15 people were asked how long, in minutes, they had been waiting for a bus.
Here are the results.
2 | 3 | 3 | 4 | 5 | 6 | 6 | 8 | 9 | 10 | 11 | 13 | 14 | 15 | 18 |
 Â
Find the interquartile range of these times.
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15 people were asked how long, in minutes, they had been waiting for a bus.
Here are the results.
2 | 3 | 3 | 4 | 5 | 6 | 6 | 8 | 9 | 10 | 11 | 13 | 14 | 15 | 18 |
 Â
Find the interquartile range of these times.
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Here is the number of goals that Henri’s team scored one summer in each water polo match.
5Â Â Â 8Â Â Â 9 Â Â Â 11 Â Â Â 13Â Â Â 13Â Â Â 14Â Â Â 15Â Â Â 16Â Â Â 17Â Â Â 20
Find the interquartile range of the numbers of goals.
Show your working clearly.
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Twenty students took a Science test and a Maths test.
Both tests were marked out ofÂ
The table gives information about their results.
 | Median | Interquartile range |
Science | ||
Maths |
Use this information to compare the Science test results with the Maths test results.
Write down two comparisons.
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The table shows information about the weights, in kg, of 40 parcels.
Weight of parcel ( kg) | Frequency |
19 | |
12 | |
5 | |
2 | |
2 |
Write down the modal class.
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The students in Class A and in Class B take the same examination.
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.
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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 |
10 | |
16 | |
19 | |
23 | |
12 |
Write down the modal class.
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The table gives information about the length of time, in minutes, that each of students took to travel to school on Monday.
Length of time ( minutes) | Frequency |
4 | |
10 | |
15 | |
25 | |
6 |
Write down the modal class interval.
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15 students took an English test.
The same 15 students took a Maths test.
Both tests were marked out of 30.
For the English test results
the median was 21
the interquartile range was 14
The Maths test results are shown below.
18 | 18 | 19 | 20 | 24 | 25 | 25 | 26 | 28 | 28 | 29 | 29 | 29 | 30 | 30 |
Use the information above to compare the English test results with the Maths test results.
Write down two comparisons.
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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.
Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Number of planes | 148 | 151 | 147 | 155 | 153 | 147 | 155 | 102 | 151 | 154 |
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.
Her prediction is too low
Her prediction is too high
Her prediction could be too low or too high
Give a reason for your answer.
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100 men and 100 women took a test.
Scores
 | Median | Interquartile range | Range |
Men | 28 | 7.5 | 31 |
Women | 30 | 9 | 37 |
Using this data, which statement must be true?
Tick one box.
 Men had a higher average score than women
 Men had more consistent scores than women
 A woman had the highest score
 A man had the lowest score
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In one month, the number of hours of exercise taken by 10 people are
4Â Â Â 7 Â Â Â 2 Â Â Â 8 Â Â Â 6Â Â Â 5 Â Â Â 1 Â Â Â 82 Â Â Â 3 Â Â Â 9
Which is the appropriate average to use in this situation?
Tick a box.
Mean      Median       Mode
Give one reason for each of the other two averages as to why they are not appropriate.
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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.
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A station manager looks at the information below.
Number of minutes late, |
Number of trains |
12 | |
0 | |
7 | |
0 | |
0 | |
1 |
Estimate the mean number of minutes late.
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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.
.......................kg
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The table shows information about the times for 10 people to complete a task.
Time, (minutes) | Frequency |
1 | |
6 | |
3 |
These statements are about the mean and range of the actual times.
Tick the correct box for each statement.
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Students in a class took a spelling test.
The diagram shows information about the scores.
Lucy is one of the 29 students in the class.
Her score was the same as the median score for her class.
Work out her score.
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Ping chooses four numbers.
The mode of these four numbers is 8, the range is 7 and the mean is 11.
Find Ping’s four numbers.
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Jenny played four games of golf.
For these games her modal score was 76 and her mean score was 75.
Her range of scores was 10.
What were her scores for the four games?
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Ed has 4 cards.
There is a number on each card.
12 | Â | 6 | Â | 15 | Â | ? |
The mean of the 4 numbers on Ed's cards is 10
Work out the number on the 4th card.
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The table shows some information about the dress sizes of women.
Dress size | Number of women |
Find the median dress size.
of the women have a shoe size ofÂ
Zoe says that if you choose at random one of the women, the probability that she has
either a shoe size of or a dress size of is because
Is Zoe correct?
