
The cumulative frequency graph gives information about the weights, in grams, of 90 bags of sweets.
Weight (grams)
Find an estimate for the median of the weights of these bags of sweets.
Roberto sells the bags of sweets to raise money for charity. Bags with a weight greater than d grams are labelled large bags and sold for 3.75 euros each bag.
The total amount of money he receives by selling all the large bags is 93.75 euros.
Find the value of d.
Also involves Percentages
The manager of a call centre asked the 120 people, who rang the call centre last week, how long they each waited before their call was answered.
The table gives information about their replies.
| Time waited (t minutes) | Frequency |
| 0 t 5 | 8 |
| 5 t 10 | 15 |
| 10 t 15 | 17 |
| 15 t 20 | 28 |
| 20 t 25 | 33 |
| 25 t 30 | 19 |
Complete the cumulative frequency table.
On the grid below, draw a cumulative frequency graph for your table.
Use your graph to find an estimate for the median of the times waited.
Using your graph, find an estimate for the percentage of the 120 people who said that they waited longer than 23 minutes before their call was answered. Show your working clearly.
Also involves Rounding
The histogram and the table give some information about the amounts of time, in hours, that Year 11 students at Bergdesh Academy spent, in total, on their homework last week. No student in Year 11 spent longer than 9 hours on their homework.
Time spent on homework (t hours)
Using the information in the histogram and in the table, work out an estimate for the mean amount of time the Year 11 students spent on their homework last week. Give your answer in hours correct to 3 significant figures.
Ava writes down five whole numbers.
For these five numbers
the median is 7
the mode is 8
the range is 5
Find a possible value for each of the five numbers that Ava writes down.
Also involves Forming and solving equations
There are 5 cocoa pods in a bag. The mean weight of the 5 cocoa pods is 398 grams.
A sixth cocoa pod is put into the bag. The mean weight of the 6 cocoa pods is 401 grams.
Work out the weight of the sixth cocoa pod that is put into the bag.
A mathematics teacher at a school asked a group of students how far, in kilometres, each student had travelled to get to school that day.
The table gives information about their answers.
| Distance travelled (dkm) | Number of students |
| 0 d 2 | x |
| 2 d 4 | 11 |
| 4 d 6 | 8 |
| 6 d 8 | 6 |
| 8 d 10 | 5 |
The teacher calculated that an estimate for the mean distance travelled by the whole group of students was 4.25 km.
Work out the value of x. Show your working clearly.
Also involves Simultaneous equations
Here is a list of six numbers written in order of size.
4 7 x 10 y y
The numbers have
a median of 9 a mean of 11
Find the value of x and the value of y.
The table gives information about the length of time, in minutes, that each of 60 students took to travel to school on Monday.
| Length of time (t minutes) | Frequency |
0 t  10 | 4 |
10 t  20 | 10 |
| 20 t 30 | 15 |
| 30 t 40 | 25 |
| 40 t 50 | 6 |
Work out an estimate for the mean length of time taken by these 60 students to travel to school on Monday. Give your answer correct to one decimal place.
Also involves Simultaneous equations · Forming and solving equations
Here is a list of six numbers written in order of size.
4 7 x 10 y y
The numbers have
a median of 9 a mean of 11
Find the value of x and the value of y.
The table gives information about the length of time, in minutes, that each of 60 students took to travel to school on Monday.
| Length of time (t minutes) | Frequency |
| 0 t 10 | 4 |
| 10 t 20 | 10 |
| 20 t 30 | 15 |
| 30 t 40 | 25 |
| 40 t 50 | 6 |
Write down the modal class interval.
Work out an estimate for the mean length of time taken by these 60 students to travel to school on Monday. Give your answer correct to one decimal place.
The frequency table gives information about the ages of the 80 people in a train carriage.
| Age (a years) | Frequency |
| 0 a 20 | 9 |
| 20 a 30 | 19 |
| 30 a 40 | 17 |
| 40 a 50 | 18 |
| 50 a 60 | 13 |
| 60 a 70 | 4 |
Complete the cumulative frequency table.
On the grid, draw a cumulative frequency graph for your table.
Age (a years)
Use your graph to find an estimate for the median age of the people in the train carriage.
