Quantitative Methods For Business - Coursework Example

Error: Reference source not found UNIVERSITY OF SOUTH AUSTRALIA Assignment Cover Sheet – Internal An Assignment cover sheet needs to be included with each assignment. Please complete all details clearly. When submitting the assignment online, please ensure this cover sheet is included at the start of your document. (Not as a separate attachment.) Please check your Course Information Booklet or contact your School Office for assignment submission locations. Name: Student ID                 Email: Course code and title: MATH 1053 – Quantitative Methods for Business School: Info. Tech. & Mathematical Sciences Program Code: Course Coordinator: Dr Belinda Chiera Tutor: Day, Time, Location of Tutorial: Assignment number: 2 Due date: by 12 noon on Wednesday, Oct. 26, 2016 Assignment topic as stated in Course Outline: Case Study Report Further Information: (e.g. state if extension was granted and attach evidence of approval, Revised Submission Date)   I declare that the work contained in this assignment is my own, except where acknowledgement of sources is made. I authorise the University to test any work submitted by me, using text comparison software, for instances of plagiarism. I understand this will involve the University or its contractor copying my work and storing it on a database to be used in future to test work submitted by others. I understand that I can obtain further information on this matter at http://www.unisanet.unisa.edu.au/learningconnection/student/studying/integrity.asp Note: The attachment of this statement on any electronically submitted assignments will be deemed to have the same authority as a signed statement. Signed: Date: Date received from student Assessment/grade Assessed by: Recorded: Dispatched (if applicable): Quantitative Methods for Business QMag Analysis [Enter the date of submission] prepared by [Enter your name] Introduction This report provides an analysis of data pertaining to the sale of QMag. It encompasses a descriptive analysis, demographic analysis, sales forecast and sales distribution so as to understand the performance of the magazine, which areas to focus on and the future performance. Descriptive Analysis The aim of this section is to provide a descriptive analysis of the quarterly sales data from Q3_2015 to Q2_2016 across the different selling points; supermarkets, news agencies, petrol stations and subscription-based sales. This is intended to paint a clearer picture of the best selling point for QMag so as to determine whether there should be a focus on print sales. Figure 1; Quarterly Sales Clustered Column Chart On average, most magazine sales are made through supermarkets and subscriptions. However, most people buy the QMag through subscription apart for quarter four when most sales were realized through supermarkets. As indicated by the mean and mode, subscription-based sales were the most in Q2_2016 whereas the other quarters posted more sales through supermarkets. The measures give more accurate information compared to the mean. This is because the mean gives an average figure while the median and the mode point to the direction where there is more concentration of the data. The median is the most appropriate measure of central tendency and dispersion. It gives a more appropriate depiction of the data, particularly when it is skewed. Table 1; Relative Percentages for Supermarkets and Subscription-Based Sales Outlet Q4 2015 Q1 2016 Q2 2016 Supermarkets 33% -6% 80% Subscription -11% 6% 37% Demographic Analysis The aim of this section is to identify the age group that purchases the most QMags. This will be appropriate in determining the age group to target. Figure 2; 100% stacked bar chart QMag is most popular in age group 18 – 30. Under 18 and Over 45 age demographics are not worth targeting given that they represent a small sales portion compared to other age groups. The overall proportion of sales to the 18-30 and 30-45 age groups is 39.8 per cent and 38.7 per cent respectively. The sales proportion to the target 18-30 age group do not depend on each other. The sales to this target age group have been increasing across the four quarters. Therefore, QMag should continue to target this age demographic. Sales Forecast The aim of this section is to develop an appropriate forecasting model. The model will be vital in helping to estimate future sales. Figure 3; Scatterplot The scatterplot shows an uphill pattern and the front cover expenditure and marginal revenue show a strong positive relationship. This shows that front cover expenditure and marginal revenue are positively related, such that, as the front cover expenditure increases, the marginal revenue also increases. The rate of change is positive 0.1143, indicating that an increase in front cover expenditure leads to an increase in marginal revenue. The data points are also closely fit together at 83 per cent. This shows that the model is trustworthy to provide insight into speculated connection between front cover expenditure and magazine revenue. There are many residuals above the stated 68% cut-off values, and thus the model over-predicts when calculating Magazine Revenue. The largest residual is 7039.63, indicating an