Cumulative frequency [160 marks]1a.Adam is a beekeeper

Cumulative frequency [160 marks]
1a.
Adam is a beekeeper who collected data about monthly honey
production in his bee hives. The data for six of his hives is
shown in the
following table.
The relationship between the variables is modelled by the
regression line with equation .
Write down the value of and of .
P = aN + b
a b
1b. Use this regression line to estimate the monthly honey
production from a hive that has 270 bees.
1c.
Adam has 200 hives in total. He collects data on the monthly
honey production of all the hives. This data is shown in the
following
cumulative frequency graph.
Adam’s hives are labelled as low, regular or high production, as
defined in the following table.
Write down the number of low production hives.

1d.
Adam knows that 128 of his hives have a regular production.
Find the value of ;k
1e. Find the number of hives that have a high production.
1f. Adam decides to increase the number of bees in each low
production hive. Research suggests that there is a probability of
0.75
that a low production hive becomes a regular production hive.
Calculate the probability that 30 low production hives become
regular
production hives.
[3 marks]
[2 marks]
[1 mark]
[3 marks]
[2 marks]
[3 marks]
2a.
A city hired 160 employees to work at a festival. The following
cumulative frequency curve shows the number of hours
employees

worked during the festival.
Find the median number of hours worked by the employees.
2b. Write down the number of employees who worked 50 hours
or less.
2c.
The city paid each of the employees £8 per hour for the first 40
hours worked, and £10 per hour for each hour they worked after
the first
40 hours.
Find the amount of money an employee earned for working 40
hours;
2d. Find the amount of money an employee earned for working
43 hours.
2e. Find the number of employees who earned £200 or less.
2f. Only 10 employees earned more than £ . Find the value of .k
k
3a.
Ten students were surveyed about the number of hours, , they
spent browsing the Internet during week 1 of the school year.
The
results of the survey are given below.
Find the mean number of hours spent browsing the Internet.
x

10∑
i=1 xi = 252, σ = 5 and median = 27.
[2 marks]
[1 mark]
[1 mark]
[3 marks]
[3 marks]
[4 marks]
[2 marks]
3b. During week 2, the students worked on a major project and
they each spent an additional five hours browsing the Internet.
For
week 2, write down
(i) the mean;
(ii) the standard deviation.
3c. During week 3 each student spent 5% less time browsing the
Internet than during week 1. For week 3, find
(i) the median;
(ii) the variance.
3d.

During week 4, the survey was extended to all 200 students in
the school. The results are shown in the cumulative frequency
graph:
(i) Find the number of students who spent between 25 and 30
hours browsing the Internet.
(ii) Given that 10% of the students spent more than k hours
browsing the Internet, find the maximum value of .k
[2 marks]
[6 marks]
[6 marks]
4a.
A school collects cans for recycling to raise money. Sam’s class
has 20 students.
The number of cans collected by each student in Sam’s class is
shown in the following stem and leaf diagram.
Find the median number of cans collected.
4b.
The following box-and-whisker plot also displays the number of
cans collected by students in Sam’s class.
(i) Write down the value of .

(ii) The interquartile range is 14. Find the value of .
a
b
4c. Sam’s class collected 745 cans. They want an average of 40
cans per student.
How many more cans need to be collected to achieve this
target?
4d.
There are 80 students in the school.
The students raise $0.10 for each recycled can.
(i) Find the largest amount raised by a student in Sam’s class.
(ii) The following cumulative frequency curve shows the
amounts in dollars raised by all the students in the school. Find
the percentage of
students in the school who raised more money than anyone in
Sam’s class.
[2 marks]
[3 marks]
[3 marks]
[5 marks]

