Data Handling Project : Heights of Girls

What we can tell from the cumulative frequency graphs?(on next the next pages)

For the Year 7 Cumulative Frequency graph for weight you can tell that the girls have a more tightly packed range of weight and that nearly all of the girls are in the middle half of the table. There is more variation either side for the males, meaning that in the girls the interquartile range is smaller.

For the Year 7 Cumulative Frequency graph for height, the graphs are very similar; the only main difference is that the girls' graphical result doesn't flow as well and some of the points don't fit the line properly. This either means that the girls' height varies a lot or my sample that I have is not a true sample of the year 7 girls' height.

Below I've drawn a box and whisker diagram to show the interquartile ranges better.

What we can tell from the Box and Whisker graphs

(on prev. page and above)

We can tell first of all from the Box and Whisker Graph for weight that the boys have an interquartile range that is smaller then the females showing that the males are more compact and are closer together, and are more even in height then the females. Also the upper quartile and the lower quartile are both higher then the females showing that contrary to my prediction that the males are actually taller then girls in their first year but the medians are the same so if you were to take everyone on average then neither would be taller.

One of the things we can tell from Box and Whisker Graph for height just by looking at it that the males this time have the bigger interquartile range and are therefore likely to be more varied then the females in weight. The median for the females is higher then the males which means on average girls weigh more then boys but the males upper quartile of the boys is higher then the females so there are probably more heavier boys but lighter ones as well.

Standard Deviation

By using the excel formula '=STDEV(D2:D41)' which I looked up and revised I was able to calculate the standard deviation of my tables and my selected data,

For year 7 Boys height the standard deviation is 0.099m to 3 d.p

For year 7 Girls height the standard deviation is 0.120m to 3 d.p.

The girls S.D. was greater then the boys which means that the boys data was closer together and more better data, I expected since when I was drawing the cumulative frequency graph I found the girls data was not following a proper curve where as the boys fitted in a lot more nicely

For year 7 Boys weight the standard deviation is 10.3kg to 3 s.f.

For year 7 Girls weight the standard deviation is 11.9kg to 3 s.f.

Since the boys S.D. was again lower then the females it is fair in saying that my random sample of boys was a better pick then my random sample of female. I could improve this by re-doing my tests or adding more people to my sample.

Unequal Histograms (On Prev. Page)

From my unequal histograms graphs I can tell that there is most of the people in the middle few bars. In the Year 7 Unequal Histogram for Height that the boys are more towards the end of the graph whereas the females and in greater numbers closer to the beginning then the boys. On the Year 7 Unequal Histogram for Weight, the girls are in greater numbers in the middle and the boys have a much more even spread. This means that the girls are more even in height then the boys.

Year 11

Scatter Graph Males and Females

I'm now going to draw some scatter graphs for the year 11 groups and find the line of best fit and other data.

What Can We Tell From The Scatter Graphs?

We can tell from these scatter graphs first of all that the girls have a poorer correlation than the boys, but are in a much closer height bracket whereas the boys have a bigger height bracket and a better correlation. In both of the graphs the majority of people are in the 1.6m to 1.8m range the boys' height however continues after 1.8m unlike the girls and one person reaching 2.06m in height.

Very like in year 7 the girls weight is not spread out and the majority are still compacted into the 40kg to 60 kg weight range, although it is now more spread out because before it was all nearly on the 40kg line whereas now it is more spread out but still very compact. The boys weight is spread out mainly in the 40kg to 80kg range. This shows us that while the girls are fairly uniform in weight the boys are a lot more varied. Like my first prediction the boys are heavier then the girls by year 11.

What we can tell from the cumulative frequency graphs?(on next the next pages)

We can tell from the year 11 cumulative frequency graph for weight that the boys are heavier because the graph ends later for boys then the girls. Also the boys have a greater interquartile range. I can tell this because of the shape of the curves. The girls have a tight distribution.

I can tell from the year 11 cumulative frequency graph for height that boys are taller since because many more boys still or the graph even after the tallest girl has been counted for. The girls once again have a tighter distribution of height then the boys do.

