Maths Project - Statistics

During  maths class we were told to complete a statistics project. My group chose look at the relationship between the amount of hours you sleep according to the amount of exercise you do. 

Below is the completed project:

AN INVESTIGATION

INTO EXERCISE IN RELATION TO

SLEEP

By Hilary Gallagher, Keelan Glennane and Bríd O’Donnell

Introduction

We have decided to base our project on a comparison between the number of hours slept by any student and the number of hours spent exercising .

The aim of our project is to discover whether or not more exercise requires more sleep. We have also decided to view the statistics of male and female members of our school population that play sport, and see if this varies with age. As we all participate in sport on a daily basis, we were interested in answering this question and forming our own theory.

Method

In order to gather results, we created a survey which contains the following questions:

• What sport do you play daily?

• students were only given a single option for this question to gather a more specified set of results

• How many hours of sport do you play daily?
• How many hours sleep would you have per night?
• What age are you? In years

We decided to use a simple random sample from the population of our school. We achieved this by assigning a number to each form group from first to sixth year which gives us a total of 24 groups. These are the following assignations:

Number	Form Group		Number	Form Group
1	5a		13	4a
2	4d		14	1d
3	3c		15	6b
4	1a		16	5d
5	1b		17	2b
6	2c		18	3b
7	4c		19	2a
8	6a		20	3d
9	6d		21	4b
10	5c		22	2d
11	1c		23	5b
12	3a		24	4d

The method we used to generate random numbers on a calculator was:

1. We typed 24Ran# into a calculator and pressed equal five times
2. We discarded the decimal and chose only to use the whole number
3. We then paired the generated number with it’s assigned form group

The random numbers generated by calculator were:

19  = 2a

5    = 1b

9    = 6d

21  = 4b

17  = 2b

The total number of students surveyed was 94 students.

Graphs

Conclusion 

Age Pie Chart:

This pie chart displays that just under half of the sample we studied were aged 13. This statistic may result in our responses being biased as younger children in non exam years would have more free time to both exercise and sleep.

Sports Pie Chart:

This pie chart shows that most of the sample studied played rugby as their daily exercise. This proves that the sample studied would have been predominantly male. Out of all the students surveyed, all participated in at least a half hour of sports daily. We found this very interesting to know. As this was not a multiple choice question, students were forced to prioritise one exercise. We did this to limit the results to be collected. It is quite possible a percentage of the sample may play two different sports daily.

Time Spent Sleeping Pie Chart:

This pie chart shows that the most popular amount of time to be spent sleeping tended to be for 8 hours, in fact over a quarter of the sample, 27%, agreed this was how much they slept. The minority of the sample slept for 5 hours. We found this interesting because there was a wide variety in the amount of time spent sleeping, ranging from approximately 4% of the sample sleeping for 5 hours to the same percentage sleeping double that.

Time spent sleeping / time spent exercising Scatter Graph:

Unfortunately there was not as clear a correlation as anticipated between the number of hours spent sleeping and the number of hours spent exercising. We have guessed that this may be due to the fact that not enough exercise is carried out to have such a large impact on the body’s need for sleep. Or perhaps students do not feel they have time to spare to get extra hours of sleep if they have a high workload. These are the theories we have made. There appears to be no correlation between these two aspects.

Female Participation in Sport Bar Chart:

This chart shows that at a younger age, such as 13, there tends to be a high number of females participating in sport for a long period of time. The bar chart shows a decline in the length of time spent exercising between the ages of 14 and 16. Before carrying out our survey, we predicted this would be the case as a variety of statisics have shown that this is a popular age for females to quit sport. We believe this is because of females feeling extra time is required to study for the Junior Cert and so stop spending as much time exercising. The time spent exercising appears to increase again at the age of 17. We speculate that this is due to a rise in awareness about the benefits of exercise with health, however I feel this may be due to a few outliers in the sample at that age who would be more sporty than most girls their age.