4e.
The mean number of cans collected is 39.4. The standard
deviation is 18.5.
Each student then collects 2 more cans.
(i) Write down the new mean.
(ii) Write down the new standard deviation.
[2 marks]
5a.
The following cumulative frequency graph shows the monthly
income, dollars, of families.
Find the median monthly income.
I 2000
5b. (i) Write down the number of families who have a
monthly income of dollars or less.
(ii) Find the number of families who have a monthly income
of more than dollars.
2000
4000
5c. The families live in two different types of housing. The
following table gives information about the number of families

living in
each type of housing and their monthly income .
Find the value of .
2000
I
p
5d. A family is chosen at random.
(i) Find the probability that this family lives in an apartment.
(ii) Find the probability that this family lives in an
apartment, given that its monthly income is greater than
dollars.4000
5e. Estimate the mean monthly income for families living in a
villa.
[2 marks]
[4 marks]
[2 marks]
[2 marks]
[2 marks]
6a.
The weights in grams of 80 rats are shown in the following

cumulative frequency diagram.
Do NOT write solutions on this page.
Write down the median weight of the rats.
6b. Find the percentage of rats that weigh 70 grams or less.
6c. The same data is presented in the following table.
Weights
grams
Frequency
Write down the value of
.
w
0 ⩽ w ⩽ 30
30 < w ⩽ 60
60 < w ⩽ 90
90 < w ⩽ 120
p
45
q
5
p
[1 mark]

[3 marks]
[2 marks]
6d. The same data is presented in the following table.
Weights
grams
Frequency
Find the value of
.
w
0 ⩽ w ⩽ 30
30 < w ⩽ 60
60 < w ⩽ 90
90 < w ⩽ 120
p
45
q
5
q
6e. The same data is presented in the following table.
Weights

grams
Frequency
Use the values from the table to estimate the mean and standard
deviation of the weights.
w
0 ⩽ w ⩽ 30
30 < w ⩽ 60
60 < w ⩽ 90
90 < w ⩽ 120
p
45
q
5
6f. Assume that the weights of these rats are normally
distributed with the mean and standard deviation estimated in
part (c).
Find the percentage of rats that weigh 70 grams or less.
6g. Assume that the weights of these rats are normally
part (c).
A sample of five rats is chosen at random. Find the probability
that at most three rats weigh 70 grams or less.
[2 marks]
[3 marks]

[2 marks]
[3 marks]
7a.
The following is a cumulative frequency diagram for the time t,
in minutes, taken by 80 students to complete a task.
Find the number of students who completed the task in less than
45 minutes.
7b. Find the number of students who took between 35 and 45
minutes to complete the task.
7c. Given that 50 students take less than k minutes to complete
the task, find the value of
.k
8a.
A running club organizes a race to select girls to represent the
club in a competition.
The times taken by the group of girls to complete the race are
shown in the table below.
Find the value of
and of
.
p

q
[2 marks]
[3 marks]
[2 marks]
[4 marks]
8b. A girl is chosen at random.
(i) Find the probability that the time she takes is less than
minutes.
(ii) Find the probability that the time she takes is at least
minutes.
14
26
8c. A girl is selected for the competition if she takes less than
minutes to complete the race.
Given that
of the girls are not selected,
(i) find the number of girls who are not selected;
(ii) find
.
x

40%
x
8d. Girls who are not selected, but took less than
minutes to complete the race, are allowed another chance to be
selected. The new times taken by these girls are shown in the
cumulative frequency diagram below.
(i) Write down the number of girls who were allowed another
chance.
(ii) Find the percentage of the whole group who were
selected.
25
[3 marks]
[4 marks]
[4 marks]
9a.
The cumulative frequency curve below represents the marks
obtained by 100 students.
Find the median mark.
9b. Find the interquartile range.

10a.
The cumulative frequency curve below represents the heights of
200 sixteen-year-old boys.
Use the graph to answer the following.
Write down the median value.
10b. A boy is chosen at random. Find the probability that he is
shorter than
.161 cm
[2 marks]
[3 marks]
[1 mark]
[2 marks]
10c. Given that
of the boys are taller than
, find h .
82%
h cm
11a.
A scientist has 100 female fish and 100 male fish. She measures
their lengths to the nearest cm. These are shown in
the following box and whisker diagrams.

Find the range of the lengths of all 200 fish.
11b. Four cumulative frequency graphs are shown below.
Which graph is the best representation of the lengths of the
female fish?
12a.
The following table gives the examination grades for 120
students.
Find the value of
(i) p ;
(ii) q .
12b. Find the mean grade.
[3 marks]
[3 marks]
[2 marks]
[4 marks]
[2 marks]
12c. Write down the standard deviation.
13a.