The table gives information about the heights, in centimetres, of some plants.
| Height (h cm) | Frequency |
10  h  20 | 35 |
20  h  35 | 45 |
35  h  50 | 75 |
50 h  70 | 40 |
70 h  80 | 8 |
On the grid, draw a histogram for this information.
Work out an estimate for the number of these plants with a height greater than 40 cm.
Paula asks 16 members of her class the number of pets they each have. Here are her results.
1 2 2 4 0 1 2 1
3 3 4 1 1 0 3 2
Complete the frequency table for her results.
Write down the mode for the number of pets.
Work out the range for the number of pets.
The table shows information about the lengths of time, in minutes, 120 customers spent in a supermarket.
| Length of time (L minutes) | Frequency |
20 < L  30 | 6 |
30 < L  40 | 26 |
40 < L  50 | 31 |
| 50 < L 60 | 40 |
| 60 < L 70 | 17 |
Write down the modal class.
Work out an estimate for the mean length of time spent by the 120 customers in the supermarket.
Alexa has five cards. Each card has a number on it.
The table gives information about the numbers on the five cards.
| Total | Median | Mode | Range |
| 45 | 8 | 5 | 10 |
Using the information in the table, complete each card by writing its number on it.
Alison buys 2 boxes of strawberries, box A and box B.
Box A contains 15 strawberries. The strawberries in box A have a mean weight of 24 grams.
Box B contains 25 strawberries. The strawberries in box B have a mean weight of 18 grams.
Alison puts all 40 strawberries into a bowl. Work out the mean weight of the 40 strawberries.
The table shows information about the lengths of time, in minutes, 120 customers spent in a supermarket.
| Length of time (L minutes) | Frequency |
| 20 < L 30 | 6 |
| 30 < L 40 | 26 |
| 40 < L 50 | 31 |
| 50 < L 60 | 40 |
| 60 < L 70 | 17 |
Write down the modal class.
Work out an estimate for the mean length of time spent by the 120 customers in the supermarket.
The table shows information about the number of minutes each of 120 buses was late last Monday.
| Number of minutes late (L) | Frequency |
0 < L  10 | 10 |
10 < L  20 | 16 |
20 < L  30 | 44 |
| 30 < L 40 | 29 |
| 40 < L 50 | 15 |
| 50 < L 60 | 6 |
Complete the cumulative frequency table below.
On the grid, draw a cumulative frequency graph for your table.
Use your graph to find an estimate for the interquartile range.
Use your graph to find an estimate for the number of buses that were more than 48 minutes late last Monday.
At 6 pm, the temperature in Victoria’s garden was 5 °C. By midnight, the temperature in Victoria’s garden had fallen by 9 °C.
Work out the temperature in Victoria’s garden at midnight.
Here is a list of 7 temperatures.
4 °C −6 °C 4 °C 0 °C −1 °C −7 °C −5 °C
For the 7 temperatures in the list,
write down the mode,
find the median.
The table shows information about the weights, in kilograms, of 40 babies.
| Weight (wkg) | Frequency |
2 w  3 | 12 |
3 w  4 | 16 |
4 w  5 | 9 |
5 w  6 | 2 |
6 w  7 | 1 |
Write down the modal class.
Work out an estimate for the mean weight of the 40 babies.
One of the 40 babies is going to be chosen at random.
Find the probability that this baby has a weight of more than 5 kg.
Also involves The four operations
5 children are playing on a trampoline. The mean weight of the 5 children is 28 kg.
2 of the children get off the trampoline. The mean weight of these 2 children is 26.5 kg.
Work out the mean weight of the 3 children who remain on the trampoline.
The table shows information about the weights, in kilograms, of 40 babies.
| Weight (wkg) | Frequency |
| 2 w 3 | 12 |
| 3 w 4 | 16 |
| 4 w 5 | 9 |
| 5 w 6 | 2 |
| 6 w 7 | 1 |
Write down the modal class.
Work out an estimate for the mean weight of the 40 babies.
One of the 40 babies is going to be chosen at random.
Find the probability that this baby has a weight of more than 5 kg.
8 5 children are playing on a trampoline. The mean weight of the 5 children is 28 kg.
2 of the children get off the trampoline. The mean weight of these 2 children is 26.5 kg.
Work out the mean weight of the 3 children who remain on the trampoline.
