Comparing The Relationship Between The Length And Width Of A Leaf

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Investigating the Relationship Between the Length and Width of a Leaf

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 …show more content…

I added all the widths and called them y.

x=3522/35

x=100.63mm

y=1709/35

y=48.83mm

The formula for standard Deviation is:

Measurement

Total

Mean

Standard Deviation

LENGTH

3522

100.63

19.99

WIDTH

1709

48.83

11.63

To check that these values are correct I shall group my data and estimate the mean and standard deviation. I will lose detail by grouping the data and I need to make the assumption that the mid class value is representative of data within each interval. Grouped frequency tables are used for continuous data or for discrete data when a lot of data has to be recorded. I am going to organise the data into classes. I am going to draw two tables. One for the length and one for the width.

Grouped frequency table for length.

Length mm

Tally

Frequency (f)

Mid-point (x)

f*x

fx²

50-59

/

1

54.5

54.5

2970.25

60-69

/

1

64.5

64.5

4160.25 …show more content…

The medians are 100mm for length and 47mm for width. In both cases the box plots indicate a positive skew.

To investigate the relationship of the length and width of the leaves as there are two [IMAGE] variables I shall draw a scatter graph.

The scatter graph indicates a strong positive correlation, as the points are close to a straight line. As the length increase the width also increases.

I shall work out the Product Moment Correlation Coefficient (PMCC)

As a check I will use the function key on the computer to find the PMCC. From the computer the PMCC=0.9232572 this matches my calculator value. This is a very strong correlation between length and width of leaves.

I shall now test whether it is statistically correct.

H p=0 there is no correlation

H p>0 there is some positive correlation that implies one tailed test.

Testing at 5% level of significance

From tables for n=35 the critical value=0.2826

As 0.9232>0.2826 the result is significant therefore we reject H .

There is evidence of a positive correlation between length and width of leaves.

As there is evidence of correlation I can calculate the

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