You must give a reason for your answer.
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The time-series graph gives some information about the number of pairs of shoes sold in a shoe shop in the first six months of 2014.
The sales target for the first six months of 2014 was to sell a mean of 96 pairs of shoes per month.
Did the shoe shop meet this sales target?
You must show how you get your answer.
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A bus company recorded the ages, in years, of the people on coach A and the people on coach B.
Here are the ages of the 23 people on coach A.
41 | 42 | 44 | 48 | 52 | 53 | 53 | 53 | 56 | 57 | 57 | 59 |
60 | 61 | 63 | 64 | 64 | 66 | 67 | 69 | 74 | 77 | 79 | Â |
Complete the table below to show information about the ages of the people on
coach A.
 Median |  |
 Lower Quartile |  |
 Upper Quartile |  |
 Least age | 41 |
 Greatest age | 79 |
Here is some information about the ages of the people on coach B.
Median | 70 |
Lower quartile | 54 |
Upper quartile | 73 |
Least age | 42 |
Greatest age | 85 |
Richard says that the people on coach A are younger than the people on coach B.
Is Richard correct?
You must give a reason for your answer.
Richard says that the people on coach A vary more in age than the people on coach B.
Is Richard correct?
You must give a reason for your answer.
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The table gives some information about the birds Paula sees in her garden one day.
Bird | Frequency |
Magpie | 15 |
Thrush | 10 |
Starling | 20 |
Sparrow | 27 |
Complete the accurate pie chart.
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Jenny has six cards.
Each card has a whole number written on it so that
the 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.
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Diyar recorded the distance, in kilometres, that he cycled each day for 11 days.
Here are his results.
Find the interquartile range of his results.
....................................................... kmÂ
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Yusuf sat 8 examinations.
Here are his marks for 5 of the examinations.
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.
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Given thatÂ
the four whole numbers and 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 .
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Sandeep sat tests in JanuaryÂ
Each test was marked out ofÂ
Here are his test results.
Find the interquartile range of these test results.
Show your working clearly.
Sandeep also sat some tests in MayÂ
Each test was marked out ofÂ
The median of the May test results isÂ
The interquartile range of the May test results isÂ
In which month, January or May, were Sandeep’s test results more consistent?
Give a reason for your answer.
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Circle the expression for the range of consecutive integers.
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Here is some information about the times taken by 40 people to fill in a form.
Time, minutes | Number of people |
3 | |
9 | |
11 | |
17 |
In which class interval is the median?
Circle your answer.
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102 boys and 85 girls took a test.
The table shows information about the mean marks.
 | Boys | Girls |
Number of students | 102 | 85 |
Mean mark | 68.5 | 72.4 |
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.
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Here is some information about 26 houses.
and are all different numbers.
Number of bedrooms | Number of houses |
1 | 7 |
2 | |
3 | |
4 | |
5 | 8 |
The median number of bedrooms is 3.5
Work out a possible set of values for and .
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200 people recorded the time they spent on social media one day.
The table shows the results.
Time, t (mins) | Frequency | Midpoint | Â |
24 | Â | Â | |
76 | Â | Â | |
52 | Â | Â | |
48 | Â | Â | |
 | Total = 200 |  |  |
Work out an estimate of the mean time.
..................................minsÂ
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The table shows information about the distances walked by 120 students on their way to school one week.
Distance, (miles) | Frequency |  |  |
20 | Â | Â | |
48 | Â | Â | |
30 | Â | Â | |
22 | Â | Â | |
 | Total = 120 |  |  |
Work out an estimate for the mean distance.
...................miles
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A shop records the time taken by its customers to complete a purchase on its website.
The results from one day are summarised in this table.
Time taken ( minutes) |
Number of customers |
 |  |
6 | Â | Â | |
10 | Â | Â | |
6 | Â | Â | |
2 | Â | Â | |
1 | Â | Â |
Calculate an estimate of the mean time taken.
....................... minutesÂ
Explain why it is not possible to use the information from this table to calculate the exact value of the mean time taken.Â
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The police record the speed of vehicles passing a speed checkpoint.
The speeds are recorded in the table below.
Speed (s mph) | Number of vehicles |
 |  |
5 | Â | Â | |
8 | Â | Â | |
37 | Â | Â | |
47 | Â | Â | |
3 | Â | Â |
..................... mph [4]
[1]
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Ceri records the time taken, minutes, to travel to school for a sample of 168 students at her Academy.
