Data Handling

In this piece of coursework I am going to test to see if my Hypothesis is correct. The aim of this investigation is to investigate the following hypothesis:

”The lower your BMI is the fitter you are so your mean resting pulse rate should be lower.“

Introduction

The data has been collected from three-year groups. Year 7, 9 and 11. The maths department has decided on these year groups, as there is two years in between each group. In years 7 and 9 the data was collected from sets A,B,C and D. Whereas year 11 the data was collected from all sets from A to F. The decision to only use A-D for years 7 and 9 was that it is more practical and some pupils from the lower sets are immature and may not take it seriously and this would obstruct the investigation. While in year 11 pupils are more grown up and act in a civilized manner.

The data had no results from girls as it is an all boys’ school in which the data was collected from. Each pupil was given a survey sheet. There was a few details that need to be filled in they were:

Do you have a medical condition? Yes / No
How old are you? Years and Months
Are you a member of a sports team? Yes / No
How many hours of sport do you do a week? Number of hours

Each class took their pulse rate 5 times and found the average of the 5 results. The mean was then recorded. Each Year group that was doing the investigation went outside and ran for 4 minutes. Then each minute each person recorded his pulse rate for approximately 15 minutes. Then from this data the maths teachers worked out how many minutes it took for each persons pulse rate to return to its mean resting rate. This was all recorded on the same survey sheet. There was a few more questions to be answered on the sheet which were:

What is your weight? (Kg)
What is you height? (m)

When measuring the weight it was done on electronic scales which are more accurate and precise. This was analysed by a maths teacher. When being weighed each person was told to remove their blazers and shoes, so there was no added weight.

From the weight and height the BMI can be produced which was done by the maths department and added to the data sheet. BMI is worked out by:

The BMI has many values which tell us if a person is underweight, Normal, overweight or obese for their height.

All the data collected from each year group was condensed into excel which made it easier to read and analyse. There may be some faults with the data collected because BMI is for adults. Muscle ways more than fat and so may reflect that some people are overweight however they may be just muscular. Medical condition has only been collected YES / NO this indicates to me that it is too vague. What is a medical condition? It covers a wide range of conditions. Another fault is how many hours of sport do you do? Does that contain P.E. lessons?

When we recorded are mean resting pulse rate as told before we recorded are pulse rate for 15 seconds and X4, we did this 5 times all together. Many factors can be analysed here, was some people not relaxed, was there any miss calculations or miss readings when taking their pulses or time-sing by 4.

PLAN

During this investigation I will:

Select the grids that I need to do to analyse my hypothesis. This is: Age – Year and BMI
Plot the data of the two grids on a box and whisker diagram.

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PLAN

During this investigation I will:

Select the grids that I need to do to analyse my hypothesis. This is: Age – Year and BMI
Plot the data of the two grids on a box and whisker diagram.
Analyse the data that is in the box and whisker diagrams.
Conclude the data analysis.
Then I shall introduce variables that have an affect on the hypothesis.
I shall plot this information on scatter graphs.
Analyse the data on the scatter graphs.
And finally conclude the investigation, analysing it and including all variables.

In my investigation I will be using results from 2 categories and all the information in them 2 categories will be used.

Analysing the Mode, Median and Mean

The mode, median and mean for mean resting rate varies for each BMI condition so I have placed the results in a table which is shown on the next page and is worked out by using a dotplot diagram.

The table indicates that the most common mean resting pulse rate is a lot lower the higher up the table you are i.e. Underweight – 54, Obese – 96. The table also shows the middle number which you can get from the box plot which is on further in the investigation. The mean shown is the average mean resting pulse rate in each BMI condition which once again increases as you go down the table. Having a BMI condition Underweight has a mode of 54, 60, 61, 62, because I am testing whether my hypothesis is correct the next BMI should have a higher mode, which it does and increases as you go down the table. Normal has a mode of 77, overweight has a mode of 83 and there were only six results for Obese so each result is equally as common.

The mean shows us the average mean resting pulse rate for each BMI condition rather than the most common resting pulse rate in each category. In order to calculate this I added all of the results collected for mean resting pulse rate in each individual BMI condition and divided it by the total amount of results in that individual BMI condition category. The mean for the mean return to resting rate for BMI condition Underweight is 61 which increase as you go down the table, Normal 71, Overweight 81, Obese 83. Once again this shows that my hypothesises is correct, showing that people who have a lower BMI are fitter as they have a lower mean resting rate i.e. Normal 18.6 – 25 has an average mean resting rate of 71.

I worked out the mean and mode by drawing a dotplot that indicates all the values to work out the mode and mean.

Box and Whisker Plots

A box and whisker plot is another way of showing the spread of collected data and statistics. The graph presents information in a simple form. It especially shows anomalous results. They are good when there is a large number of data to analyse, this is why it is a good way to analyse my data this way because the information I have is on a large scale and using this method is a quick and easy way to analyse the information selected. The diagram below indicates what a box and whisker diagram looks like:

The diagram shows the range, median and the quartiles. It is measured on a scale. By looking at my diagrams I drew my results from.

In my investigation I am measuring that if you are younger you are fitter and healthier and so your BMI should be below 25.

From the data on the boxplot above I can draw conclusions. On the box plot it firstly indicates whether my hypothesis is right or wrong. We can see the interquartile range, the upper quartile, the lower quartile, the median and it shows you the highest and lowest values.

By looking at the boxplot I can see if my hypothesis is right or wrong. The boxplot does show that my hypothesis is right because as the BMI condition increases (i.e. Underweight being the smallest and Obese being the largest) the mean resting pulse rate increased. The highest point increased, the lowest point increased. The median increased, the interquartile range increased.

