Internal Assessment Resource

Exemplar for internal assessment resource Mathematics 2.10A for Achievement Standard 91265

© Crown 2011

Exemplar for Internal Assessment Resource

Mathematics Level 2

Resource title: Teenagers and Caffeine

This exemplar supports assessment against:

Achievement Standard 91265

Conduct an experiment to investigate a situation using statistical methods

Student and grade boundary specific exemplar

The material has been gathered from student material specific to an A or B assessment resource.

Date version published by Ministry of Education

December 2011 To support internal assessment from 2012

For this task students are required to conduct an experiment investigating the effects of caffeine on teenagers. They need to pose an investigative question and conduct an experiment using statistical methods to investigate their selected situation.


© Crown 2011

Grade Boundary: Low Excellence

1. For Excellence a student must conduct an experiment to investigate a situation using statistical methods, with statistical insight. Statistical and contextual knowledge must be integrated throughout the investigation process; this may involve reflecting about the process or considering other relevant variables. The student has integrated statistical and contextual knowledge throughout the investigation process. For a more secure Excellence the research needs to be more clearly linked to the experiment. For example, the student could develop the comments on the time frame that caffeine can affect the body so that there is a clearer link to the experiment, and also link the research on how much caffeine will affect a person’s heart rate.

The purpose of my investigation is to see if time the consumption of caffeine through an energy drink affects a student’s heart rate Question: Is there any difference in a student’s heart rate after resting and drinking a 330ml can of V containing caffeine? I looked on Wikipedia and found that caffeine does increase heart rate for a limited time. This increase can last for a short or long time depending on the individual. For my experiment I will survey a class of 30 year 10 students. They will need to have a piece of blank paper and a pen. The variables will be heart rate after resting and the heart rate after consuming a 330ml can of V containing caffeine. Every student will rest for 5 minutes. I will then ask each student to take their pulse for 30 seconds, double it and record it. I will show the student how to take their pulse in their wrist and will count the 30 second time period. Once they have recorded their result I will then give each student a can of V (which contains caffeine) and ask them to drink the can of V containing caffeine allowing them 2 minutes to do it. I will then wait 15 minutes and then ask the students to take their pulse again for 30 seconds, double it and record it. It is important during this time that the students are not active as this could also cause an increase in heart rate so during this time I will require the students to do some silent reading. I chose 15 minutes because my research suggested that caffeine affected people differently and by different times. However, after approximately 15 minutes the effects of the caffeine on the heart rate will begin to show. For each student I will allocate a number from 1-30 so they won’t be identified and shouldn’t feel any peer pressure about their own individual heart rate. Other considerations: 1. I have chosen a 15 minute interval because caffeine is water soluble and therefore

is absorbed quickly into the persons system and therefore the affects upon heart rate will usually start to show.

2. Most student consume energy drinks so it is of interest to them to see what effects this may be having on their own heart rates.

I think the heart rate initially will be lower than the heart rate after the consumption of a can of V containing caffeine because based on my own experience my heart rate increases when I consume a caffeinated drink. For this experiment I will investigate if there is a difference in a student’s heart rate after consuming caffeinated drink. To do this I am going to take each individual student’s results immediately after they have recorded their heart rate (at rest) away from the heart rate after consuming a can of V containing caffeine by the same student. Data from the class: Student Heart rate after

5 mins resting Heart rate after can of V has been consumed (15 mins)

Difference in heart rate

1 72 84 12 2 68 82 12 3 82 96 14 4 66 74 8 5 74 78 4

Student 1: Low Excellence

6 72 74 2 7 62 76 14 8 74 76 2 9 76 78 2 10 72 76 4 11 68 76 8 12 88 92 4 13 66 70 4 14 70 72 2 15 74 76 2 16 74 78 4 17 76 80 4 18 72 82 10 19 78 84 6 20 68 86 18 21 70 82 12 22 76 78 2 23 82 96 14 24 84 90 6 25 76 80 4 26 62 64 2 27 76 78 2 28 74 78 4 29 76 82 6 30 72 78 6

Mean heart rate after 5 minutes resting = 73.33 (2dp) Standard deviation after 5 minutes of resting = 5.85 (2dp) Mean heart rate 15 mins after can of V has been consumed = 79.80 (2dp) Standard deviation 15 mins after can of V has been consumed = 6.78 (2dp) Initially, the mean heart rate in the year 10 class was 73.33 beats per minute but after consuming the can of V the mean heart rate had increased to 79.80 beats per minute. There was more variation in the heart rates after the consumption of the can of V (spread about the mean after consumption of a can of V containing caffeine is more than at rest). The box and whisker plot also shows there is more spread in the heart rates after the consumption of the can of V and less spread for the middle 50%, than when the student was resting.