A fisherman catches 200 fish to sell. He measures the lengths, l
cm of these fish, and the results are shown in the
frequency table below.
Calculate an estimate for the standard deviation of the lengths
of the fish.
13b. A cumulative frequency diagram is given below for the
lengths of the fish.
(i) Estimate the interquartile range.
(ii) Given that
of the fish have a length more than
, find the value of k.
40%
k cm
13c. In order to sell the fish, the fisherman classifies them as
small, medium or large.
Small fish have a length less than
.
Medium fish have a length greater than or equal to
but less than
.
Large fish have a length greater than or equal to
.
Write down the probability that a fish is small.

20 cm
20 cm
60 cm
60 cm
[1 mark]
[3 marks]
[6 marks]
[2 marks]
13d. The cost of a small fish is
, a medium fish
, and a large fish
.
Copy and complete the following table, which gives a
probability distribution for the cost
.
$4
$10
$12
$X
13e. Find
.E(X)

14a.
Write down the median.
14c. Complete the frequency table below.
[2 marks]
[2 marks]
[1 mark]
[3 marks]
[2 marks]
Printed for American Creativity Academy
© International Baccalaureate Organization 2019
International Baccalaureate® - Baccalauréat International® -
Bachillerato Internacional®
15a.
In a school with 125 girls, each student is tested to see how
many sit-up exercises (sit-ups) she can do in one minute.
The results are given in the table below.

(i) Write down the value of p.
(ii) Find the value of q.
15b. Find the median number of sit-ups.
15c. Find the mean number of sit-ups.
[3 marks]
[2 marks]
[2 marks]
Cumulative frequency [160 marks]
Writing your introduction
AS GP – Research Essay
Purpose
Your introduction has three main purposes:
1) introduce the context of the argument
2) Introduce any key terms or vocabulary needed to understand
the argument.
3) Introduce the scope of the argument
Each of these points can literally be a short paragraph, if that
makes it easier for you.
Context
Here you would provide details with which to understand
“where is this argument coming from?”
The type of information given depends on:

The general topic perspective taken (economic, educational,
environmental, social, technological, etc)
The historical factors that may be required
The academic background in which this conversation is taking
place.
Only say what needs to be said. If you don’t know what is
important and you find yourself making stuff up, go back to the
body of the essay and make notes.
Context continued…
Questions to help:
Why is this topic important? What is the impact of various
outcomes?
What important events happened before this discussion became
important?
What discussions are taking place in academic circles or in the
media around this topic?
Remember to double check your topic – keep your answers
relevant to the argument you have created.
Vocabulary
You may have used some key words in your argument that could
be difficult to understand for a non-specialist audience.
This does not include new English words you have learned
while researching.
It should not include words with a dictionary definition.
It does include words that have a particular definition within the
scope of this argument.
It does include key terms that may not be understood by non-
specialists.
You can start, “For this argument to be fully understood, the
following key terms should be explained.”

Scope
Tell us what is included in your argument.
Tell us what is not included in your argument.
End with a thesis statement. You can literally rewrite your
original research question as a statement:
“Should students complete teacher evaluation assessments?”
“This essay will explore whether students should complete
teacher evaluation assessments”.
Final notes
AVOID CLICHÉS
If any of you write something like “The discussion of (my
topic) has become a hot topic in recent years”….
…I will break lockdown, swim across the ocean, avoid the
authorities, travel by night, break into your apartment and
throttle you.
Kidding! I love you too much, but I’ll give you -5% for being
boring, and unoriginal, and annoying.
Your entire introduction should be no longer than 250 words.
Next period, I’ll answer any questions you have on Skype.
Send me an introduction by 5pm today if you want feedback.
Writing your conclusions
AS GP – Research Essay
Purpose
The conclusions have four main purposes:
1) Summarise the key points of your argument

