IB SL Mathematics International Assessment
Is there a correlation between gender and the change in
heart rate before and after physical activity in young adults
and middle-aged adults?
Word count: 6538
Date of Submission: November 13th, 2020
1
,Table of Contents
I. INTRODUCTION ..................................................................................................................................... 3
II. THEORY ................................................................................................................................................. 3
III. METHOD .............................................................................................................................................. 3
1. COLLECTION OF DATA ....................................................................................................................... 3
2. CALCULATION OF HEART RATE CHANGE ........................................................................................... 4
3. CALCULATION OF MEAN HEART RATE CHANGE ............................................................................... 5
4. CONVERSION OF RESULTS FROM DISCRETE TO CONTINUOUS DATA .............................................. 6
5. CALCULATION OF FREQUENCY DENSITY FOR EACH PARTICIPANT ................................................... 6
6. FIRST PRESENTATION OF DATA – HISTOGRAMS .............................................................................. 7
7. CONVERSION OF RESULTS FROM CONTINUOUS BACK TO DISCRETE DATA .................................... 9
8. FINDING X2 TEST STATISTIC ............................................................................................................. 10
9. SECOND PRESENTATION OF DATA – SCATTER GRAPH AND REGRESSION LINES ........................... 11
10. REPRESENTATION OF DATA – PRODUCT MOMENT CORRELATION COEFFICIENT (PMCC) .......... 14
IV. REFLECTION ....................................................................................................................................... 16
V. CONCLUSION ...................................................................................................................................... 17
VI. BIBLIOGRAPHY .................................................................................................................................. 18
2
, I. Introduction
This investigation aims to find out whether or not there is a correlation between gender and the
change in heart rate before and after physical activity in young adults and middle-aged adults. I decided
to select the topic of fitness and combine it with Mathematics, as fitness is an area I am passionate
and fascinated about, since I find it very enjoyable and it is also well incorporated in my daily life. Ever
since I was little, I was always involved in sports, such as football, hockey, swimming and gym, meaning
sports and fitness surrounded me throughout my childhood and life, which I think is one of the reasons
why I enjoy it so much today. Prior to choosing this question, I knew from my Biology knowledge, that
biologically, males are generally composed of more muscle mass than females - with the exceptions
that certain females may exercise more than men, therefore, are composed of more muscle mass.
Thus, I was very interested and intrigued in further investigating, whether or not, the amount of muscle
mass a person has, impacts the amount by which our heart rate increases after physical activity.
Therefore, I came to the realisation that this could be a great opportunity for me to explore my
curiosity, by gathering my own data and bringing forward my own procedure, which led me to come
up with my question. My null hypothesis (H0) is that there is no correlation between gender and change
in heart rate, and my alternative hypothesis (H1) is that there is a correlation between gender and the
change in heart rate. By the end of this investigation, I will be able to come to a conclusion and prove
or disprove my H0. From my results, I would personally expect the females’ mean heart rate to be
higher than the males’ and I would also expect the overall 16-25 age group to have a lower mean heart
rate change compared to the 45-54 age group. In order to reach a conclusion, I will be using plenty of
Mathematical skills and methods, which include: calculating the mean heart rate change of each
participant throughout the 4 weeks, presenting the mean heart rate change of each participant in
histograms and calculating the X2 test statistic of the overall data – both genders and age groups
combined. Additionally, I will also be using scatter graphs to present the relationship between the
mean heart rate change and height for each gender, along with their regression line and I will be
calculating Pearson’s Correlation Coefficient for each gender to find out how strongly positive or
negative the relationship between mean heart rate change and height is.
II. Theory
Heart rate is the speed at which our heart beats, and it is measured in heart beats per minute (bpm).
(Mandal, 2019) When we exercise, our heart rate increases from our resting heart rate, and the more
vigorous the exercise, the higher the rate at which our heart rate increases. This rate can alter
depending on several different factors including; amount of exercise, emotions, age, diet and water
intake. For example, if a participant has a lot of adrenaline within their body or feels anxious, their
resting heart rate will already be higher than their usual resting heart rate, and the amount by which
their heart rate increases, would be larger. Similarly, if a participant ate or drank minutes before
exercising, their resting heart rate would be higher than their usual one and their change in heart rate
would also increase by a bigger amount, due to changes in blood pressure. Therefore, it is important
to take in consideration the fact that several different factors can affect the participants’ change in
heart rate – not only the jumping jacks, which can skew the final results and limit their reliability.
III. Method
1. Collection of Data
In order to carry out my investigation, I have gathered 4 females and 4 males under the “young adults”
category, of ages 16-25, as well as 3 females and 3 males under the “middle-aged adults” category, of
ages 45-54. The reason I decided to gather 8 young adults and 6 middle-aged adults is, in order to have
3
Is there a correlation between gender and the change in
heart rate before and after physical activity in young adults
and middle-aged adults?