Time taken ( minutes) |
Frequency |
54 | |
50 | |
44 | |
20 |
Ceri says
The longest time that any of these students took to travel to school was 80 minutes.
Is she correct?
Give a reason for your answer.
Ceri also claims that 25% of all of the students at this Academy took more than 30 minutes to travel to school.
[2]
[1]
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Hertford Juniors is a basketball team.
At the end of 10 games, their mean score is 35 points per game.
At the end of 11 games, their mean score has gone down to 33 points per game.
How many points did the team score in the 11th game?
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There are 18 packets of sweets and 12 boxes of sweets in a carton.
The mean number of sweets in all the 30 packets and boxes is 14.
The mean number of sweets in the 18 packets is 10.
Work out the mean number of sweets in the boxes.
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There are 15 children at a birthday party.
The mean age of the 15 children is 7 years.
9 of the 15 children are boys.
The mean age of the boys is 5 years.
Work out the mean age of the girls.
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There are 10 boys and 20 girls in a class.
The class has a test.
The mean mark for all the class is 60
The mean mark for the girls is 54
Work out the mean mark for the boys.
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Walkden Reds is a basketball team.
At the end of 11 games, their mean score was 33 points per game.
At the end of 10 games, their mean score was 2 points higher.
Jordan says,
   "Walkden Reds must have scored 13 points in their 11th game."
Is Jordan right?
You must show how you get your answer.
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Mr Brown gives his class a test.
The 10 girls in the class get a mean mark of 70%
The 15 boys in the class get a mean mark of 80%
Nick says that because the mean of 70 and 80 is 75 then the mean mark for the whole class in the test is 75%
Nick is not correct.
Is the correct mean mark less than or greater than 75%?
You must justify your answer.
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Bob asked each of friends how many minutes they took to get to work.
The table shows some information about his results.
Time taken (m minutes) | Frequency |
Work out an estimate for the mean time taken.
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Sumeet records the times, in minutes, for 40 runners to finish a half marathon.
Information about these times is shown in the table.
Time ( minutes) | Frequency |
Calculate an estimate for the mean time.
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The table gives information about the heights of trees.
Height(Â metres) | Frequency |
Work out an estimate for the mean height of the trees.
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The table gives information about the heights of girls.
Height( metres) | Frequency |
Find the class interval that contains the median.
Work out an estimate for the mean height.
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The table shows information about the weekly earnings of people who work in a shop.
Weekly earnings() | Frequency |
Work out an estimate for the mean of the weekly earnings.
Nadiya says,
   "The mean may not be the best average to use to represent this information."
Do you agree with Nadiya?
You must justify your answer.
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The table shows some information about the foot lengths of adults.
Foot length( cm) | Number of adults |
Write down the modal class interval.
Calculate an estimate for the mean foot length.
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Jenny works in a shop that sells belts.
The table shows information about the waist sizes of customers who bought belts from the shop in May.
Belt size | Waist(Â inches) | Â Frequency |
Small | ||
Medium | ||
Large | ||
Extra Large |
Calculate an estimate for the mean waist size.
Belts are made in sizes Small, Medium, Large and Extra Large.
Jenny needs to order more belts in June.
The modal size of belts sold is Small.
Jenny is going to order of the belts in size Small.
The manager of the shop tells Jenny she should not order so many Small belts.
Who is correct, Jenny or the manager?
You must give a reason for your answer.
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25 students in class A did a science exam.
30 students in class B did the same science exam.
The mean mark for the 25 students in class A is 67.8
The mean mark for all the 55 students is 72.0
Work out the mean mark for the students in class B.                                          Â
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The pie charts give information about the ages, in years, of people living in two towns,
Adley and Bridford.
The ratio of the number of people living in Adley to the number of people living in Bridford is given by the ratio of the areas of the pie charts.
What proportion of the total number of people living in these two towns live in Adley and are aged 0 – 19?
Give your answer correct to 3 significant figures.
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Here are two sets of numbers, A and B.
mean of Set A : mean of Set B = 3 : 8
Work out the value of
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Fran asks each of 40 students how many books they bought last year.
The chart below shows information about the number of books bought by each of the 40 students.
Work out the percentage of these students who bought 20 or more books.
 ...........%Â
Show that an estimate for the mean number of books bought is 9.5
You must show all your working.
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