Task 1: Ungrouped Descriptive Statistics [16 marks]
To gain some insights into the typical price consumers are willing to pay for a stand mixer, a retailer of kitchen appliances randomly selected 200 relevant invoices for transactions completed in October 2022. Descriptive statistics, computed to summarise the data, are presented in Table 1 below.Table 1.Expenditure (£) on Stand MixersMeanMedian 224.00Mode 220.00Standard DeviationSample Variance 5041.00RangeMinimum 68.00Maximum 369.00Sum 46400.00CountLower QuartileUpper Quartile 336.00Inter-quartile range (IQR) 241.00Coefficient of VariationRequired for Task 1 (50 words Max)With reference to Table 1, copy and fill in the table. Note: you must use a calculator and show all your workingsfor this task.a. State the value of the count and use it to calculate the mean [1+2 =3marks]b. Calculate the range [1mark]c. Calculate the Lower quartile [2marks]d. Calculate the standard deviation of the sample [2marks]e. Calculate the coefficient of variation, giving your answer as a percentage (%) to the nearest whole number [2marks]f. Interpret the Standard deviation in the context of the scenario provided. [2marks]g. Interpret the Interquartile range in the context of the scenario provided. [2marks]h. Interpret the coefficient of variation [2marks](NB: You should not describe calculation methods).
Task 2: Grouped Descriptive Statistics [22marks]
It was suggested to the retailer that the 200 transaction values could also be summarised in a grouped table (see Table 2 below). Table 2 have been made available in the Excel file named “MN4063QANOVS22CWK1 Data” under the worksheet named Task 2.
Required for Task 2 (50 words Max)
a. Using the two table templates provided in the Excel data file named “MN4063QANOVS22CWK1Data” under the tab labelled Task 2:
Complete table 2a to show the percentage frequencies, cumulative frequencies and cumulative percentage frequencies columns. [1+1+1 = 3marks]. Round all answers to the nearest whole number
Complete table 2b and use your results to estimate the mean and the standard deviation. [10 +2+2 = 14marks]. Round all answers to the nearest whole number(Copy the Excel output (2 tables) and paste it into your Word document)
b. From table 2 estimate the median expenditure of the consumers using the interpolation method. Show all your working using a calculator. [2 + 3 = 5marks]. Round your answer to the nearest whole number
Task 3: Data Types [8 marks]To better understand its target consumers and strengthen its position in the market, the kitchen appliances retailer seeks to survey its customers to gain insights into key consumer characteristics, such as demographic profiles and lifestyle preferences. However, before outsourcing the data collection fieldwork, the retailer seeks clarification on data types, as outlined in the requirements below.
Required for Task 3 (100 words Max)
a. With reference to examples relevant to the retailer’s information needs, discuss the differences between cross-sectional data and time series data. [4marks]
b. State whether cross-sectional data, time series data or both types of data should be collected to gain insights into the demographic profile and lifestyle preferences of its customers. Justify your answer [4mark] (Use c r e d i b l e sources. The citation and reference must be credited using the Harvard method).
Task 4: Sampling [8marks] [max 120 words]Explain how the kitchen appliances retailer can apply the stratified sampling technique to select the required 200 relevant invoices to make the right decision in task 3 above.(Use c r e d i b l e sources. The citation and reference must be credited using the Harvard style).
Task 5: Networking [16 marks]The retailer has seen a shift in the way in which consumers purchase items, such as kitchen appliances. Online retailing now accounts for over 80% of their sales and, to reflect this change, the retailer has decided to convert some of its retail space into warehouse space. This conversion project consists of 10 activities.
For example,Activity C takes 3 weeks to complete and can only be started after Activity A has been completed. Informationon the 10 activities is outlined in Table 3 below.Precedence Table
Activity Preceding Activity Duration (Weeks)A ……… 6B ……… 4C A 4D B 2E C 6F C,D 5G D 3H …….. 8I E,F,G 5J H,I 2Required for Task 4 (50 words Max)With reference to the precedence table above, construct a network diagram by going through the:a. Forward and backward. passes [4 +4 = 8marks]b. Identify the critical path and duration of the project. [2+2= 4marks]c. Comment on the difference between critical activities and non-critical activities. [2 +2 =4marks]Note: Draw your network diagram in Excel. The network diagram needs to be copied into your Word file.
Task 6: Correlation and Regression [30 marks]
To allocate resources effectively, the retailer wants to better understand the reason why sales revenue may increase or decrease. To this end, refer to the data provided under the worksheet named Task6 in the “MN4063QANOVS22CWK1Data” Excel file.
Required for Task 6 (150 words Max)
a. Construct a correlation matrix using Excel to show the correlation coefficients between Sales Revenue, Total Costs, Average Order value and Gross Profit. Copy and paste the correlation matrix into your Wordfile. [4marks]
b. With reference to the correlation matrix, identify the ‘best’ predictor of Sales Revenue and justify the reason for your choice. [2marks]
c. Create a scatter graph, plotting Sales Revenue against the ‘best’ predictor selected under part (b) above.
The trend line, regression equation and coefficient of determination should be shown on the graph. Copy the correctly labelled graph, with the correct units of measurement, into your Word file. [10marks]
d. Interpret the correlation coefficient in context. [3mark]
e. Interpret the coefficient of determination in context. [3mark]
f. State the regression equation in context. [2mark]
g. Interpret the value of the intercept in context. [3mark]
h. Interpret the value of the gradient in context. [3mark]
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