Word count: 6538
Date of Submission: November 13th, 2020
1
,Table of Contents
I. INTRODUCTION ..................................................................................................................................... 3
II. THEORY ................................................................................................................................................. 3
III. METHOD .............................................................................................................................................. 3
1. COLLECTION OF DATA ....................................................................................................................... 3
2. CALCULATION OF HEART RATE CHANGE ........................................................................................... 4
3. CALCULATION OF MEAN HEART RATE CHANGE ............................................................................... 5
4. CONVERSION OF RESULTS FROM DISCRETE TO CONTINUOUS DATA .............................................. 6
5. CALCULATION OF FREQUENCY DENSITY FOR EACH PARTICIPANT ................................................... 6
6. FIRST PRESENTATION OF DATA – HISTOGRAMS .............................................................................. 7
7. CONVERSION OF RESULTS FROM CONTINUOUS BACK TO DISCRETE DATA .................................... 9
8. FINDING X2 TEST STATISTIC ............................................................................................................. 10
9. SECOND PRESENTATION OF DATA – SCATTER GRAPH AND REGRESSION LINES ........................... 11
10. REPRESENTATION OF DATA – PRODUCT MOMENT CORRELATION COEFFICIENT (PMCC) .......... 14
IV. REFLECTION ....................................................................................................................................... 16
V. CONCLUSION ...................................................................................................................................... 17
VI. BIBLIOGRAPHY .................................................................................................................................. 18
2
, I. Introduction
This investigation aims to find out whether or not there is a correlation between gender and the
change in heart rate before and after physical activity in young adults and middle-aged adults. I decided
to select the topic of fitness and combine it with Mathematics, as fitness is an area I am passionate
and fascinated about, since I find it very enjoyable and it is also well incorporated in my daily life. Ever
since I was little, I was always involved in sports, such as football, hockey, swimming and gym, meaning
sports and fitness surrounded me throughout my childhood and life, which I think is one of the reasons
why I enjoy it so much today. Prior to choosing this question, I knew from my Biology knowledge, that
biologically, males are generally composed of more muscle mass than females - with the exceptions
that certain females may exercise more than men, therefore, are composed of more muscle mass.
Thus, I was very interested and intrigued in further investigating, whether or not, the amount of muscle
mass a person has, impacts the amount by which our heart rate increases after physical activity.
Therefore, I came to the realisation that this could be a great opportunity for me to explore my
curiosity, by gathering my own data and bringing forward my own procedure, which led me to come
up with my question. My null hypothesis (H0) is that there is no correlation between gender and change
in heart rate, and my alternative hypothesis (H1) is that there is a correlation between gender and the
change in heart rate. By the end of this investigation, I will be able to come to a conclusion and prove
or disprove my H0. From my results, I would personally expect the females’ mean heart rate to be
higher than the males’ and I would also expect the overall 16-25 age group to have a lower mean heart
rate change compared to the 45-54 age group. In order to reach a conclusion, I will be using plenty of
Mathematical skills and methods, which include: calculating the mean heart rate change of each
participant throughout the 4 weeks, presenting the mean heart rate change of each participant in
histograms and calculating the X2 test statistic of the overall data – both genders and age groups
combined. Additionally, I will also be using scatter graphs to present the relationship between the
mean heart rate change and height for each gender, along with their regression line and I will be
calculating Pearson’s Correlation Coefficient for each gender to find out how strongly positive or
negative the relationship between mean heart rate change and height is.
II. Theory
Heart rate is the speed at which our heart beats, and it is measured in heart beats per minute (bpm).
(Mandal, 2019) When we exercise, our heart rate increases from our resting heart rate, and the more
vigorous the exercise, the higher the rate at which our heart rate increases. This rate can alter
depending on several different factors including; amount of exercise, emotions, age, diet and water
intake. For example, if a participant has a lot of adrenaline within their body or feels anxious, their
resting heart rate will already be higher than their usual resting heart rate, and the amount by which
their heart rate increases, would be larger. Similarly, if a participant ate or drank minutes before
exercising, their resting heart rate would be higher than their usual one and their change in heart rate
would also increase by a bigger amount, due to changes in blood pressure. Therefore, it is important
to take in consideration the fact that several different factors can affect the participants’ change in
heart rate – not only the jumping jacks, which can skew the final results and limit their reliability.
III. Method
1. Collection of Data
In order to carry out my investigation, I have gathered 4 females and 4 males under the “young adults”
category, of ages 16-25, as well as 3 females and 3 males under the “middle-aged adults” category, of
ages 45-54. The reason I decided to gather 8 young adults and 6 middle-aged adults is, in order to have
3