The table below shows the various points that show whether my hypothesis is right.

As shown in the table you can see that as the BMI increases the mean resting pulse rate goes up. This is shown in every column of the table.

The table indicates clearly that as your BMI increases (go down the table – column 1) that your mean resting pulse rat goes up this suggest that the lower your BMI is the lower your mean resting pulse rate is so you are fitter which suggest that my hypothesis is correct.

Scatter graphs are a way of illustrating paired data or information about two related values. There are many examples which can be illustrated on a scatter graph such as Height and weight and rain and sunshine. The two related a values that I will be studying is in my hypothesis which is BMI and mean resting pulse rate. A line of best fit is drawn which passes through as many points as possible, this has roughly the same amount of points on each side of the line. The less scatter there is about the line of best fit the stronger the relationship is between the two variables. A scatter graph can be positive, negative or either has no correlation.

In my graph showing the BMI and mean resting pulse rate shows a small positive correlation. It shows that as the BMI goes up the mean resting pulse rate goes up which proves that my hypothesis is correct which indicates that fitter people have a lower BMI and lower mean resting pulse rate.

Conclusion

In my hypothesis I was trying to find out that the lower your BMI is the lower your mean resting pulse rate is so you are fitter. From the results in the boxplot and the scatter graph this is indicated correctly which suggests that my hypothesis is correct. I decided to analyse my data using a boxplot and a scatter graph as it indicated clearly the increase in mean resting pulse rate when BMI increased. I used a scatter graph as I had two sets of data : BMI and Mean resting pulse rate. The scatter graph conclusively showed that there was a slight correlation that had an R-value of 0.2926. Overall my hypothesis was proved correct however there are many different variables that could have also affected he result of a person being fitter with a lower BMI. I will investigate these variables in the next part of the investigation.

Analysing variables that affect the hypothesis.

3 variables which could effect the hypothesis is:

How old you are? – What year you are in?
How many hours of sport you do a week?
Return to resting rate?

I am now going to investigate the effect of these variables on my hypothesis. Firstly I am going to draw up some scatter graphs that will show two variables that can be easily analysed. I will then draw up a conclusion and finally write an overall conclusion for the whole investigation.

Firstly I am going to draw an overall scatter graph for the whole data. I will then draw up scatter graphs for each individual year group to see if age is a factor that affects my hypothesis.

The scatter graph above shows how the number of sports hours affects BMI. The graph shows virtually no correlation. The graph therefore indicates that my hypothesis may be affected by the number of hours doing sport a week. As BMI goes up the number of hours doing sport a week decreases. I am now going to see if the younger you are the fitter you are so the number of hours doing sport a week should be high with a low BMI.

affected the hypothesis, the age of someone and the number of hours of sport they do each week. The more hours of sport you do a week the fitter you should be so your BMI should be lower. This is indicated in Year 7, as there is a slight negative correlation, in Year 9 there is no correlation and in Year 11 as BMI increases the number of hours of sport a week also increases, so his suggest that my hypothesis is right. This therefore also indicates the younger you are the fitter you are as you have a low BMI and do more hours of sport.

Another factor which could affect how fit you are, is the time taken for your pulse rate to return to resting pulse rate.

year 7. In year 11 the positive correlation is 0.4512 which is less than year 7 but more than year 9. From the results shown it does show that as BMI increase time taken to return to resting rate increases but on the scatter graphs it does not seem that age affects it. Time taken to return to resting rate can affect my hypothesis as it can affect fitness. Therefore it would support my hypothesis as you increase the BMI your fitness decreases.

Conclusion

My investigation involved drawing boxplots and scatter graphs, and analysing the data produced from them results. The main theme was do analyse my hypothesis which was:

The lower your BMI is, the fitter you are, so your mean resting pulse rate should be lower.

In the investigation I was using data collected from a 4 minute run from Years 7, 9 and 11. In the boxplots my hypothesis is shown, as you increase your BMI your mean resting pulse rate goes up, each mean, mode and median was higher than the previous result. (Underweight = Median 64, Normal = Median 74) These results all support the hypothesis.

In order to prove or disprove my hypothesis I collected the data and drew a boxplot, which I could then analyse to test if my hypothesis is right, the results then were placed into a table for me to analyse further. I choose all the data to get a wide variety of results and to make the investigation more precise and accurate. The median, mode, mean, range, upper quartile, lower quartile, highest value and lowest values were recorded into tables for further analyse.

By looking at the values I could see that my hypothesis is strongly supported by the data. The average mean resting pulse rate for underweight was 64, normal was 74, overweight was 82 and obese was 82.5. This indicates my hypothesis was correct.

I then decided to investigate factors that could affect my hypothesis. Age, number of hours of sport per week and time to return to resting rate. The data was placed into scatter graphs which is easy to analyse two variables. The results all grouped together suggest that:

The younger you are the fitter you are because your BMI is lower, your mean resting pulse rate is lower and the time to return to resting rate is lower.

This data is shown in the scatter graphs and boxplot. If I was to do this investigation again I would have collected data from each person in all year groups ranging from year 7-11 and use all classes in each year group. The bigger sample would have made my results more accurate.

I would also experiment with different techniques to record my data to easily analyses it and compare it with the test I have done in this investigation. Also I would use more accurate data with more precise measuring instruments for example measuring height, use a ruler to the nearest millimetre instead of nearest centimetre. This would then improve precision and close to the true value. I would also do the investigation twice over 1 week an average the results. This would therefore increase the reliability which would make it more of a fair investigation.

By Matthew O’Hara