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 150 relevant invoices for transactions completed in March 2023 from their

Birmingham Branch. Descriptive statistics, computed to summarise the data, are presented in Table 1 below.

Table 1.

Expenditure (£) on Stand Mixers

Minimum 150

Maximum 400

Sum 45000

Count

Lower Quartile 120

Upper Quartile

Inter-quartile range (IQR) 220

Coefficient of Variation

Mean

Median 225

Mode 200

Standard Deviation

Sample Variance 2500

Range 250

Required 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 workings

in a word document for this task.

a. State the value of the count and use it to calculate the mean [1+2 =3marks]

b. Calculate the upper quartile [2marks]

c. Calculate the standard deviation of the sample [2marks]

d. Calculate the coefficient of variation, giving your answer as a percentage (%) to the nearest

whole number [2marks]

e. Comment on the distribution of the data [3mark]

f. Interpret the Standard deviation in the context of the scenario provided. [2marks]

g. Interpret the median in context of the scenario provided [2marks]

(NB: You should not describe calculation methods).

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MN4063QA Understanding and Managing Data APRIL23 Intake

Task 2: Grouped Descriptive Statistics [22marks]

It wassuggested to the retailer that the 150 relevance invoices transaction in Question (1)from Birmingham Branch above

could be grouped (see Tables below).

Required for Task 2 (50 words Max)

2a. Complete the table below to show the percentage frequencies, cumulative frequencies, and cumulative

percentage frequencies columns. [1+1+1 = 3marks]. Round all answers to the nearest whole number

Price band (£) Number of Invoices

140 to less than 160 18

160 to less than 170 21

170 to less than 180 46

180 to less than 200 30

200 to less than 250 25

250 to less than 350 10

2b. Use the information on table below to estimate the mean and the standard deviation. [10 +2+2 = 14marks]. Round

all answers to the nearest whole number. Show all your working out

Price band (£) Number of Invoices

140 to less than 160 18

160 to less than 170 21

170 to less than 180 46

180 to less than 200 30

200 to less than 250 25

250 less than 350 10

2c. From the table above (2b), estimate (interpolate) the median expenditure of the consumers. Show all your working

using a calculator. [3marks]. Round your answer to the nearest whole number

2d. A similar survey is conducted on the retailer shop located in London. The mean is estimated to be £200,000

with a standard deviation of £15,000. Use two brief sentences to describe the main differences between the

Birmingham and London Branches, considering the means and the standard deviations. [2marks]

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MN4063QA Understanding and Managing Data APRIL23 Intake

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 Harvardmethod).

Task 4: 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 ActivityA has been completed. Information on

the 10 activities is outlined in Table 3 below.

Precedence Table

Activity Preceding Activity Duration (Weeks)

A ….. 5

B ….. 3

C A 4

D B 3

E C 5

F C, D 3

G D 6

H ….. 4

I E, F, G 2

J H, I 3

Required 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 5: Sampling [8marks] [max 120 words]

Explain how the kitchen appliances retailer can apply the stratified sampling technique to select the required 150 relevant

invoices from a total number of 3000 invoices, for the survey.

(Use c r e d i b l e sources. The citation and reference must be credited using the Harvard style)

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MN4063QA Understanding and Managing Data APRIL23 Intake

PART 2 [30marks]

Task 6: Correlation and Regression [30 marks]

To allocate resources effectively, the retailer wants to better understand the relationship between the variables

shown on the table below.

Average order value Value of sales (£millions)

12.8 8.7

16.8 9.6

5.5 5.2

20.5 10.3

14.2 6.4

28 11.8

10.9 9.2

15.6 8.5

19.6 8.4

7.5 5.9

Required for Task 6 (150 words Max)

a. State, giving a brief explanation which variable would be the dependent variable [4marks]

b. Create a scatter graph, plotting value of sales against the average order value. 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]

c. Interpret the correlation coefficient in context. [4mark]

d. Interpret the coefficient of determination in context. [4mark]

e. State the regression equation in context. [2mark]

f. Interpret the value of the intercept in context. [3mark]

g. Interpret the value of the gradient in context. [3mark]