I am going to test the three hypotheses by selecting a sample size of 300. I am going to select the 300 pupils randomly using a graphics calculator. The way I can do this is by using the random key on the calculator. The way we can use the random key is by clicking the key “rnd” which is short for random, and then inserting a bracket. In the bracket, we multiply 1 by the maximum number and then I click close bracket. For example, in year 7, there are 282 pupils, so I must click: “Rnd (1x282)”. Every time I click the “equal” key, a random number between 1 and 282 would appear. The pupils are all numbered and therefore, the number which appears would be the pupil which I would use to help me with my coursework.
I am going to use the method of stratified sampling which would allow me to choose my sample fairly without being biased. Stratified sampling means dividing a whole population into subgroups and choosing a sample size that reflects the properties of each group. This sampling method includes dividing the number of students into year groups and taking a sample size of which represents each year group.
I think that by the end of my investigation, my box plots would show that the height and weight of girls and boys in Year 7 would not have as much difference. However, the box plots for year 9 may show that the boys are “catching up” to the height and weight of girls, i.e. the boys in year 9 are taller and weightier than girls in year 9.
This table contains information about the number of students in the years 7, 9 and 11 from Mayfield Secondary School.
The first column in the table for Mayfield Secondary School shows the year groups 7, 9 and 11. Column 2 shows the number of boys in each year group. Column 3 shows the number of girls in each year group. Column 4 shows the number of students in each year group. I’ll be using this information to calculate my stratified sampling.
Here is the stratified table
This table shows the sample sizes of the years 7, 9 and 11. I have obtained the sample sizes by dividing the number of pupils in each year group by the overall total of people from the three years. I then multiplied the answer by the sample size of 300. For example, the number of people in year 7 is 151. I divided the number by overall total of 712. I then multiplied the answer by 300.
I used the method of stratified sampling to help me choose my sample size. The reason why I chose this method was because I felt that my results would be more representative if my sample size was in proportion to the original totals. I also felt that this way, I could keep my investigation from being biased. I thought that it wouldn’t be as reliable if I used the same sample size of boys and girls because the actual total of girls were higher than of boys.
For each year group, I am going to draw a stem and leaf diagram. I am going to use the stem and leaf diagrams to help me find the upper and lower quartiles and also the median, mode and lowest and highest values. A stem and leaf diagram would be appropriate in order to establish my findings through visualisation. By using the information I had found through drawing a stem and leaf diagram, I am also going to draw box plots. Box plots are helpful to represent data, for example height and weight. Both techniques of representing data would be appropriate to compare height and weight between the different genders.
I am going to draw two sets of tables in order to record my results. The tables will help me to look for patterns and would help me compare height and weight value between girls and boys. Finally, I would be drawing two scatter graphs. Scatter graphs are useful to find a relationship between height and weight. For example, whether there is a positive or negative correlation within the two variables.
I could have used a cumulative frequency graph but I feel that my sample size is too small to help me gain an accurate result. I am aware that I might face inaccuracy while plotting and drawing curves. I think that I would be able to come up with better results when drawing scatter graphs and stem and leaf diagrams.
Analysis
Stem and Leaf Diagrams
Key:
Leaf || Stem || Leaf
Means 131 <<< 1 || 13 || 0 >>> Means 130cm
Stem and Leaf diagram for Year 7 pupils:
This stem and leaf diagram shows the height of girls and boys in year 7. This diagram shows similarities between the height and weight of girls and boys in year 7. For example, there are 4 girls and also 4 boys who are in the 170cm boundary. There are 14 girls and 14 boys who fall in the 140-149cm category. It is also common for both gender groups to be the height of 150-159cms. This shows that the girls and boys of year 7 are similar in height. However, in this diagram, the tallest girl is 180cm, whereas the tallest boy is 175cm. The tallest girl in ear 7 may be an outlier, however, I decided to keep it because of the girl who came before her in terms of height. The girl who came before her is the height of 179cm, which is very close to 190cm.
The slight difference between the tallest girl and the tallest boy could show that girls in Year 9 can be only slightly taller than boys in Year 9; however, the shortest girl is 125cm, whereas the shortest boy is 130cm. The shortest boy is taller than the shortest girl. This could be showing that where the height for the girls in Year 9 varies slightly, boys are more similar with their heights between each other.