over-prediction of Magazine Revenue. y = 0.1143x + 42.068 Most data points are close to the fitted line, therefore, the model provides a good prediction tool. Data Distribution The aim of this section is to find out how data is spread out. This will enable us to determine if data is equally spread or is concentrated to some particular side. Most of the data points are close concentrated. There is no data point above the upper limit as well as below the lower limit. There no huge difference between the average figure of 34,539 and middle figure of 33,580. Besides, most data points lie closely above the average figure showing that most Buy it Now! Income earned is slightly above the average earning. Figure 3; Histogram of Buy it Now! Income Up to 0.6 per cent of Buy it Now! Income will be negative representing a loss for QMag. The company will earn $43,846 from 75 per cent sale of the QMag. Between 75 per cent - 90 per cent, QMag will earn an extra $8,474. Since the loss made in petite, and QMag has produced more income. Therefore, QMag should continue the Buy it Now! Conclusions and Recommendation In general, most magazine sales are made through supermarkets and subscriptions. QMag is most popular in age group 18 – 30 and the magazine should continue with Buy it Now! since the loss made in petite, and QMag has produced more income. Appendix 1 – Descriptive Analysis a) Q3_2015 Q4_2015 Q1_2016 Q2_2016 Mean 2.717029 2.669205 2.602312 2.519639 Standard Error 0.014438 0.014783 0.014764 0.011474 Median 3 3 3 2 Mode 3 3 3 2 Standard Deviation 0.807001 0.880277 0.868448 0.818783 Sample Variance 0.65125 0.774888 0.754201 0.670406 Kurtosis -0.39251 -0.76803 -0.65883 -0.5297 Skewness -0.23694 -0.059 -0.1095 0.071195 Range 3 3 3 3 Minimum 1 1 1 1 Maximum 4 4 4 4 Sum 8488 9465 9004 12830 Count 3124 3546 3460 5092 Q1 2 2 2 2 Q3 3 3 3 3 IQR 1 1 1 1 b) Outlier = 1.5 x IQR Minimum value = 2 – 1.5 = 0.5 Maximum value = 3 + 1.5 = 4.5 The minimum and maximum value in the data are 1 and 3 respectively. So there are no outliers. c) (i) Quantitative discreet data (ii) There are no outliers. For Q3_2015 to Q1_2016 have an equal median of 3 whereas Q2_2016 has a lower median of 2. The whisker lengths are the same for all the quarters. (iii) The distribution is distributed to the left, that is, the median is greater than the mode. Boxplot_chaty102 d) e) Outlet Q4 2015 Q1 2016 Q2 2016 Supermarkets 33% -6% 80% Subscription -11% 6% 37% Appendix 2 – Demographic Analysis a) b) Probability that a person who purchases QMag is in the demographic target age demographic of 18-30 = Number of people who purchases QMag is in the demographic target age demographic of 18-30 / Total number of people who purchases QMag = 6738 / 16923 = 0.398 Probability that a person who purchases QMag is in the demographic target age demographic of 30-45 = Number of people who purchases QMag is in the demographic target age demographic of 30-45 / Total number of people who purchases QMag = 6543 / 16923 = 0.387 c) P (A| B) = P (A) P (a person who purchases QMag is in the demographic target age demographic of 18-30) = 6738 / 16923 = 0.398 P (a person who purchases QMag is in the demographic target age demographic of 18-30 / Q3_2015) = 933 / 2824 = 0.330 P (a person who purchases QMag is in the demographic target age demographic of 18-30 / Q4_2015) = 1142 / 3146 = 0.363 P (a person who purchases QMag is in the demographic target age demographic of 18-30 / Q1_2016) = 1965 / 4660 = 0.422 P (a person who purchases QMag is in the demographic target age demographic of 18-30 / Q2_2016) = 2698 / 6293 = 0.429 0.398 ≠ 0.330 ≠ 0.363 ≠ 0.422 ≠ 0.429 Sales proportions to the target age demographic 18-30 are not statistically independent across the four sales quarters (Q3 2015, Q4 2015, Q1 2016 and Q2 2016). Appendix 3 – Sales Forecast a) b) The scatterplot shows an uphill pattern and the front cover expenditure and marginal revenue show a strong positive relationship. This shows that front cover expenditure and marginal revenue are positively related, such that, as the front cover expenditure increases, the marginal revenue also increases. Marginal revenue is the dependent variable while front cover expenditure is the independent variable. c) d) There are many residuals above the stated 68% cut-off values, and thus the model over-predicts when calculating Magazine Revenue. The largest residual is 7039.63, indicating an over-prediction of Magazine Revenue. Appendix 4 – Data Distribution a) Buy It Now ($ '000s)_chaty102 Descriptive Statistics Mean 34.5394044 Standard Error 0.636077065 Median 33.58011283 Mode #N/A Standard Deviation 13.89213279 Sample Variance 192.9913534 Kurtosis -0.055626351 Skewness 0.155825909 Range 81.5069638 Minimum -5.674920613 Maximum 75.83204319 Sum 16475.2959 Count 477 b) Probability that Income will be negative = number of negative outcomes / total number of outcomes = 3 / 477 = 0.006 i. 𝑧 = 𝑥 – 𝜇 / 𝜎 = x − 34539 / 13892 = 0.67 x − 34539 = 9307 x = 34539 + 9307 x = 43846 ii. 𝑧 = 𝑥 – 𝜇 / 𝜎 = x − 34539 / 13892 = 0.67 x − 34539 = 9307 x = 34539 + 9307 x = 43846 𝑧 = 𝑥 – 𝜇 / 𝜎 = x − 34539 / 13892 = 1.28 x − 34539 = 17781 x = 34539 + 17781 x = 52320 Amount of Income (in $’000 AUD) made between 75%-90% = 52320 – 43846 = 8474 Read More