Question: Hello, I need help with these questions:) A random sample of 25 leaves from an ivy plant is collected. For each leaf, the length (at
Hello, I need help with these questions:)
A random sample of 25 leaves from an ivy plant is collected. For each leaf, the length (at its longest point) and the width (at its widest point) are measured. The data representing the length of leaves are shown in the zod column of Table 1; shaded green. The data representing the width of leaves are shown in the 3" column of Table 1; shaded blue Width For each leaf, the ratio of length to width is recorded in the 4th column of Table 1; shaded pink. Table 1 Table 2 Sample Length Width Length to Width Leaf Length (mm) Number (mm) (mm) Ratio - Ranked in Order 28 52 0.54 2 17 0.55 0.63 45 0.6 5 0.76 0.8 0.8 0.9 1.0 1.20 1.3 1.35 1.39 1.44 110 1.47 The Leaf Length and Ratio [14 Marks] (a) In Table 2 above, using the column labelled 'Leaf Length (mm) - Ranked in Order', re-arrange [1) the lengths of leaves in order from shortest (at the top) to longest (at the bottom). (b) Use your rank order arrangement to find the median value of leaf length within the sample. (1) In the spare column of Table 2, draw a single arrow that points exactly to the median value. (c) Describe what the median value - of the length of leaves in the sample - represents. [1) (d) Calculate the mean value of the length of leaves in the sample, correct to one decimal place. [2] Describe what the mean value of the leaf length represents. (e) State the modal value/s of the leaf length (from Table 2) and explain what is meant by any (2] modal values in the context of this investigation. (f) In Table 1, the column for Length to Width Ratio is missing one entry. Calculate its value. [1] (g) Considering in particular the leaves whose Length to Width Ratio equals 1, what can be [1] determined about their shape? (h) Considering in particular the leaves whose Length to Width Ratio is less than 1, what can be [1] determined about their shape? (i) Calculate the Length to Width Ratio of a leaf that has Length of 98 mm and width of 40 mm. [3] What makes this leaf an 'outlier' compared to the sample of 25 ivy leaves that were collected, and what is a simple, real-world situation that could plausibly account for this observation? (j) As leaves on the ivy plant grow, their Length to Width Ratio tends to develop in a certain way. [1] Considering length and width, what tendency is there for the growth rates of an ivy leaf? (Hint: Examine the graph in Part 3 (b), which visually shows the data from Table 1.]