# Mathematical Analysis for Information Technology

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Mathematical Analysis for Informatics 2014/15 BIF-4-MAI Page 1 Assessed Group Coursework Introduction The instructions given below describe a two-part assessment to be undertaken as a group assignment, with the group size being no larger than four. Part 1 consists of four questions, each to be undertaken by one member of the group. However, each group member is required to display a high level of knowledge for all four questions (see Assessment and Marking Scheme below). In your submission, you must clearly state which group member is responsible for doing which question. Part 2 is to be undertaken as a group exercise in which the work is to be equally divided within the group. You will have an oral assessment on both parts, where you will be interviewed about your work (see details below). You should prepare a written report (word processed) describing your answers to each of the questions. When you are preparing your report, you must have in mind that you need to give explanations of your reasoning where necessary and that good structure, presentation, accuracy of working and English are important in this and any work that you produce. Submission This coursework is to be submitted by uploading to Moodle) by 4pm on Monday 11 May 2015. The first page must be a contents page showing exactly where to find the particular questions. Also state your group tutor’s name on this first page. It is imperative that your work is submitted on or before the deadline in order that it can be available for your interview. It is imperative for the panel of assessors to have your work available during your Viva. If your work is not available at least two days before your Viva, you would run the risk of failing the assessment. Mathematical Analysis for Informatics 2014/15 BIF-4-MAI Page 2 Assessment The assessment will include an interview where the group will have to face a panel of assessors who will be armed with a number of preprepared questions. If any member of a group displays any areas of weakness, it would be reflected in the overall score of the individual member. This ensures that the individual does not drag down the other members of the group. It also ensures that the no individual can hide behind the other members of her/his group. Please be assured that if any individual goes into the interview unprepared, she/he would be exposed and appropriately penalised. Marking Scheme The weighting of the two parts of this paper is 40/60. i.e., 40% for Part 1 and 60% for Part 2. For Part 1, each question has a weighting of 20 marks. Therefore, each individual group member has an equal chance of scoring 20 marks from doing his/her chosen question. Each group member can score a further 20 marks from the oral by adequately answering the questions relating to the other three questions. For Part 2, each group member has an equal chance of scoring the available 60 marks. Your overall mark for this coursework will then be weighted to contribute to 35% of the module. Your Phase Test marks, your Personal reflective Log and your Integrated Assignment provide the other 65%. Mathematical Analysis for Informatics 2014/15 BIF-4-MAI Page 3 Part 1 Question 1 This question is concerned with analysing the length of words in the English language. Choose a sample piece of writing of about 100 words, in English, from a magazine, book, or article. (a) Count how many words there are in the article of different lengths and draw up a frequency table. (Include in your submission a copy of the text you have chosen.) [5 marks] (b) Calculate the mode word length, the median word length and the mean word length from your frequency table. [6 marks] (c) Which of the three averages in part (b) do you think is the most appropriate to use with your data and why? [2 marks] (d) Draw up a cumulative frequency table and from this draw a cumulative frequency polygon. [6 marks] (e) Use the cumulative frequency polygon to estimate the lower quartile and upper quartile. [4 marks] (g) How representative of the English language, in terms of word length, do you think your sample is, and why? [2 marks] Mathematical Analysis for Informatics 2014/15 BIF-4-MAI Page 4 Question 2 Toss five coins and record the number of heads. The number of heads is outcome 1. Toss the five coins again and record the number of heads. This is outcome 2. Repeat this process until you have a total of 25 outcomes. (You can simulate this in a spreadsheet if you wish but include a print out of the sheet of your trials, displaying any formulae, in your submission.) (a) Construct a frequency distribution table of the outcomes. [5 marks] (b) Construct a bar chart from this frequency distribution table. [ 5marks] (c) Use the frequency distribution table to calculate the mean number