60 70 80 90

Before Caffeine

After Caffeine

Heart Rate

Statistics for the difference in heart rates (Heart rate after consumption of caffeinated drink – heart rate after resting). Min 2 LQ 2 Median 4 UQ 10 Max 18 Range 16

Difference in number of heart beats per minute (after caffeine – before caffeine)

Looking at the box and whisker plot the range in the differences in heart rates was 16. The largest increase was 18. The median of 4 heart beats per minute and a lowest value of 2 heart beats per minute shows that there is very little spread in

the bottom 50%. Dot plot of Difference in number of heart beats per minute (after caffeine – before caffeine)

The difference in the heart rates varied with the most common difference being 2 and 4 heart beats per minute. All of the class increased their heart rate after consuming a can of V. There was 1 student whose heart rate increased by almost a quarter of their resting heart rate after consuming the can of V.

The arrow graph shows that every person in the experiment increased their heart rate after consuming a can of V. It does not clearly show that people with a slower heart rate when resting also had a slower heart rate after consuming the caffeinated drink. For example two students had a resting heart rate of 62 beats per minute but after the consumption of V one student increased to 64 while the other student increased to 76 heart beats per minute. Looking at the raw data the largest difference in the heart rate after consuming the caffeinated drink was 18 and this corresponds to the point (68,

86). The next largest difference was 14 and this corresponds to the points (82, 96), (62, 76) and (82, 96). The aim of my investigation was to see if there was any difference in heart rate after consuming a caffeinated drink (a can of V). The results I gathered show that this is the case as all the students in the class had an increase in their heart rates after consuming the caffeinated drink. This has been graphically shown in the scatter plot. The dotted line would represent the students whose heart rate remained the same. All the students are above this line because their heart rates all increased. From the reading I did, I learnt that the amount of caffeine consumed will affect heart rates. It will also affect how long the affects last i.e the more caffeine taken the longer the effects can last. However, based on numerous experiments conducted around the world, caffeine does affect heart rate. As all of the year 10 students had an increase in heart rate I can conclude that caffeine is likely to increase a person’s heart rate. As a follow up, I could investigate the effect of dose on the body’s response to caffeine to see how much caffeine is required to increase a student’s heart rate. To do this I could take different groups of students and get each group to drink different amounts of caffeinated drink. For example, students could drink 100ml, 150ml, 200ml, 250ml or 300ml of the drink. I would also have a control group who would not drink and caffeinated drink. For example caffeine-free drink could serve as the control if it is consumed in equal amounts to the caffeinated variety.


© Crown 2011

Grade Boundary: High Merit

2. For Merit a student must conduct an experiment to investigate a situation using statistical methods, with justification. This involves linking components of the process to the context, explaining relevant considerations in the investigation and supporting findings with statements that refer to evidence gained from the experiment.

The student has linked components of the investigation process to the context.

For the award of Excellence the student needs to provide some reflection on the experimental process and more evidence of the contextual knowledge.

Question: Is there any difference in a student’s heart rate after resting and drinking a 330ml can of V containing caffeine? I looked on Wikipedia and found that caffeine does increase heart rate for a limited time. This increase can last for a short or long time depending on the individual. For my experiment I will survey a class of 30 year 10 students. The variables will be heart rate after resting and the heart rate after consuming a 330ml can of V containing caffeine. Every student will rest for 5 minutes. I will then ask each student to take their pulse for 30 seconds, double it and record it. Once they have recorded their result I will then give each student a can of V (which contains caffeine) and ask them to drink the can of V containing caffeine giving them 2 minutes to do it. I will wait 15 minutes as research suggests it takes approximately 15 minutes for the caffeine to take effect. It is important that students do not do anything once they have consumed the can of V containing caffeine as this could affect the experimental results. I shall then ask the students to take their pulse again for 30 seconds, double it and record it. Each student will be allocated a number from 1 – 30 so they won’t be identified. I choose 15 minutes because my research suggested that caffeine affected people differently and by different times. I think that heart rate initially will be lower than heart rate after the consumption of a can of V containing caffeine because based on my own experience my heart rate increases when I consume a caffeinated drink. For this experiment I will investigating if there is a difference in a student’s heart rate after consuming a caffeinated drink. To do this I will take each individual students results immediately after they have recorded their heart rate (at rest) away from the heart rate after consuming a can of V containing caffeine by the same student. Data from the class: Student Heart rate after