Also involves Percentages
A total of 80 men and women took part in a race. The cumulative frequency graph gives information about the times, in minutes, they took for the race.
Time (minutes)
Use the graph to find an estimate for the interquartile range.
60% of the men took 50 minutes or less for the race. No women took 50 minutes or less for the race.
Work out an estimate for the number of men who took part in the race.
The cumulative frequency graph gives information about the waiting times, in minutes, of people with appointments at Hospital A.
Use the graph to find an estimate of the median waiting time at Hospital A.
Use the graph to find an estimate of the interquartile range of the waiting times at Hospital A.
At a different hospital, Hospital B, the median waiting time is 28 minutes and the interquartile range of the waiting times is 19 minutes.
Compare the waiting times at Hospital A with the waiting times at Hospital B.
Egor rolled a dice 24 times. Here are his results.
| 2 | 3 | 5 | 4 | 6 | 2 |
| 1 | 3 | 3 | 5 | 1 | 3 |
| 3 | 5 | 5 | 6 | 2 | 5 |
| 4 | 3 | 4 | 3 | 3 | 4 |
Complete the frequency table for Egor’s results.
Write down the mode of the numbers that Egor rolled.
Egor thinks the dice he rolled is biased.
Give a reason why the results could show that the dice is biased.
Also involves The four operations
There are 25 pens in a packet. 7 of the pens are green. 10 of the pens are black. The rest of the pens are red. Jurgen takes at random a pen from the packet.
Find the probability that
the pen is black,
the pen is red.
Heidi records the number of packets of pens sold in her shop to each customer last Friday. The table shows information about her results.
| Number of packets | Frequency |
| 1 | 14 |
| 2 | 17 |
| 3 | 15 |
| 4 | 12 |
| 5 | 9 |
Write down the mode of the number of packets.
Work out the total number of packets of pens sold last Friday.
Also involves Forming and solving equations
Here are four different numbers written in order of size.
3 6 m n
The range of the four numbers is 13 The median of the four numbers is 8.5
Find the value of m and the value of n.
The table gives information about the amount of money, in £, that Fiona spent in a
Work out an estimate for the total amount of money that Fiona spent in the grocery store during 2019
The table gives information about the amount of money, in £, that Fiona spent in a
Work out an estimate for the total amount of money that Fiona spent in the grocery store during 2019
Max kept a record of the marks he scored in each of the 11 spelling tests he took one term.
Here are his marks.
18 5 7 12 11 18 15 16 17 13 14
Find the interquartile range of the marks.
Here are the shoe sizes of 11 people.
7 8 4 4 4 10 5 7 7 4 4
Write down the mode.
Work out the range.
Find the median.
Clark works in a shoe shop.
On Tuesday morning he sold some pairs of shoes. The mean price of the pairs of shoes was £34
On Tuesday afternoon he sold only two pairs of shoes. The prices of these pairs of shoes were £31 and £49
Is the mean price of all the pairs of shoes Clark sold on Tuesday more or less than £34? You must give a reason for your answer.
Also involves Tables, charts and diagrams
The pictogram gives information about the number of emails Sami sent on each of five days last week.
Work out the mean number of emails Sami sent on these 5 days.
There are 10 people in a lift. These 10 people have a mean weight of 79.2 kg.
3 of these people get out of the lift. These 3 people have a mean weight of 68 kg.
Work out the mean weight of the 7 people left in the lift.
The table shows information about the heights, in cm, of 48 sunflowers in a garden centre.
| Height of sunflower (h cm) | Frequency |
90 h  100 | 8 |
100 h  110 | 12 |
110 h  120 | 15 |
120 h  130 | 10 |
| 130 h 140 | 3 |
Work out an estimate for the mean height of the sunflowers.
7 30 students in a class sat a Mathematics test. The mean mark in the test for the 30 students was 26.8
13 of the 30 students in the class are boys. The mean mark in the test for the boys was 25
Find the mean mark in the test for the girls. Give your answer correct to 3 significant figures.
The table gives information about the times taken, in minutes, for 80 taxi journeys.
| Time taken (t minutes) | Frequency |
| 0 t 5 | 7 |
| 5 t 10 | 10 |
| 10 t 15 | 12 |
| 15 t 20 | 19 |
| 20 t 25 | 18 |
| 25 t 30 | 14 |
Complete the cumulative frequency table.
