Reference no: EM133898352
Understanding and Managing Data
PART 1
Task 1: Ungrouped Descriptive Statistics
To gain some insights into the typical price consumers are willing to pay for a Multi mixer, a retailer of kitchen appliances randomly selected relevant invoices for transactions completed in Jan 2024 from their Birmingham branch shop. Descriptive statistics, computed to summarise the data, are presented in the table below. Round all answers to the nearest whole number.
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Expenditure (£) on Multi Mixers
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|
Mean
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205
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Median
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219
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Mode
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195
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Standard Deviation
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72
|
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Sample Variance
|
|
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Range
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300
|
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Minimum
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120
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Maximum
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420
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Sum
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30,750
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Count
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|
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Lower Quartile
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|
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Upper Quartile
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290
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Inter Quartile Range (IQR)
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170
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Coefficient of Variation
|
|
Required for Task 1
With reference to table above, copy and fill in the table and show all your working out as follows:
Correct completed table
Calculate the count
Calculate the lower quartile
Calculate the coefficient of variation, giving your answer as a percentage (%) to the nearest whole number
Calculate the sample variance
Comment on the distribution of the data
Interpret the Standard deviation in the context of the scenario provided.
Interpret the mode in context of the scenario provided
Task 2: Grouped Descriptive Statistics
It was suggested to the retailer that the invoices transactions from their London Branch above could be grouped (see Tables below).
Required for Task 2 (Max 50 words)
2a. Complete the table below to show the percentage frequencies, cumulative frequencies, and cumulative percentage frequencies columns. Round all answers to the nearest whole number.
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Price band (£): Lower- and Upper-class boundary
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Number of
Invoices(f)
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Percentage Frequency
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Cumulative Frequency
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Percentage cumulative
Frequency
|
|
100
|
150
|
20
|
|
|
|
|
150
|
200
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34
|
|
|
|
|
200
|
250
|
30
|
|
|
|
|
250
|
300
|
29
|
|
|
|
|
300
|
350
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24
|
|
|
|
|
350
|
400
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13
|
|
|
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2b. Use the information on table below to estimate the mean and the standard deviation.
|
Price band (£): Lower- and Upper-class boundary
|
Number of
Invoices(f)
|
|
100
|
150
|
20
|
|
150
|
200
|
34
|
|
200
|
250
|
30
|
|
250
|
300
|
29
|
|
300
|
350
|
24
|
|
350
|
400
|
13
|
2c. From the table above (2b), estimate (interpolate) the median expenditure of the consumers.
2d. A similar survey is conducted on their retailer shop located in Manchester. The mean is estimated to be £215 with a standard deviation of £73. Use two brief sentences to describe the main differences between Manchester compared to Birmingham, and London Branches, considering the means and the standard deviations.
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 (Max 100 Words)
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: Networking
The retailer is considering manufacturing a state-of-the-art boiler. The table shows the processes required from product research to product launch. The table also includes the necessary staffing requirements to undertake the project. Get Assignment Help from the Best tutors!
Precedence table
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Activity
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Description
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Preceding
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Duration
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|
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activities
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(Weeks)
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A
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Product research
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-
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5
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B
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Preliminary market research
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-
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7
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C
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Design boiler
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A
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5
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D
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Make prototype
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C
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6
|
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E
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Costing
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B
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4
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F
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Feasibility report
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D, E
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5
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G
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Product testing
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D
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6
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H
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Market research
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F
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5
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I
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Initial advertising campaign
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H
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7
|
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J
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Produce first commercial batch
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G, I
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5
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Required for Task 4 (Max 50 Words)
Draw a network diagram for the project
Determine how long it will take from product research to product launch and the activities on the critical paths.
Identify the activities and their duration on the non-critical paths Get Assignment Help from the Best tutors!
Explain the significance of the critical paths.
Task 5: Sampling (Max 120 words)
Explain how the kitchen appliances retailer can apply the stratified sampling technique to select 300 invoices from a total number of 2500 invoices, for a survey.
PART 2
Task 6: Correlation and Regression
To allocate resources effectively, the retailer wants to better understand the relationship between the variables shown on the table below.
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Average order value (£000)
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Value of sales (£millions)
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£12
|
12
|
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£16
|
16
|
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£13
|
14
|
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£10
|
11
|
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£27
|
20
|
|
£22
|
23
|
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£14
|
15
|
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£19
|
18
|
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£25
|
23
|
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£23
|
22
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Required for Task 6
State, giving a brief explanation which variable would be the dependent variable.
Create a scatter graph, plotting the value of sales against the average order value. All variables with units. The trend line, regression equation and coefficient of determination should be shown on the graph.
Interpret the correlation coefficient in context.
Round answers to 2 decimal places. Show your working.
Interpret the coefficient of determination in context.
Round answers to the nearest whole number. Show your working.
State the regression equation in context.
Interpret the value of the intercept in context.
Interpret the value of the gradient in context.