2) Restate the judgement you have reached
3) Think about the implications of implementation /
recommendations
4) Consider further research needed
These points can literally be covered in 3 short paragraphs, if
that makes it easier for you.
Summary + Judgement
Your summaries should be no more than 3-4 sentences.
“We have considered (these perspectives). We have found that
…. (This perspective) is considerably stronger because …”
Make sure your summary sentences are clear grammatically.
Often in your summaries, your sentences become quite long,
and the compound constructions become a little blurry because
of the grammar. It is better to keep your sentences simple, than
to overburden the grammar with complex thoughts.
Remember – a summary is a distillation of what has already
been said. These are the lasting thoughts you want your reader
to leave with, and they should be simple enough to remember.
Summary + Judgement continued…
Take a minute to look at the judgement you have written.
Make sure it is clear and concise. Think about adding
“persuasion” to the statement. You can do this in much the
same way as you did with empathy:
Word choices
A simple phrase, “It is easy to be persuaded by such a
perspective when you consider …”
Consider returning to your Perspective 3 and weaving some
“persuasion” into this part as well. Do not repeat the same
grammatical structures!!!

Implications of implementation/ recommendations
Think about the ways in which your chosen perspective would
need to be implemented.
If there are some negative sides or difficulties that might arise
because of the perspective, think about ways to mitigate
(prevent) these things from happening. You do not have to go
into great detail here, but make general suggestions. They
could be explored in the “further research” part.
Further research
Considerations for further research largely stem from:
Impact of the chosen perspective
Implications for implementation
Again, please avoid clichés!
Your conclusions should be no more than 250 words.
In second period today, we will go through this together on
Skype and discuss any questions you might have.
Email me a paragraph today if you want feedback.
descriptive statistics [219 marks]
1a.
The following box-and-whisker plot shows the number of text
messages sent by students in a school on a particular day.
Find the value of the interquartile range.

1b. One student sent k text messages, where k > 11 . Given that
k is an outlier, find the least value of k.
2a.
A data set has n items. The sum of the items is 800 and the
mean is 20.
Find n.
2b.
The standard deviation of this data set is 3. Each value in the
set is multiplied by 10.
Write down the value of the new mean.
2c. Find the value of the new variance.
[2 marks]
[4 marks]
[2 marks]
[1 mark]
[3 marks]
3a.
A city hired 160 employees to work at a festival. The following
cumulative frequency curve shows the number of hours

employees
worked during the festival.
Find the median number of hours worked by the employees.
3b. Write down the number of employees who worked 50 hours
or less.
3c.
The city paid each of the employees £8 per hour for the first 40
hours worked, and £10 per hour for each hour they worked after
the first
40 hours.
Find the amount of money an employee earned for working 40
hours;
3d. Find the amount of money an employee earned for working
43 hours.
3e. Find the number of employees who earned £200 or less.
3f. Only 10 employees earned more than £ . Find the value of .k
k
[2 marks]
[1 mark]
[1 mark]
[3 marks]
[3 marks]

[4 marks]
4a.
Consider the following frequency table.
Write down the mode.
4b. Find the value of the range.
4c. Find the mean.
4d. Find the variance.
5a.
Ten students were surveyed about the number of hours, , they
spent browsing the Internet during week 1 of the school year.
The
results of the survey are given below.
Find the mean number of hours spent browsing the Internet.
x
10∑
i=1 xi = 252, σ = 5 and median = 27.
5b. During week 2, the students worked on a major project and
they each spent an additional five hours browsing the Internet.
For
week 2, write down
(i) the mean;

(ii) the standard deviation.
5c. During week 3 each student spent 5% less time browsing the
Internet than during week 1. For week 3, find
(i) the median;
(ii) the variance.
[1 mark]
[2 marks]
[2 marks]
[2 marks]
[2 marks]
[2 marks]
[6 marks]
5d.
During week 4, the survey was extended to all 200 students in
the school. The results are shown in the cumulative frequency
graph:
(i) Find the number of students who spent between 25 and 30
hours browsing the Internet.
(ii) Given that 10% of the students spent more than k hours

browsing the Internet, find the maximum value of .k
6a.
A school collects cans for recycling to raise money. Sam’s class
has 20 students.
The number of cans collected by each student in Sam’s class is
shown in the following stem and leaf diagram.
Find the median number of cans collected.
6b.
The following box-and-whisker plot also displays the number of
cans collected by students in Sam’s class.
(i) Write down the value of .
(ii) The interquartile range is 14. Find the value of .
a
b
[6 marks]
[2 marks]
[3 marks]
6c. Sam’s class collected 745 cans. They want an average of 40
cans per student.

