Maths Leaf It to Me

this term in year 11 we have collected data from two different species of trees and compared this data in graphs and statistics. we needed to prove or decline that as trees grow larger there leavs get smaller due to the fluid flow within the tree

TABLE OF CONTENTS

Part A:

INTRODUCTION

EXPECTAIONS, PREDICTIONS AND ASSUMPTIONS PAGE 3

DATA

SECONDARY DATA – STEM AND LEAF PLOT PAGE 4
SECONDARY DATA – LINE GRAPH AND OGIVES PAGE 6
SECONDARY DATA – BOX PLOT AND HISTOGRAMS PAGE 7
SECONDARY DATA – MEASURMENTS OF RANGE PAGE 12
SECONDARY DATA – BELL CURVE PAGE 12/11
INVESTIGATION PAGE 11

ANALYSIS

CONCLUSION PAGE 13

APENDIX

PRIMARY/ RAW DATA PAGE 13/15

PART B

Simpsons paradox Page 16/17

INTRODUCTION

The purpose of this mathematical report is to investigate a tree’s ability to capture sunlight in relation to possible correlations between the tree’s growing capacity and leaf length. A variety of mathematic techniques will be used to examine how a tree’s height relates to the length of its leaves. This data will then be used to analyse the tree’s ability to efficiently capture sunlight and move liquid around the tree.

It is predicted that this report will prove that as a tree’s growing capacity increases the average, median and mean leaf size will decrease. This is likely due providing a more efficient means of transporting fluid around the tree. However to compensate for the shorter leaves’ having less ability to capture sunlight there will be an increased quantity of them to ensure that adequate sunlight is absorbed

This study will make use of a variety of mathematical concepts, more specifically with many of them relating, or having to do with statistics. This investigation will draw on over 200 collected values for leaf length from 2 separate tree’s (100