Question 1 [Unit 1] 7' marks A student is carrying out a biology project on trees. {a} They need to record three pieces of information about each tree: {i} The altitude at which it grows [compared to sea level] {ii} The height of the tree {iii} The height above the ground of the first branch from the trunk For one tree. they entered the data in the wrong columns in their table. The three data items recorded are. A: 12.1 metres 13: 800 metres C: 2.3 metres Match each piece of data with the appropriate feature of the tree. justifying your answer. {b} The student nds data from an earlier project which quotes the mean leaf length of this type of tree as 0.934155 cm. They feel this is not an appropriate level of accuracy. Round this measurement to an appropriate level of accuracy, justifying your answer. The word counts for the projects produced by this student and their immediate friends on the course are 4671. 5022. 4893, 5144. 4026. 5000, 5008. 4770' {i} Calculate by hand the median word count. Show your working. {ii} Calculate by hand the range of word counts. Show your working. A teacher is interested in how the scores of children in her class on a standardised yocabulary test change over a school year. The score for each child is recorded when they start the school year in September and again at the end of that school year in July. The Minitab worksheet teetscores.n1wx contains two columns. The column Start: gives the score for each child at the start of the school year and the column End gives the corresponding score for the same child at the end of the school year. Run Minitab and open this worksheet. {a} Use Minitab to calculate a column of values headed Increase, containing the increases in test. scores from the beginning to the end of the year. Use Minitab to produce the default stemplot. of these increases {i.e. the stemplot produced when the Increment eld is left blank and the Trim outliers option is not. selected}. Include a copy of your plot. in your answer. {b} A new stemplot of the increases obtained in part. {a} using Minitab has been produced and is shown in Figure l: Stem-and-Ieaf of Increase N = 32 5 [II 03444 12 El 5556??? {1D} 1 0112233444 11} 1 ESEEETTTB 1 2 1 2 5 Leaf Unit = 1' Figure 1 Compare the new stemplot in Figure 1 with the default stemplot you obtained in part (a). (i) Describe any one difference between these two stemplots. (ii) Explain which stemplot provides the most useful information. Justify your answer. (c) Briefly describe the shape of the stemplot given in Figure 1 of part (b). Your answer should include whether the distribution is unimodal, bimodal or multimodal, whether it is left-skew, right-skew or symmetric and whether or not there are outliers. In each case, justify your answer.The Office for National Statistics publishes data on the retail sales index for different sectors. The current figures have 2019 as the base year, which takes the value 100. Reference (you do not need to visit this website): https://www.ons.gov.uk/businessindustryandtrade/retailindustry/datasets/retailsalesindexreferencetables (a) Figure 2 below shows the scatterplot of the sales index for large food businesses against time from the start of 2019 to the third quarter of 2022. There are four readings for each completed year, corresponding to the four quarters of the year. Scatterplot of Sales index (large food stores) vs Time 112.5 110.0 107.5 105.0 Sales index (large food stores) 102.5 100.0 97.5 95.0 2019 2020 2021 2022 2023 TimeFigure 2 Describe two features of the scatterplot. (b) Discuss with justification whether or not it would be appropriate to use a straight line to represent the data points on the scatterplot in Figure 2. If there are any time periods where you feel a straight line would be appropriate, state them, explaining your reasoning. (c) The Minitab worksheet smallfood.mwx contains the comparable data for small food businesses and has two columns. The column Time indicates the year and the quarter (for example, the time value for the first quarter in 2019 is 2019.125). The column Sales index (small food stores) gives the index value for that quarter. Produce a scatterplot of the index values against time. Include the plot in your answer. (d) Compare the scatterplots for the large and small food businesses