of heads. [5 marks] (d) Use the frequency distribution table to calculate the standard deviation. [10 marks] Mathematical Analysis for Informatics 2014/15 BIF-4-MAI Page 5 Question 3 Preliminary percentage marks of students taking a mathematics module: 32 36 48 75 40 44 27 27 51 36 34 18 44 9 9 36 59 36 29 24 42 27 64 50 45 44 45 55 65 26 40 2 73 46 45 2 2 61 11 12 36 58 64 57 24 59 36 63 59 26 58 43 3 44 36 37 29 45 34 17 49 37 38 56 34 25 51 65 64 2 19 48 33 65 38 39 65 44 0 38 3 45 50 30 56 17 11 41 25 38 Use a spread sheet to answer this question but remember to make explicit where and how you are using any formulae. (a) Calculate the mean from the raw data. [ 2 marks] (b) Create a grouped frequency table for this data. [7 marks] (c) Suppose you did not have access to the raw data above, but just the grouped frequency table you created in part (b). Estimate the mean from this grouped frequency table. How close was your estimate to the actual mean? [5 marks] (d) Construct a histogram for this data from the grouped frequency table you created in part (b) so as to get a picture of the distribution. [5 marks] (e) Calculate the median, upper-quartile and lower-quartile from the raw data and use them to draw a box plot. [6 marks] Mathematical Analysis for Informatics 2014/15 BIF-4-MAI Page 6 Question 4 You are involved in programming a computer game and decide a character has a 50% chance of being eaten when bumping into a ‘Nemesis’ dragon. To get an idea how this will affect the length of the game you want to know the likelihood of how many times a player can bump into the dragon before being eaten. This can be calculated theoretically but here we want you to simulate the problem by tossing a coin to estimate the result. Toss a coin several times until you get the queen’s head (this represents being eaten). Record how many tosses it takes. For example, if you get the sequence < Tail, Tail, Tail, Head> this will be recorded as 4. This will be called a trial. (a) Conduct the trial 25 times and record the results of each trial. [2 marks] (b) Construct a frequency distribution table of your observations. [3 marks] (c) Construct a bar chart of your observations. [5 marks] (d) Using the frequency distribution table calculate the average number of times of bumping into the dragon before getting eaten. [5 marks] Suppose the chance a character has of being eaten is now reduced to 15%. (e) Use a spread sheet and a function which generates random numbers to conduct the experiment again using this new probability of being eaten. Include a print out of the sheet, displaying its formulae, and the outcome of the 25 trials. (You may find it helpful to first repeat part (a) but using a spreadsheet instead of flipping coins.) [5 marks] (f) Draw a bar chart as before and calculate the new average number of bumps before being eaten. [3 marks] (g) Do some research and find what the theoretical averages are for both the 50% and the 15% scenarios. Specify the source of the solution. [2 marks] Mathematical Analysis for Informatics 2014/15 BIF-4-MAI Page 7 Part 2 A consumer watchdog organisation has asked you to write an article both to compare prices of products between the four leading supermarkets (Asda, Morrisons, Tesco, Sainsbury’s) and between the prices they charge for products in their stores and online. You will base your article on data collected in a

survey of the prices of various products found in these supermarkets. To accomplish this task you will have to visit the supermarkets in question and record the prices of the products, as well as visiting their online stores. Select twelve items typically found in a family’s weekly shop. The onus is on you to make decisions regarding sizes and quantities, but once a particular size or quantity is decided upon for a particular product, it must be applied with consistency. (a) Present the data you have collected in a table or tables, in as clear a way as possible. Remember to observe the principles learnt from your lecture/tutorial notes and apply the skills acquired from your workshop exercises. [marks 15] (b) Create any charts, graphs, scatter plots, box plots which you think are helpful and appropriate in illustrating the data and making comparisons. [marks 20] (c) Extract appropriate statistics (measures of central tendency, measures of dispersion, correlations etc) to extract from the data whatever information you deem to be relevant and appropriate to your article. [marks 10] (d) Write a short article (up to 300 words) describing what you found from your survey after analysing your data. Include references to your tables, charts and statistics to illustrate and backup any comments and conclusions you make. Write the article in a concise and logical manner; marks will be awarded for clarity. [marks 15]

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