On the grid opposite, draw a cumulative frequency graph for your table.
Time taken (minutes)
Use your graph to find an estimate for the median.
Use your graph to find an estimate for the interquartile range.
Also involves Probability
Sandeep recorded the length of time, in minutes, that each of 100 adults went for a walk one Saturday afternoon.
The cumulative frequency table gives information about these times.
| Time (t minutes) | Cumulative frequency |
30 t  40 | 6 |
| 30 t 50 | 20 |
| 30 t 60 | 56 |
| 30 t 70 | 84 |
| 30 t 80 | 95 |
30 t  90 | 100 |
On the grid, draw a cumulative frequency graph for the information in the table.
Use your graph to find an estimate for the median length of time that these adults went for a walk.
One of the 100 adults is chosen at random.
Use your graph to find an estimate for the probability that this adult went for a walk for more than 72 minutes.
The table shows information about the weights, in kg, of 40 parcels.
| Weight of parcel ( p kg) | Frequency |
| 0 p 1 | 19 |
| 1 p 2 | 12 |
| 2 p 3 | 5 |
| 3 p 4 | 2 |
| 4 p 5 | 2 |
Write down the modal class.
Work out an estimate for the mean weight of the parcels.
The table shows information about the weights, in kg, of 40 parcels.
| Weight of parcel ( p kg) | Frequency |
| 0 p 1 | 19 |
| 1 p 2 | 12 |
2 p  3 | 5 |
| 3 p 4 | 2 |
4 p  5 | 2 |
Write down the modal class.
Work out an estimate for the mean weight of the parcels.
The table gives information about the times, in hours, some students spent doing sport one week.
| Time (T hours) | Frequency |
| 0 T 2 | 5 |
| 2 T 4 | 9 |
| 4 T 6 | 24 |
| 6 T 8 | 40 |
| 8 T 10 | 7 |
Calculate an estimate for the mean time these students spent doing sport. Give your answer in hours, correct to 1 decimal place.
The cumulative frequency graph shows information about the length, in minutes, of each of 80 films.
Length (minutes)
Use the graph to find an estimate for the interquartile range.
Clare says,
“More than 35% of these films are over 120 minutes long.”
Is Clare correct? Give a reason for your answer.
The table shows information about the number of goals scored by a football team in each of 20 matches.
| Number of goals scored | Frequency |
| 0 | 6 |
| 1 | 5 |
| 2 | 7 |
| 3 | 1 |
| 4 | 0 |
| 5 | 1 |
Write down the mode of the number of goals scored.
Find the median number of goals scored.
Work out the total number of goals scored.
Also involves Forming and solving equations
x, 10 and y are three integers written in order of size, starting with the smallest integer.
The mean of x, 10 and y is 11 The range of x, 10 and y is 7
Work out the value of x and the value of y.
The students in Class A and in Class B take the same examination.
There are 28 students in Class A and 32 students in Class B. The mean score for all the students in both classes is 72.6 The mean score for the students in Class A is 75
Work out the mean score for the students in Class B.
The lowest score in Class A is 39 The range of scores for Class A is 57 The lowest score in Class B is 33 The range of scores for Class B is 60
Find the range of scores for all the students in both classes.
Also involves Forming and solving equations
The students in Class A and in Class B take the same examination.
There are 28 students in Class A and 32 students in Class B. The mean score for all the students in both classes is 72.6 The mean score for the students in Class A is 75
Work out the mean score for the students in Class B.
The lowest score in Class A is 39 The range of scores for Class A is 57 The lowest score in Class B is 33 The range of scores for Class B is 60
Find the range of scores for all the students in both classes.
The table shows information about the amount of money spent on holiday by each of 120 families.
| Money spent (£m) | Frequency |
| 0 m 100 | 10 |
| 100 m 200 | 36 |
| 200 m 300 | 34 |
| 300 m 400 | 20 |
| 400 m 500 | 15 |
| 500 m 600 | 5 |
Write down the modal class.
Complete the cumulative frequency table for the information in the table.
On the grid, draw a cumulative frequency graph for your table.
Use your graph to find an estimate for the interquartile range.
Use your graph to find an estimate for the number of families that spent more than £450 on holiday.
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