mayfield statistics

 

This is the method I use to get the number of samples I need from the database.

Girls

131 / 360 x 60 = 22         (Year 7)                1 = Girls in Year  2 = Girls in all 3 years

(1)      (2)    (3)                                        3 = My sample number                

143 / 360 x 60 = 24        (Year 9)

86 / 360 x 60 = 14         (Year 11)

Boys

151 / 354 x 60 = 26         (Year 7)

118 / 354 x 60 = 20        (Year 9)

84 / 354 x 60 = 14        (Year 11)

                        

Hypotheses 1

I earlier stated that I believe in Year 7, girls will be taller than year 7 boys in general whilst year 11 boys will be taller then Year 11 girls in general. I will test this by drawing a box plot graph and showing the inter quartile range which will give us a clearer idea and this should prove my theory correct.

(Graph)

Hypotheses 2

My second hypotheses is that boys, in general, will weigh more then girls because as boys go through puberty, they naturally grow height and with this height, they also gain weight naturally for needs to work such as physical activity.

To do this, I shall create graphs plotting height against weight for boys and girls and comparing these.

 

Graph 1          

To see if there was a positive correlation between height and weight as I had predicted, I plotted my sample results onto a scatter graph and found that the first part of my hypothesis (that there is a positive correlation between height and weight) was not well supported by my results. As you can see, there is relative positive correlation between the two parties. This evidence can lead me to suggest that the taller you are, the heavier you way if you’re a girl. Even though there is slight variation, with the two extremes being on show, we c an still form a conclusion out of this. The line equation suggests that for every meter you grow, you gain approximately 21 kg on average. To see differentiation between girls and boys, I shall now make a graph plotting boy’s height vs. weight and see if there’s a correlation and compare that with the above graph.

Graph 2

As you can see, the correlation is very good as the gradient is quite steep. This evidence can also lead me to suggest that the taller you are, the more you weigh if you’re a boy. However, the line equation suggests that for every meter you grow if you’re a boy, you gain approximately 51 kg on average. This means boys are taller and weigh heavier than girls, thus proving my second hypotheses exact.  

I will now advance to work out the product moment correlation (PMC) of each graph so I can see how strong the correlation is for each graph and the difference between the strength of the correlation for boys and girls.

Product Moment Correlation

I will use this to find out how much correlation there is between height and weight for both genders and for all the year groups I am studying. This will hopefully give us a deeper insight into the difference there is between everyone.

I will start by working out the PMC for the girls. The way to do this is by using this table:

Height will be x and weight will be y. I will fill in the table below for the girls, and then proceed to work out the PMC

The other formulas that are needed to help me work out the PMC:

SXX = Σx²- (Σx)²

SYY = Σy²- (Σy)²

SXY = Σxy – (Σx*Σy)

        n

I then put these into another formula:

r =         SXY        s 

      √(SXX*SYY)

But, I have discovered a quicker way to work out the PMC, without using the extra formulas SXX, SYY and SXY. This method is inserting a formula into Microsoft Excel. The formula is =CORREL(height,weight).

These are all of the heights and weights for all of the boys:

Using the two columns of data (height, weight) I worked out the PMC of both the boys and the girls to see if there is a strong correlation.

PMC for girls is 0.25397

PMC for boys is 0.516677

The correlation for the boys is 0.516677, meaning that the overall graph for boys has a higher correlation than the graph for the girls (0.25397). I can tell that the graph for the boys has a higher correlation than the graph for the girls because 0.516677 is closer to 1 than 0.25397 and that is how PMC correlation works.

Conclusion

During this investigation, I have used data about Mayfield high school to test my hypotheses that girls will be taller in year 7 but by year 11 boys will be taller, and that there is a positive correlation between height and weight.

I chose samples out of the data as using all of it would be too time consuming. To test my first hypothesis (that girls are taller than boys in year 7 but by year 11 boys are taller) I put my samples on a box plot so that I could compare them more efficiently. I found that my results did support my first hypothesis because the results showed girls being taller than boys at the start of year 7 but by the time year 11 was finished, the boys were taller then the girls . Although my results did support my first hypothesis, they don’t fully approve it either as the sample size is too small to know for sure if my hypothesis is correct.

To test my second and third hypothesis (that boys are taller and heavier than the girls and that there is a positive correlation between height and weight) I needed to see the link between height and weight so I plotted height and weight against each other. Because I also wanted to see the difference between boys and girls, I made two scatter graphs, one for each. I found that the results of the scatter graph did support the second part of my hypothesis because the trend line of the graph clearly shows a slight positive correlation between height and weight, for boys and girls, even though the gradient wasn’t very steep. The first part of my hypothesis (that boys are taller and heavier than girls) was also supported by my results. I viewed the equation of the trend line for both graphs and found that the gradient for the boys graph was roughly 51, meaning they put on 51kg for every metre that they grow. The girls put on average 21kg for every metre they grow. This shows that boys put on more weight than girls, and will end up heavier. However, the PMC results concluded that there wasn’t much correlation between height and weight for the girls, while for the boys the correlation wasn’t too high either. This didn’t support my hypotheses unfortunately but maybe if I had a bigger sample, then results and conclusions could have been different.

I could have improved my investigation by increasing my sample size to create a more accurate result. This might have changed my results but would have taken longer. I also could have obtained primary data because then I could control the accuracy of the data. This would have prevented any anomalies occurring and would have lead to more reliable data being produced.