Leafy Maths Investigating leaf size for different trees

Leafy Maths

Investigating leaf size for different trees • How can we collect a random sample of 20 leaves? • What measurement shall we take?

Leaf A length mm Leaf B length mm Leaf C Length mm 54 78 46 65 94 56 66 105 58 35 51 16 41 54 20 41 52 16 48 68 41 50 68 44 33 45 13 41 63 25 71 105 58 102 115 64 24 45 12 33 46 15 54 75 45 15 35 5 62 83 49 44 63 32 59 81 49 22 36 6

Stem and leaf plot

Leaf A length mm Leaf B length mm Leaf C Length mm 15 35 5 22 36 6 24 45 12 33 45 13 33 46 15 35 51 16 41 52 16 41 54 20 41 63 25 44 63 32 48 68 41 50 68 44 54 75 45 54 78 46 59 81 49 62 83 49 65 94 56 66 105 58 71 105 58 102 115 64 Median

Analysing the Data • Measure the leaves mm • Put this data into a excel • Sort it smallest to largest • Calculate min, max, Q 1, Q 2, Q 3

What are quartiles? Here are 20 leaf lengths 12 15 15 16 18 Min 12 Q 1 19 Q 2 26. 5 Q 3 37 Max 61 20 24 25 26 26 27 30 30 32 34 40 48 51 52 61

Leaf A length mm Min Q 1 Q 2 Q 3 Max Leaf B length mm Leaf C Length mm 15 35 5 22 36 6 24 45 12 33 45 13 33 46 15 35 51 16 41 52 16 41 54 20 41 63 25 44 63 32 48 68 41 50 68 44 54 75 45 54 78 46 59 81 49 62 83 49 65 94 56 66 105 58 71 105 58 102 115 64 Quartiles

Draw a box plot Min, Q 1, Q 2, Q 3, Max

Calculate mean and Standard deviation Each pair work out A, B or C You can draw a similar box plot to the quartiles now

Leaf A length mm Leaf B length mm Leaf C Length mm Ordered Leaf A length mm 54 78 46 65 94 56 66 105 58 35 51 16 41 54 20 41 52 16 48 68 41 50 68 44 41 33 45 13 41 41 63 25 41 71 105 58 44 102 115 64 48 24 45 12 50 33 46 15 54 54 75 45 54 15 35 5 59 62 83 49 62 44 63 32 65 59 81 49 66 22 36 6 71 15 22 24 33 33 35 102 Leaf B length mm 35 36 45 45 46 51 52 54 63 63 68 68 75 78 81 83 94 105 115 Leaf C Length mm 5 6 12 13 15 16 16 20 25 32 41 44 45 46 49 49 56 58 58 64