How many more cans need to be collected to achieve this
target?
6d.
There are 80 students in the school.
The students raise $0.10 for each recycled can.
(i) Find the largest amount raised by a student in Sam’s class.
(ii) The following cumulative frequency curve shows the
amounts in dollars raised by all the students in the school. Find
the percentage of
students in the school who raised more money than anyone in
Sam’s class.
[3 marks]
[5 marks]
6e.
The mean number of cans collected is 39.4. The standard
deviation is 18.5.
Each student then collects 2 more cans.
(i) Write down the new mean.
(ii) Write down the new standard deviation.
7a.

There are 10 items in a data set. The sum of the items is 60.
Find the mean.
7b.
The variance of this data set is 3. Each value in the set is
multiplied by 4.
(i) Write down the value of the new mean.
(ii) Find the value of the new variance.
8a.
Let .
For the graph of f:
(i) write down the -intercept;
(ii) find the -intercept;
(iii) write down the equation of the horizontal asymptote.
f(x) = e0.5x − 2
y
x
[2 marks]
[2 marks]
[3 marks]

[4 marks]
8b. On the following grid, sketch the graph of , for
.
f
−4 ⩽ x ⩽ 4
9a.
The following box-and-whisker plot represents the examination
scores of a group of students.
Write down the median score.
The range of the scores is 47 marks, and the interquartile range
is 22 marks.
9b. Find the value of
(i) ;
(ii) .
c
d
[3 marks]
[1 mark]

[4 marks]
10a.
The following cumulative frequency graph shows the monthly
income, dollars, of families.
Find the median monthly income.
I 2000
10b. (i) Write down the number of families who have a
monthly income of dollars or less.
(ii) Find the number of families who have a monthly income
of more than dollars.
2000
4000
10c. The families live in two different types of housing. The
following table gives information about the number of families
living in
each type of housing and their monthly income .
Find the value of .
2000
I
p
10d. A family is chosen at random.

(i) Find the probability that this family lives in an apartment.
(ii) Find the probability that this family lives in an
apartment, given that its monthly income is greater than
dollars.4000
10e. Estimate the mean monthly income for families living in a
villa.
[2 marks]
[4 marks]
[2 marks]
[2 marks]
[2 marks]
11a.
The weights in grams of 80 rats are shown in the following
cumulative frequency diagram.
Do NOT write solutions on this page.
Write down the median weight of the rats.
11b. Find the percentage of rats that weigh 70 grams or less.
11c. The same data is presented in the following table.

Weights
grams
Frequency
.
w
0 ⩽ w ⩽ 30
30 < w ⩽ 60
60 < w ⩽ 90
90 < w ⩽ 120
p
45
q
5
p
[1 mark]
[3 marks]
[2 marks]
11d. The same data is presented in the following table.
Weights
grams

Frequency
Find the value of
.
w
0 ⩽ w ⩽ 30
30 < w ⩽ 60
60 < w ⩽ 90
90 < w ⩽ 120
p
45
q
5
q
11e. The same data is presented in the following table.
Weights
grams
Frequency
Use the values from the table to estimate the mean and standard
deviation of the weights.
w
0 ⩽ w ⩽ 30
30 < w ⩽ 60

60 < w ⩽ 90
90 < w ⩽ 120
p
45
q
5
11f. Assume that the weights of these rats are normally
part (c).
Find the percentage of rats that weigh 70 grams or less.
11g. Assume that the weights of these rats are normally
part (c).
A sample of five rats is chosen at random. Find the probability
that at most three rats weigh 70 grams or less.
12a.
Consider the following cumulative frequency table.
Find the value of
.p
12b. Find
(i) the mean;
(ii) the variance.
13. A random variable

is normally distributed with
and
.
Find the interquartile range of
.
X
μ = 150
σ = 10
X
[2 marks]
[3 marks]
[2 marks]
[3 marks]
[2 marks]
[4 marks]
[7 marks]
14a.
The weekly wages (in dollars) of 80 employees are displayed in
the cumulative frequency curve below.

