From this data I have found that I need to take a stratified sample of the following numbers from each year group.
When rounded up these numbers become the following Data
As you can see there is one too few in the girls group. I solved this problem by adding another girl into the group. To decide how to do this I used the following method.
I started by taking all of my results down to 2 decimal places as before and seeing which two was the closest to being rounded up that weren’t rounded up.
After that I now know my final information so that I can take a sample of the boys and girls in Mayfield High School.
My sample ended up as:
My Tally chart is as Follows:
And For Weights:
See Histograms
From these histograms you can draw the conclusion that the boys and the girls are in a standard distribution about the middle of the data and you can see that in both the modal group is 150<H<160. Because of this you know that most of the boys and the girls fall into this category. From the two histograms you can see that the mean averages are already strained as it shows that there are taller boys in the year than girls but there are also some shorter boys in the year. There are more girls in the middle group and they are more compressed into a shorter range than the boys are.
See Frequency Polygon
From this frequency polygon you can see that the girls are much more even in their distribution than the boys and you can also see that they are taller in the centre group. Because the boy’s line is very jagged it shows that there is a greater variation of the number of boys in each group and that there are some boys that are taller than the girls
Stem and leaf Diagram for Boys Heights
I have produced this stem and leaf diagram because it is a very orderly way to show groups of data whilst still preserving each individual value and also it looks like a bar chart when turned on its side.
Averages
From these averages we can see that the girls are taller than the boys in the mean values but the boys have a larger range which means that there are taller boys than there are girls and there are also shorter boys than there are girls.
At this point I want to extend my investigation by finding out if there’s a link between the heights of boys and girls and their weight.
See Scatter Diagrams
From these scatter diagrams you can see that on the girls diagram there is no correlation that the computer can determine. I have found a line of best fit however it is a very weak correlation. Because I have only taken a representative sample of the girls there is a high probability that the sample that I took is very close together and not an accurate sample. On the boys graph there is a strong positive correlation. This shows that the taller a person is, the heavier they are going to be. On the boys graph there is a very extreme value and this is probably because that person is very heavy.
From the lines of best fit you can see that a girl who is 1.55m tall is going to be about 46kg in weight. A boy who is 1.55m tall is going to be about 49kg in weight.
The equation for the boys line of best fit is: y=2/3x + 25
The equation for the girls line of best fit is: y=1/3x + 37
Cumulative Frequency Table
See Cumulative Frequency Graphs
From this cumulative frequency curves I can get the medians and the IQR. These are put into the table below.
From this information we can draw the conclusion that the boys are taller than the girls. As there is a higher IQR on the girls than on the boys there are almost certainly some girls that are taller than the tallest boy and some really short boys. There is a higher median for the boys than the girls and this shows that there are taller boys than there are taller girls.
See Box and Whisker Diagrams
From the box and whisker diagrams you can see that there is almost no difference in the IQRs and the way that the values are distributed. From all of the data that I have produced you can see that there is almost no difference in the average heights of boys and girls. However I have used all of the data from the whole school. If I were to only use Y7 and Y11 data and compare that then my results maybe very different. Also I know that the girls sample is not very representative by the fact that there is no correlation in the scatter diagram.