5 mins resting Heart rate after 15 mins of caffeinated drink taken


1 72 84 12 2 68 82 12 3 82 96 14 4 66 74 8 5 74 78 4 6 72 74 2 7 62 76 14 8 74 76 2 9 76 78 2 10 72 76 4 11 68 76 8 12 88 92 4 13 66 70 4 14 70 72 2 15 74 76 2 16 74 78 4 17 76 80 4 18 72 82 10 19 78 84 6 20 68 86 18

Student 2: High Merit

21 70 82 12 22 76 78 2 23 82 96 14 24 84 90 6 25 76 80 4 26 62 64 2 27 76 78 2 28 74 78 4 29 76 82 6 30 72 78 6

Mean heart rate after 5 minutes resting = 73.33 (2dp) Standard deviation after 5 minutes of resting = 5.85 (2dp) Mean heart rate 15 mins after caffeinated drink consumed = 79.86 (2dp) Standard deviation 15 mins after caffeinated drink consumed = 7.04 (2dp) At rest the heart rate of the student was 77.33 beats per minute. However, after consuming the can of V the mean heart rate was 79.80 beats per minute for students in the year 10 class. The standard deviation after consuming a can of V was higher than the standard deviation at resting. This shows there was more variation in the heart rates after the consumption of V than at rest.

Before caffeine

After caffeine

60 70 80 90

Heart rate The box and whisker plot also shows there is more overall spread but a smaller spread in the middles 50% for the heart rates after the consumption of the can of V containing caffeine. The box and whisker for the heart rates after the consumption of a can of V containing caffeine is further along the scale than the box and whisker for the heart rates when resting which shows that the students heart rates increase with caffeine. Statistics for the difference in heart rates (Heart rate after consumption of caffeinated drink – heart rate after 5 minutes resting). Min 2 LQ 2 Median 4 UQ 10 Max 18 Range 16 Difference in number of heart beats (Heart rate after caffeine consumption - initial)

Looking at the box and whisker plot the range in the differences in heart rates was 16 and the

largest increase was 18. The median of 4 and a lowest value of 2 shows that there is very little spread in the bottom 50%. Dot plot of Difference in number of heart beats (Heart rate after caffeine consumption - initial)

The difference in the heart rates varied with the most common difference being 2 and 4. All of the class increased their heart rate after consuming a can of V. There was only 1 student whose heart rate increased by almost a quarter of their resting heart rate after consuming the can of V.

Heart rate at start vs Heart rate after caffeinated drink consumed

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Heart rate at start

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I chose to do a scatter plot to see if there is any relationship between student’s heart rate a rest and students heart rate after consuming a can of V. The scatter graph is not as clear as I had hoped because it only shows 24 points. This is because some of the points are repeated, for example (76, 78) is repeated twice. The scatter plot shows a positive relationship. The people that had a slower heart rate at rest mostly had a slower heart rate after drinking the can of V containing caffeine. The aim of my investigation was to see if there was any difference in heart rates once caffeine was consumed. From the results I gathered it showed that this is the case as all the students in the class had an increase in heart rate after consuming caffeine can of V containing caffeine. The mean difference in heart rate from resting to after consuming a can of V was an increase of 4 beats per minute. From the reading that I did I found that caffeine can affect heart rates over a varying time but based on the results of a experiments it usually starts to have an effect after approximately 15 minutes but can last for over an hour. My results mirror this experiment so I am confident that caffeine will increase a student’s heart rate.


