correctly calculate relevant statistics, analyse the data and provide/ demonstrate:

Understanding and Managing Data

You are required to correctly calculate relevant statistics, analyse the data and provide/ demonstrate:

Clear interpretations of all statistical analyses (do not just state the values but comment on what the values imply without speculating, where required).

Graphs and tables with informative titles, appropriate labelling and units stated.
Accurate calculations where required (equations are stated in the context of the data);
Comments written in the context of the meaning of the data or analysis.
Appropriate use of Excel functions, as evidenced by the output.
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Task 1: Ungrouped Descriptive Statistics

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 Mixers

Mean

 

Median

224.00

Mode

220.00

Standard Deviation

 

Sample Variance

5041.00

Range

 

Minimum

68.00

Maximum

369.00

Sum

46400.00

Count

 

Lower Quartile

 

Upper Quartile

336.00

Inter-quartile range (IQR)

241.00

Coefficient of Variation

 

 

Required for Task 1

With reference to Table 1, copy and fill in the table. Note: you must use a calculator and show all your workings for this task.

State the value of the count and use it to calculate the mean
Calculate the range
Calculate the Lower quartile
Calculate the standard deviation of the sample
Calculate the coefficient of variation, giving your answer as a percentage (%) to the nearest whole number
Interpret the Standard deviation in the context of the scenario provided.
Interpret the Interquartile range in the context of the scenario provided.
Interpret the coefficient of variation

Task 2: Grouped Descriptive Statistics

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
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. Round all answers to the nearest whole number

From table 2 estimate the median expenditure of the consumers using the interpolation method. Show all your working using a calculator. Round your answer to the nearest whole number

Task 3: Data Types
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)
With reference to examples relevant to the retailer`s information needs, discuss the differences between cross-sectional data and time series data.
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

Task 4: Sampling

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.

Task 5: Networking
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. Information on the 10 activities is outlined in Table 3 below.

Required for Task 4 (50 words Max)
With reference to the precedence table above, construct a network diagram by going through the:
Forward and backward. passes
Identify the critical path and duration of the project.
Comment on the difference between critical activities and non-critical activities.

PART 2

Task 6: Correlation and Regression
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
Construct a correlation matrix using Excel to show the correlation coefficients between Sales Revenue, Total Costs, Average Order value and Gross Profit.

With reference to the correlation matrix, identify the ‘best` predictor of Sales Revenue and justify the reason for your choice.

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.
Interpret the correlation coefficient in context.
Interpret the coefficient of determination in context.
State the regression equation in context.
Interpret the value of the intercept in context.
Interpret the value of the gradient in context.