What can we tell from the Box And Whisker Graphs?

(Above)

In both of the box and whisker diagrams the girls have the smaller interquartile range, which I had predicted after seeing my cumulative frequency graph.

First of all I will look at the diagram for weight, the males are definitely heavier then the females by year 11. The lower quartile of the males nearly surpasses the upper quartile of the females. This shows me that nearly 75% of the males are heavier then the bottom 75% of the females. In this graph the female and male interquartile range are nearly the same, but the males interquartile range is slightly bigger showing that the males are more varied. As I predicted the males were heavier in year 11.

In the second diagrams involving height, the females have a very small interquartile range showing me that by year 11 all the girls are nearly on a level height, the boys interquartile range is a lot bigger so that in year 11 the boys are still more uneven. The median in the boys is bigger then the upper quartile of the girls proving that boys are taller in year 11. This is what I had predicted in the first place and is shown to be true.

Standard Deviation

Once again I used the excel formula '=STDEV(D2:D41)' to find the standard deviation of my data

For year 11 Boys height the standard deviation is 0.134m to 3 d.p

For year 11 Girls height the standard deviation is 0.081m to 3 d.p.

This time it was the boys that strayed more from the mean since the standard deviation was greater in the boys. I could improve the standard deviation by making it lower by having more people in my sample and this should bring the standard deviation down since there is a more accurate mean for one reason and also because there would be more samples which should in theory follow the mean.

For year 11 Boys weight the standard deviation is 12.0kg to 3 s.f.

For year 11 Girls weight the standard deviation is 6.72kg to 3 s.f.

In this one the standard deviation of the females was nearly half that of the boys showing that the boys often strayed from the mean a lot. I could tell this because if you look at the cumulative frequency graph for male and female weight year 11 that the data distribution is very tight.

What Can I Tell From My Unequal Histograms?

(On Next Page)

With my Unequal Histograms for Year 11you can tell that the girls' bars often are bigger then the boys in the centre or in a few bars in a row but the boys' say more on a level, with the biggest and smallest bars difference being less, thus showing that the boys are more dispersed then the females in their height and weight. In my Unequal histogram for year 11's height the girls' highest bars are towards the beginning of the table and the boy's bars are bigger towards the end also proving my original statement how boys in year 11 are taller than girls. In the histogram for year 11's weight it has stayed nearly the same and once again the boy's bars are bigger towards the end of the table showing my original statement to be true.

Main Conclusion

My prediction In the beginning was that in year 7 boys were shorter and weighed more and girls were taller but weighed less, I thought this was so due to real life and just looking around, with the data I have been given I see that this is not so. Boys in year 7 are taller then girls in Mayfield High School and also weigh more then girls, this may just be the random sample I had or more likely year's height ranges from school to school. My prediction was that year 11 boys were both heavier and taller then year 11 girls, I thought this because in general girls grow quicker but stop growing earlier I would say that prediction was correct and year 11 boys are taller then year 11 girls, because in my graph there was quite a difference between the boys and girls. I have found that there is some correlation between year and height and weight, as people get older they grow so this is not surprising but I thought I should point out how the year 11 boys were a lot taller and heavier then year 7 boys and the same for year 11 girls and year 7 girls.

Other Conclusions

Something I noticed in my graphs was the variation in the data, on nearly all of the graphs the girls had the tighter data, and boys were more even. This means that while most of the girls will be on the same level the boys will vary a lot in height and weigh, no matter which year they are in this seems to be true. That would be why when I found the standard deviation of the data the females S.D. was a lot lower.

Limitations

There were some limitations of my scatter graphs for example, they are not very clear and the points are too big for my likening, you cannot get a true idea of what the graph is showing because it is to small. Another limitation is doing some work by hand but others by computer, I had to this due to the fact I did not know how to draw more complex graphs on the computer, if a computer had done it, the graph word be more accurate and therefore so would the data I got from the graph.