© Crown 2011

Grade Boundary: Low Merit

3. For Merit a student must conduct an experiment to investigate a situation using statistical methods, with justification. This involves linking components of the process to the context, explaining relevant considerations in the investigation and supporting findings with statements that refer to evidence gained from the experiment.

The student has linked components of the investigation process to the context. For a more secure Merit, there needs to be more detailed explanations of some of the considerations in the investigations.

Question: is there any difference in a student’s heart rate after drinking a 330ml can of V containing caffeine? I looked on Wikipedia and found that caffeine does increase heart rate for a limited time. For my experiment I will survey a class of 30 year 10 students. The variables will be heart rate after resting and the heart rate after consuming a 330ml can of V containing caffeine. Every student will rest for 5 minutes. I will then ask each student to take their pulse for 30 seconds, double it and record it. I will show the students how to take their pulse from their wrist. Once they have recorded their result I will then give each student a can of V (which contains caffeine) and ask them to drink the can of V containing caffeine giving them 2 minutes to do it. I will wait 15 minutes and then ask the students to take their pulse again for 30 seconds, double it and record it. Each student will be allocated a number from 1 – 30 so they won’t be identified I will then compare the heart rate before the can of V containing caffeine is consumed and the heart rate after the can of V containing caffeine has been consumed to see if there is any difference. For this experiment I plan to investigate if there is a difference in a student’s heart rate after consuming caffeinated drink. To do this I will to take the individual students heart rates immediately after they have recorded their heart rate (at rest) and subtract this from their heart rate after they have consumed the can of V containing caffeine. Data from the class: Student Heart rate after

5 mins resting Heart rate after can of V has been consumed


1 72 84 12 2 68 82 12 3 82 96 14 4 66 74 8 5 74 78 4 6 72 74 2 7 62 76 14 8 74 76 2 9 76 78 2 10 72 76 4 11 68 76 8 12 88 92 4 13 66 70 4 14 70 72 2 15 74 76 2 16 74 78 4 17 76 80 4 18 72 82 10 19 78 84 6 20 68 86 18 21 70 82 12 22 76 78 2 23 82 96 14 24 84 90 6

Student 3: Low Merit

25 76 80 4 26 62 64 2 27 76 78 2 28 74 78 4 29 76 82 6 30 72 78 6

No students heart rate was slower after consuming the can of V containing caffeine. The most common differences in heart rate were 2 and 4.

Mean heart rate after 5 minutes resting = 73.33 (2dp) Standard deviation after 5 minutes of resting = 5.85 (2dp) Mean heart rate after consumption of a can of V containing caffeine = 79.86 (2dp) Standard deviation after consumption of a can of V containing caffeine = 7.04 (2dp) At the start the average heart rate was 73.33 beats per minute and the average after 5 minutes was 79.80 beat per minute which shows that the student’s heart rates increased.

Before caffeine

After caffeine

60 70 80 90

Heart rate There was more variation in the heart rates after the consumption of the can of V containing caffeine, than in heart rates initially. The box and whisker plot also shows there is more overall spread but a smaller spread in the middles 50% for the heart rates after the consumption of the can of V containing caffeine than for the heart rates before the caffeine was consumed. Statistics for the difference in heart rates (Heart rate after consumption of caffeinated drink – heart rate after 5 minutes resting). Min 2 LQ 2 Median 4 UQ 10 Max 18 Range 16

Difference in in number of heart beats per minute (after caffeine – before caffeine)

Dot plot of Difference in number of heart beats per minute (after caffeine – before caffeine)

For the students in the year 10 class the smallest difference in heart rate was 2 and the largest difference was 18 as shown on the dot plot. The box and whisker plot shows a range of 16 indicating that there was quite a variation in the change of student’s heart rates from the start to after drinking the can of V with caffeine present.

Heart rate at start vs Heart rate after caffeinated drink consumed

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Heart rate at start

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The scatter graph is not very clear because it only shows 24 points. This is because some of the points are repeated, for example (76, 78) is repeated twice. The scatter plot shows a positive relationship. The people that had a slower heart rate at the beginning mostly had a slower heart rate after drinking the can of V containing caffeine.

My investigation was to see if there was any difference in heart rates after consuming a can of V containing caffeine. From the results I gathered it showed that this is the case as all the students in the class had an increase in heart rate after consuming a can of V containing caffeine.