This stem and leaf diagram is of the weight of pupils in Year 7. I have noticed that most pupils fall into the 40-49kg group. There are more girls than boys in the 40-49kgs category. Also, more boys than girls weigh over 60kg. This shows that boys are generally taller than girls. In this stem and leaf diagram, I spotted an outlier. One of the girls’ in year 7 weighs 110kg which is much higher than the average weight for girls which is 45kg.
Stem and Leaf diagram for Year 9 pupils:
Here is a stem and leaf diagram for the pupils in Year 9. It shows that more boys are the height of 180-189cm. The tallest girls in this year group are both the height of 180. However, the tallest boy in this year group is 182. Compared to the number of girls, there also much more boys in this category. This shows that boys are generally taller than girls in year 9. The shortest girls fall in the category of 10cm, whereas the shortest boy is 132cm.
I felt that the shortest girls, where one is the height of 102cm and the other was 106, may have been outliers. But I decided to keep them because even though it is rare to find girls this short, it is possible to find them. Also, there were two girls, not one. This made it seem more likely that there could be girls who are really this short. I have also noticed that in this stem and leaf diagram, the girls in year 9 compared to Year 7’s don’t have much difference between their heights. This could be showing that girls aren’t growing as fast.
This diagram shows the weight of pupils in Year 9. Through looking at this stem and leaf diagram, I have noticed that it is common for girls in year 9 to weigh 40-49kg. Boys in year 9 are more likely to weight 50-59kg. This shows that in year 9, boys weigh more than girls in general. The heaviest boy in year 9 weighs 90kg. This could be an outlier but I felt it is possible to find someone who weighs that much although it is rare. In this diagram, I had realised that the boys are much weightier compared to the boys in year 7.
Stem and Leaf diagram for Year 11 pupils:
The stem and leaf diagram for Year 11 students show that more girls have a height which is lesser than 169cm. It also shows that it is common for year 11 boys to be the height which is more than 180cm. This shows that it is more common for a boy to be taller than a girl in year 11. Compared to the heights of boys between Years 7 and 9, in Year 11, they seem to be much taller. This could mean that in year 11, boys will have grown much more compared to their heights in the previous years. The girls however, have stayed roughly the same compared to the Years 7 and 9. This could mean that girls don’t grow as much by the time they are in Year 11 compared to boys.
This stem and leaf diagram shows the weight of year 11 students. In this diagram, we can see that there is a clear difference in weight between the two gender groups in year 11. We can see that boys are much taller than girls in year 11.The diagram shows that no girls in this year group weigh more than 70kg, whereas there are 13 boys who do. This also shows that in year 11, boys usually weigh more than girls.
By drawing a stem and leaf diagram, I found calculating the averages (for example, means, medians and modes) easy. I also easily worked out my upper and lower quartiles. I have presented my results in the following tables.
Results Table for Heights
This table shows the heights of the girls and boys from years 7, 9 and 11. I have obtained this information from the stem and leaf diagram I had produced. The table also shows that the quartile values for boys is higher than girls apart from the upper quartiles of the boys and girls in year 7 which are the same. The modes of the girls and boys of year 9 are also the same. The table also shows an increase in mode value as the years increase.
By looking at this table, I have spotted that the lowest value for girls in Year 7 is 125, whereas in Year 9, the lowest value is 102. This is due to the outliers I had come across. However, I had decided to keep it as it is possible to find someone who were of these certain heights. The inter quartile ranges for the girls are going lower each time instead of higher. This is irregular compared to the boys’ results which go higher each time. Apart from those certain result, all other data seem to be much more accurate as they are all steadily going higher.
Results Table for Weights
This table shows the values of the quartiles and modes of the weights for years 7, 9 and 11. This table shows that the median values for girls and boys in year 7 are the same. However, in years 9 and 11, girls have a lower median than boys. I have also noticed that the inter quartiles, upper quartiles and lower quartiles for girls are lower than the boys. I have noticed a pattern that the mode of the weight between the girls and boys increases as the years increase. For example, the mode value shows that the most common weight for year 7 girls is 40 whereas for boys, it is 45. Year 9’s have mode weights of 46 to 50. The difference between the modes of the two years has increased.
