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  • Level: GCSE
  • Subject: Maths
  • Word count: 3774

In this investigation, we are studying the relationship between height and weight at Mayfield High School

Extracts from this document...

Introduction

GCSE Statistics Coursework Paul Nicoll In this investigation, we are studying the relationship between height and weight at Mayfield High School. There are several lines of enquiry I will look at and assess: * The relationship between girls and boys in different years- with regards to both height and weight. * How boys' heights and weights compare in different years. * How girls' heights and weight compare in different years. When I look at the conjectures, I will have to take into account defects that could affect my data and my conclusions. The clearest example of a defect in this investigation is adolescence, where processes such as growth spurts and weight problems caused by hormones may affect the data. As a result of this, the affected data may in turn influence the mean and standard deviation of the sets of information. Predictions I predict that my calculations will show the following about my hypothesis: * That boys will generally have a greater height mean and weight mean than girls. * That boys will have greater standard deviations for height and weight than girls. * That as the pupil gets older, the weight and height increases. Sampling In order to carry out this investigation, the data needs to be sampled. With 1183 sets of data available, it is necessary to work with a smaller number of samples, as this enables a more manageable group of figures to manipulate. This may also be useful because a general error with the data will be less emphasised by a smaller data set. Furthermore, because the selected sample is over one tenth of the size of the full data set, any trends that I notice in my sample should be the same as those in the rest of the data. I will be using 120 samples- 60 boys and 60 girls. I will use the same number for both genders to avoid any bias towards either boys or girls. ...read more.

Middle

On the cumulative frequency, we can work out the Upper Quartile, the Lower Quartile and Median. We find the Upper Quartile by multiplying the total cumulative frequency number by 3/4, as we want to find the term that is 3/4 of the total, so we can read a value from the x axis. Therefore, 120 x 3/4 = 90 , which means we read across from the 90th value. Similarly, we find the Lower Quartile by multiplying the total cumulative frequency number by 1/4 , as we want to find the term that is 1/4 of the total, enabling us to read across the graph. Therefore, 120 x 1/4 = 30 , which means we read across from the 30th value. We find the median by taking the middle term, the 60th, and reading across. Therefore, from reading across from our graph, we find out the following: Upper Quartile (UQ) = 1.70m Lower Quartile (LQ) =1.535m Median = 1.625m We can also find out the Interquartile Range (IQR) by subtracting the LQ from the UQ. So, in this case, the IQR = UQ - LQ = 1.70 - 1.535 = 0.165m. Now that we know the UQ and the LQ of the height, we are now able to draw the box and whisker diagram, which is another technique to show the spread of data. On the box and whisker, we only mark the UQ, the LQ and the median, shown below: The box is not very wide, therefore we can tell that the spread of data is concentrated mainly in the 1.60m region. The lines, or 'whiskers', shows the extremes the data is collected from- there are people with heights in the 1.00's, and in the 2.00's, so there is still a significant width to the data. Weight We can now do the same for the weight. Below is the stem and leaf diagram for the overall weight of the sample: Stem Leaf Frequency Cumulative Frequency 2 96 2 2 3 28707858 8 10 ...read more.

Conclusion

Looking at the standard deviations, we can conclude that, due to larger S.D.'s in both height and weight, the Year 11 boys have a larger spread of data than the Year 7 boys. This, like the means, could be down to adolescence- as the Year 7s may not have started going through puberty, the boys would have a closer height spread than Year 11s. If we take the same approach to the Year 7 and Year 11 girls, we find the same results occur. The Year 11 girls have larger means than the Year 7s, but an interesting difference between this comparison of girls and the comparison of boys, is that the Year 7 girls have larger standard deviations than the Year 11s. This could be due to one or two girls in Year 7 being larger, or smaller, than the rest of the year, which would raise the S.D. of the year group. As is shown on the scatter graph, there are a few points that do not fit with the general trend, as they are very far from the line of best fit, and the rest of the data. This may be down to an error with the data collection, where the wrong figure was noted, or it may be a real error. As this is real life data, there may be errors, or it may simply be a case of a very large person. There is a very large weakness with this investigation, however, and that is that we are limited by this data. We have taken this information from one school in the UK, and therefore it is not representative of the whole population. We have only looked at one area, when we should also look to other places. This would result in our calculations, and our conclusions, being more accurate, and more reliable than if we were just going by this data. I would expect the same conclusions to be reached with other data across the country; therefore the probability of this happening across the country would be high. 1 GCSE Statistics Coursework Paul Nicoll ...read more.

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