© Crown 2011

Grade Boundary: High Achieved

4. To Achieve this standard a student must conduct and experiment to investigate a situation using statistical measure. This involves showing evidence of using each component of the investigation process in conducting the experiment. The student has used each component of the investigation process. For the award of Merit the discussion needs to more clearly linked to the context.

Question: Does drinking a 330ml can of V containing caffeine increase a student’s heart rate? In my experiment I will survey a class of 30 year 10 students. They will need to have a piece of blank paper and a pen. I will ask each student to rest for 5 minutes. The students will then be asked to take their pulse for 30 seconds, double it and record it. I will then give each student a can of V (which contains caffeine) and ask them to drink the can of V giving them 2 minutes to do it. I will wait 15 minutes and then ask the students to take their pulse again for 30 seconds, double it and record it. I will then compare the heart rate before the can of V is consumed and the heart rate after the can of V has been consumed to see if there is any difference. I want to see if there is any difference in a student’s heart rate after consuming caffeinated drink so I am going to find the difference between the resting heart rate and heart rate after caffeinated drink has been consumed. Data from the class: Student Heart rate after

5 minutes resting

Heart rate after can of V has been consumed


1 72 84 12 2 68 82 12 3 82 96 14 4 66 74 8 5 74 78 4 6 72 74 2 7 62 76 14 8 74 76 2 9 76 78 2 10 72 76 4 11 68 76 8 12 88 92 4 13 66 70 4 14 70 72 2 15 74 76 2 16 74 78 4 17 76 80 4 18 72 82 10 19 78 84 6 20 68 86 18 21 70 82 12 22 76 78 2 23 82 96 14 24 84 90 6 25 76 80 4 26 62 64 2 27 76 78 2 28 74 78 4 29 76 82 6 30 72 78 6

No students heart rate was slower after consuming the can of V.

Student 4: High Achieved

The most common differences in heart rate were 2 and 4. Mean heart rate after 5 minutes resting = 73.33 (2dp) Standard deviation after 5 minutes of resting = 5.85 (2dp) Mean heart rate after consumption of a caffeinated drink = 79.86 (2dp) Standard deviation after consumption of a caffeinated drink = 7.04 (2dp) At the start the average heart rate was 73.33 beats per minute and the average after 4 minutes was 79.80 beat per minute which shows that the student’s heart rates increased.

Statistics for the difference in heart rates (Heart rate after consumption of caffeinated drink – heart rate after 5 minutes resting). Min 2 LQ 2 Median 4 UQ 10 Max 18 Range 16

Box and whisker graph of difference in heart rates. 0 3 6 9 12 15 18 21 24 Dot plot of difference in heart rates

For the students in the year 10 class the smallest difference in heart rate was 2 and the largest difference was 18 as shown on the dot plot. The box and whisker plot shows a range of 16 indicating that there was quite a change between the student’s heart rate at the start and after drinking the can of V.

The arrow graph shows that most students had a very small increase after drinking the can of V containing caffeine.

From my investigation I wanted to see if there was any difference in heart rates after the consumption of a can of V (caffeinated drink). Based on my experiment there is a difference as all the year 10 students in the class increased their heart rates after consuming a can of V.


© Crown 2011

Grade Boundary: Low Achieved

5. To Achieve this standard a student must conduct and experiment to investigate a situation using statistical measure. This involves showing evidence of using each component of the investigation process in conducting the experiment. The student has posed an investigative question, planned and conducted the experiment and made a conclusion. The student has selected appropriate displays and measures and there is some discussion of the displays and measures. For a more secure Achieved there needs to be more discussion of the displays and measures.

Question: Does drinking a caffeinated drink increase your heart rate? In my experiment I will be using the energy drink V which contains caffeine. I will survey a class of 30 year 10 students. Each student will need a piece of paper and a pen. I will get each student to rest for 5 minutes. The students will then be asked to take their pulse for 30 seconds, double it and record it. I will give each student 2 minutes to drink a can of V and wait 15 minutes before asking the students to take their pulse again for 30 seconds, double it and record it. I will work out the difference in the heart rates before and after consuming caffeine. I want to see if there is any difference in a student’s heart rate after consuming caffeine.

