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• Level: GCSE
• Subject: Maths
• Word count: 1722

# Investigate if there is a relationship between the length and width of the leaves.

Extracts from this document...

Introduction

Statistics Coursework Aim: To investigate if there is a relationship between the length and width of the leaves. I will also investigate summary measures to represent my data. Data Collection: I choose to collect my leaves from a tree in my back garden, as it was easy to access. I picked the leaves from different places and different heights around the tree so that my sample of leaves would be random. I choose a sample size of 35 leaves because it is large enough to reflect the trend amongst the width and length of the leaves on the tree, but still keeping it to a manageable size. When I collected 35 leaves I measured the length of each leaf in millimetres from the end of the stalk where it is attacked to the tree to the tip. I measured the widest part also in millimetres to find out the width. The results are in the table below: - Length mm Width mm Length mm Width mm 130 60 110 50 90 40 96 44 100 50 105 50 70 30 70 34 67 33 80 43 95 45 110 40 97 47 111 55 123 60 119 62 115 58 81 43 136 64 120 63 120 57 110 50 93 47 103 46 112 58 93 40 83 41 ...read more.

Middle

5 0 0 0 0 5 7 4 3 2 1 0 0 6 7 8 1 7 0 0 7 8 0 1 3 5 9 9 0 2 3 3 5 6 7 10 0 3 5 11 0 0 0 1 2 5 9 12 0 0 3 5 8 13 0 0 6 From the stem and leaf diagram I can find Measurement Length Width Minimum 57mm 25mm Lower quartile 85mm 40mm Median 103mm 47mm Upper quartile 120mm 60mm Maximum 136mm 78mm Inter-quartile range 35mm 20mm Range 79mm 53mm I can check these values by putting my original data into order of size and the first term will be the minimum, the ninth term the lower quartile, the 18th term the median, the twenty seventh term the upper quartile, and the thirty fifth term the maximum. As you can see from the sorted data on the following page the values match those I found using the back-to-back stem and leaf diagram above. Ordered data to find median and inter-quartile range. Rank Position Length mm (x) Width mm (y) 1 57 25 Minimum 2 67 30 3 70 33 4 70 34 5 77 36 6 80 39 7 81 40 8 83 40 9 85 40 Lower Quartile 10 89 41 11 90 43 12 92 43 ...read more.

Conclusion

It also showed dangers of extrapolating as a measurement of zero for the length gives a negative value for the width of course impossible. Models often break down outside the original range of the data. The regression line of y on x means we can predict values for y the response variable given the value of x the exploratory variable. For example if x=67mm then we would expect y to be 30.774mm. Looking at our original data the leaf with length 67mm the width is 30mm, which is very close to our predicted value. I calculated the mean and median as measures of location. The values obtained were fairly close. For the length I found Mean for original data = 100.63mm Estimated mean from grouped data = 101.93mm Median from stem and leaf and ordered data = 100mm For the widths I found Mean for original data = 48.83mm Estimated mean from grouped data = 49.93mm Median from stem and leaf and ordered data = 47mm The mean in this case is the best measure of centrality as it uses all the data and there are no extreme values. From the box plots both sets of data show a slight positive skew. To improve this work I would need to take larger samples and preferably from a variety of trees, bushes and plants in different locations so that I could generalize my findings. 1 ...read more.

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