(i) Write down the median weekly wage.
(ii) Find the interquartile range of the weekly wages.
14b. The box-and-whisker plot below displays the weekly wages
of the employees.
(i)
;
(ii)
;
(iii)
.
a
b
c
14c. Employees are paid
per hour.
Find the median number of hours worked per week.
$ 20
[4 marks]
[3 marks]
[3 marks]

14d. Employees are paid
per hour.
Find the number of employees who work more than
hours per week.
$20
25
15a.
The cumulative frequency curve below represents the marks
obtained by 100 students.
Find the median mark.
[5 marks]
[2 marks]
[3 marks]
16a.
The histogram below shows the time T seconds taken by 93
children to solve a puzzle.
The following is the frequency distribution for T .

(i) Write down the value of p and of q .
(ii) Write down the median class.
16b. A child is selected at random. Find the probability that the
child takes less than 95 seconds to solve the puzzle.
16c. Consider the class interval
.
(i) Write down the interval width.
(ii) Write down the mid-interval value.
45 ≤ T < 55
16d. Hence find an estimate for the
(i) mean;
(ii) standard deviation.
16e. John assumes that T is normally distributed and uses this to
estimate the probability that a child takes less than 95 seconds
to
solve the puzzle.
Find John’s estimate.
[3 marks]
[2 marks]

[2 marks]
[4 marks]
[2 marks]
17a.
A scientist has 100 female fish and 100 male fish. She measures
their lengths to the nearest cm. These are shown in
the following box and whisker diagrams.
Find the range of the lengths of all 200 fish.
17b. Four cumulative frequency graphs are shown below.
Which graph is the best representation of the lengths of the
female fish?
18a.
A standard die is rolled 36 times. The results are shown in the
following table.
Write down the standard deviation.
18b. Write down the median score.
18c. Find the interquartile range.
19a.
The following frequency distribution of marks has mean 4.5.

Find the value of x.
19b. Write down the standard deviation.
[3 marks]
[2 marks]
[2 marks]
[1 mark]
[3 marks]
[4 marks]
[2 marks]
20a.
The following table gives the examination grades for 120
students.
Find the value of
(i) p ;
(ii) q .
20b. Find the mean grade.
20c. Write down the standard deviation.
21a.

A fisherman catches 200 fish to sell. He measures the lengths, l
cm of these fish, and the results are shown in the
frequency table below.
Calculate an estimate for the standard deviation of the lengths
of the fish.
[4 marks]
[2 marks]
[1 mark]
[3 marks]
21b. A cumulative frequency diagram is given below for the
lengths of the fish.
(i) Estimate the interquartile range.
(ii) Given that
of the fish have a length more than
, find the value of k.
40%
k cm
21c. In order to sell the fish, the fisherman classifies them as
small, medium or large.

Small fish have a length less than
.
Medium fish have a length greater than or equal to
but less than
.
Large fish have a length greater than or equal to
.
Write down the probability that a fish is small.
20 cm
20 cm
60 cm
60 cm
21d. The cost of a small fish is
, a medium fish
, and a large fish
.
Copy and complete the following table, which gives a
probability distribution for the cost
.
$4
$10
$12
$X
21e. Find

.E(X)
[6 marks]
[2 marks]
[2 marks]
[2 marks]
22a.
The following diagram is a box and whisker plot for a set of
data.
The interquartile range is 20 and the range is 40.
Write down the median value.
22b. Find the value of
(i)
;
(ii)
.
a
b
23a.

Write down the median.
23c. Complete the frequency table below.
[1 mark]
[4 marks]
[1 mark]
[3 marks]
[2 marks]
Printed for American Creativity Academy
© International Baccalaureate Organization 2019
International Baccalaureate® - Baccalauréat International® -
Bachillerato Internacional®
24a.
A box contains 100 cards. Each card has a number between one
and six written on it. The following table shows the
frequencies for each number.
Calculate the value of k.
24b. Find

(i) the median;
(ii) the interquartile range.
25a.
In a school with 125 girls, each student is tested to see how
many sit-up exercises (sit-ups) she can do in one minute.
The results are given in the table below.
(i) Write down the value of p.
(ii) Find the value of q.
25b. Find the median number of sit-ups.
25c. Find the mean number of sit-ups.
[2 marks]
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[3 marks]
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[2 marks]
descriptive statistics [219 marks]

Cumulative frequency [160 marks]1a.Adam is a beekeeper

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