TH50117E Statistics Assignment: Data Analysis and Interpretation

This statistics assignment solution provides a detailed analysis and interpretation of data, including calculations of mean for grouped and ungrouped data, explanations of nominal and ordinal data, and the application of moving averages for forecasting. The solution covers calculations and interpretations of four-year moving averages to forecast sales, along with graphical representations of seasonal variations and sales forecasts. It also identifies factors impacting forecasts, such as changes in the moving average model and forecasting methods. This assignment, likely part of the TH50117E course, offers insights into statistical methods relevant to sales and marketing contexts. Desklib provides this solution and other resources to aid students in their studies.

Running head: STATISTICS
STATISTICS
Name of the Student
Name of the University
Author Note

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Table of Contents
Part 2................................................................................................................................................2
Answer to Question 1..................................................................................................................2
Answer to Question 2..................................................................................................................3
Answer to Question 3..................................................................................................................3
Part 3................................................................................................................................................4
Answer to Question 1..................................................................................................................4
Answer to Question 2..................................................................................................................5
Answer to Question 3..................................................................................................................6
Answer to Part 4..........................................................................................................................6
Answer to Question 5..................................................................................................................7
Bibliography....................................................................................................................................8

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Part 2
Answer to Question 1
The mean of a grouped data is different from ungrouped because in the ungrouped data,
the mean is often exact whereas in ungrouped data, the mean is generally an average of the
specific range which is given.
Ungrouped data
1, 2, 4,5,6,7
Mean=25/6
Mean=4
Grouped data
Groups Frequency Class mark fX
1-3 2 2 4
4-6 3 5 15
7-9 1 8 8
Total 6 27
Mean: 4.3

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As it can be seen that the mean which is present in both the given set of data is quite
different from one another and hence, the manager needs to go with the mean of the ungrouped
data but it is more true to the real answer. Moreover, in cases the manager is unable to decide
upon the selection of the right mean, then the median can be used instead of the mean.
Answer to Question 2
The nominal scaled data can be rightfully described as that data which is used to label the
variables which do not have a quantitative value. This means the nominal data makes the user
choose between different options. Examples for this may be questions like whether the user is a
make or a female, the color of their hair, the location, their choices and preferences. It is simply
termed as labels.
On the other hand, the ordinal data can be described as the data whereby the values for
each data is crucial for the analysis but the differences between those data’s are not known. In
cases like the ratings like 4, 3, 2 or 1, there is no manner in which it can be quantified hoe better
or how good one is. The ordinal data generally measures the non-numeric concepts like
discomfort, satisfaction and happiness.
Hence, for a hotel café, both the nominal data as well as the ordinal data is crucial as the
nominal data helps them in understanding the consumer choice and the ordinal data helps them
in understanding whether the particular customer will be satisfied with the services of the firm or
not.
Answer to Question 3
The mean can be rightfully defined as the average of all the numbers and is often known
as the arithmetic mean which helps in understanding what number is the most adaptable to every

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situation. The mean power helps in power distribution and determining the most common
number of all.
On the other hand, the median is the middle number of all sequence of numbers. To find
the median, the numbers need to be arranged in ascending order and the answer can be found.
Between the mean and the median, the mean serves as an accurate source of measure to
understand. For instance between numbers like 1, 22,333,444,555. The mean would be the
average that is approximately 4 whereas the median might be 3, 4 or 5.
Part 3
Answer to Question 1
The four year moving average is the model choice which has been taken for the particular
data. In the analysis of this, it will be suitable to calculate the average for each year based on the
quarter.
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3
2015 2016 2017 2018
0
10
20
30
40
50
60
70
80
90
100
Moving Average
Graph 1

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Answer to Question 2
Year Quarter
s
Sales
2015 Q1 3 #N/A #N/A
Q2 22 #N/A #N/A
Q3 45 #N/A #N/A
Q4 6 19 #N/A
2016 Q1 5 19.5 #N/A
Q2 25 20.25 #N/A
Q3 61 24.25 20.9306
9
Q4 12 25.75 21.0501
6
2017 Q1 8 26.5 21.8199
3
Q2 30 27.75 21.7194
5
Q3 75 31.25 24.7509
5
Q4 17 32.5 25.0081
2
2018 Q1 12 33.5 25.6009
Q2 56 40 26.7981

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5
Q3 93 44.5 28.7695
6
In the given method, the sum of the sales of every four quarters is taken and divided by
four. This calculation continues till the end of the particular quarter. The given graph reflects the
seasonal average of the particular sales figure. The final values achieved reflect that the average
sales every season will be between the ranges of 20 to 50 which reflects that the sales will be
consistent throughout. Hence, the manager needs to understand that 20-50 needs to be the
expected range of sales to be incurred by the company.
Answer to Question 3
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3
2015 2016 2017 2018
0
10
20
30
40
50
60
70
80
90
100
Moving Average
Actual
Forecast
Time period
Sales
Graph 2
`Hence, the given graph shows the average seasonal variation with respect to the sakes
figures of the hotel café. The orange line depicts the forecasts which have been made using the

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moving average of 4 years and the blue graph line represents the actual sales figure until the year
2018. The x axis represents the quarters and the y axis represents the sales figures in £000`s.
Answer to Part 4
Year
Quarter
s Sales
Average after one
analysis
Average after second
analysis
2015 Q1 3
Q2 22
Q3 45
Q4 6 19 #N/A
2016 Q1 5 19.5 #N/A
Q2 25 20.25 #N/A
Q3 61 24.25 20.93068919
Q4 12 25.75 21.0501633
2017 Q1 8 26.5 21.81993068
Q2 30 27.75 21.71944693
Q3 75 31.25 24.75094695
Q4 17 32.5 25.00812368
2018 Q1 12 33.5 25.6009033

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Q2 56 40 26.79814592
Q3 93 44.5 28.76955856
Answer to Question 5
The three different factors which can have an impact on the forecasts are as follows:
 The change in the model choice of moving average. In case three years or five years are
chosen, the results will be different.
 The change in the method of forecasting
 The range of the numbers of the time period used.
Bibliography
Berenson, M., Levine, D., Szabat, K.A. and Krehbiel, T.C., 2012. Basic business statistics:
Concepts and applications. Pearson higher education AU.
Black, K., 2009. Business statistics: Contemporary decision making. John Wiley & Sons.
Croxton, F.E. and Cowden, D.J., 1939. Applied general statistics.
Groebner, D.F., Shannon, P.W., Fry, P.C. and Smith, K.D., 2011. Business statistics: A decision
making approach. Prentice Hall/Pearson.
Lind, D.A., Marchal, W.C. and Wathen, S.A., 2006. Basic statistics for business & economics.
Newbold, P., Carlson, W. and Thorne, B., 2012. Statistics for business and economics. Pearson.
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