Data from the class: Student Heart rate after

5 minutes of resting

Heart rate after energy drink consumed

Difference in heart rates

1 72 84 12 2 68 82 12 3 82 96 14 4 66 74 8 5 74 78 4 6 72 74 2 7 62 76 14 8 74 76 2 9 76 78 2 10 72 76 4 11 68 76 8 12 88 92 4 13 66 70 4 14 70 72 2 15 74 76 2 16 74 78 4 17 76 80 4 18 72 82 10 19 78 84 6 20 68 86 18 21 70 82 12 22 76 78 2 23 82 96 14 24 84 90 6 25 76 80 4 26 62 64 2 27 76 78 2 28 74 78 4 29 76 82 6 30 72 78 6

No student’s heart rate was slower after consuming the energy drink. In the difference column the most common difference is 2.

Student 5: Low Achieved

Mean after 5 minutes resting = 73.33 (2dp) Standard deviation after 5 minutes of resting = 5.85 (2dp) Mean after consumption of caffeine = 79.80 (2dp) Standard deviation after consumption caffeine = 7.04 (2dp) After the class had rested the average heart rate was 73.33 beats per minute and the average after consuming the energy drink was 79.80 beat per minute which shows that the students heart rate increased. Statistics for difference in heart rates (Heart rate after consumption of energy drink – heart rate after 5 minutes resting). Min 2 LQ 2 Median 4 UQ 10 Max 18 Range 16

Box and whisker graph of difference in heart rates 0 3 6 9 12 15 18 21 24 Dot plot of difference in heart rates

In the box plot the range is 16 which indicates a reasonable difference in heart rates between the resting phase and the after the consumption of the energy drink. The largest difference in heart rates was 18. There were eight students whose heart rates increased by 2 beats per minute and eight students whose heart rate

increased by 4 beats per minute.

Students in my experiment showed that their heart rates were higher after consuming an energy drink than they were at the start so the consumption of the energy drink did increase the student s heart rates.


© Crown 2011

Grade Boundary: High Not Achieved

6. To Achieve this standard a student must conduct and experiment to investigate a situation using statistical measure. This involves showing evidence of using each component of the investigation process in conducting the experiment. There is some evidence for planning the experiment but the variable has not been identified. The student has conducted an experiment and the displays and measures that have been selected are appropriate. In order to Achieve there needs to be more detail in the experiment plan and further discussion of the displays and measures.

Question: What kind of effect does caffeine have on teenagers heart rate?

For my experiment I am going survey a class of 30 year 10 students. I will ask each student to rest for 5 minutes. The students will then take their pulse for 30 seconds, double it and record it. I will ask each student to drink a can of caffeinated energy drink. Once all the students have finished I will get them to take their pulse for 30 seconds, double it and record the result. Data from the class:

Student Heart rate after 5 minutes resting

Heart rate after can of V

Difference in heart rates

1 72 84 12 2 68 82 12 3 82 96 14 4 66 74 8 5 74 78 4 6 72 74 2 7 62 76 14 8 74 76 2 9 76 78 2 10 72 76 4 11 68 76 8 12 88 92 4 13 66 70 4 14 70 72 2 15 74 76 2 16 74 78 4 17 76 80 4 18 72 82 10 19 78 84 6 20 68 86 18 21 70 82 12 22 76 78 2 23 82 96 14 24 84 90 6 25 76 80 4 26 62 64 2 27 76 78 2 28 74 78 4 29 76 82 6 30 72 78 6

Mean after 5 minutes resting = 73.33 (2dp) Mean after drinking a can of a caffeinated drink = 79.80 (2dp) No student had a slower heart rate after drinking the can of a caffeinated drink as shown by the difference in the two heart rates.

Student 6: High Not Achieved

Statistics from the experiment Min 2 LQ 2 Median 4 UQ 10 Max 18 Range 16

Box and whisker graph of difference in heart rates. 0 3 6 9 12 15 18 21 24 Dot plot of difference in heart rates

Box plot the range is only 16. The largest difference of heart rates was 18. Students in my experiment showed that their heart rates did increase after consuming a can of a caffeinated drink. So caffeine did affect their heart rates.

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