Box and Whisker Diagrams
The box and whisker diagrams that I have drawn show the differences between the height and weight of the two gender groups. I drew box plots was because I felt that box plots are one of the best ways to compare two sets of data, for example, height and weight. Using the box plot diagrams, I can visualise the differences between the heights or weights of the different years.
Through the box plot diagrams I have drawn, I can see that the height and the weight of boys’ are generally higher than the girl’s. I have noticed however the median height for the girls in Year 7 is the same as the boys in Year 7. The median weight for girls and boys in year 7 is roughly the same. This shows that in year 7, girls and boys have similar heights and weights in average.
The box plot diagrams show that between the Years 7, 9 and 11, the height and weight of boys’ were increasing. But the box plots for the girls’ weight shows only a slight increase between years 7 and 9. The diagram for the girls’ weights in year 11 was very similar to the weights of girls in year 9. This shows that where the weights of boys were increasing through time, the weights of girls were remaining very similar.
When looking at the heights, both gender groups had an increase as the years increased. During the investigation, I came across a few outliers where the result was much bigger than the average. For example, in year 7, there was a female who weighed 110kg. There was a year 9 girl who was the height of 105 which was also an outlier. These outliers have an affect on my research because they can alter my results.
Scatter Graph
The two graphs that I had created for the height and weight for Year 7 girls and boys show positive correlations. However, I have noticed that, if I had drawn lines of best fit, the line for girls would be much steeper than the line for boys. This is because height of girls increases to more than 179cm, whereas the weight does not go beyond 60kg. But for boys, there is a much positive relationship between the height and weight and the weight goes much higher compared to the scatter graph for girls. This may be because of the different diets that boys and girls have, for example, girls may follow a certain diet in order to stay a certain shape, whereas boys wouldn’t.
The heights of these girls seem to be similar to the boys, but when looking at the weight, girls weigh similarly towards each other. This could show that girls probably like to weigh the same as each other or are trying to keep to the same weights due to peer pressure, media etc.
Conclusion
This coursework was based on height and weight and the differences in the two variables within the two gender groups. Through this investigation, I have found that there is a strong link between my findings and my hypothesis. My first hypothesis was that “Girls in year 7 are generally taller than boys in year 7”. Through doing this investigation and looking at my box plots, I have realized there is not much difference between the two genders in that certain year.
My second hypothesis was that “the height and weight of boys will rapidly increase between year 9 and 11”. My results have proved that compared to the girls, boys grow much taller and also gain more weight compared to the girls. Girls in year 9 and 11 don’t have as much difference to their heights whereas when looking at the box plots I have made, the boys have a much bigger increase.
Finally, my third hypothesis was that “in year 11, the boys would have a much bigger height and weight compared to the girls”. Through my investigation I found that the boys in year 11 did weigh more than girls. They were also much taller. By looking at my box plots, I can see a big difference between the two gender groups and their height and weight.
The evidence considered by the results tables and box and whiskers diagrams I had created, demonstrates that the increase of height and weight for girls are usually lower than boys. Through my findings, I have found that Year 9 and Year 11 girls didn’t have as much difference to their height and weight compared to the Year 9 and Year 11 boys. Year 9 and Year 11 boys have rapid increases in their height and weight. Although I found a few outliers during this coursework, my results weren’t as altered as I had expected it to be.
Evaluation
In future when doing the same research, I may increase the sample size in order to gain more accuracy. For example, instead of looking at just year 7 and 9 and 11, I would include year 8 and year 10 too. I feel that if I have more pupils to look at, my results would also be more reliable. I would choose to increase the sample sizes because bigger sample sizes can be convenient because you can present finding onto graphs, etc.
Another thing I would do is collect my own data. This is because the data which I used to help me with this investigation was secondary data which I had to assume to be reliable. If I had collected my own primary data, I think it would be less biased.
However, I some people may find that decreasing the sample size could also be a good idea. This is because when looking at big sample sizes, we may make errors as there is too much to count and look at. For example, we may accidently skip a pupil, etc. During this research I miscounted several times when trying to find the mean and modes and also quartiles. And so, I had to keep going back and correcting my mistakes and checking whether I had missed anymore out. This can be time consuming. With a smaller sample, errors like such can be avoided. Although you can still achieve well results with small sample sizes, I feel that accuracy is more important so a bigger sample size is better.