BPP Business School: Business Mathematics Coursework Report

This coursework report for a Business Mathematics module covers a range of statistical analysis techniques applied to real-world business scenarios. The report begins with an analysis of daily frozen yogurt sales data using time series analysis, including plotting the data, calculating seven-point moving averages, and constructing a decomposition model to identify trends. The report then moves on to descriptive statistics, including clustered and stacked bar charts, and pie charts to interpret employment status of students. Further analysis includes frequency tables, histograms, and calculations of mean, median, mode, and standard deviation for exam scores, followed by a comparative commentary. Finally, the report examines the relationship between house size and sales price using scatter diagrams, correlation coefficients, and regression analysis to predict house prices based on size, explaining the gradient and intercept of the regression equation, and providing commentary on the findings.

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Business mathematic
coursework

Contents
QUESTION 1..................................................................................................................................1
a) Plotting the data over time.......................................................................................................1
b) Seven-point moving averages.................................................................................................1
c) Decomposition model..............................................................................................................3
QUESTION 2..................................................................................................................................4
a) Clustered bar chart...................................................................................................................4
b) Stacked bar chart.....................................................................................................................4
c) Pie chart...................................................................................................................................5
d) Interpretations..........................................................................................................................5
QUESTION 3..................................................................................................................................5
a) Suitable frequency table using an interval of 10.....................................................................5
b) Plotting a histogram.................................................................................................................6
c) Calculation of Mean, Median, Mode and Standard deviation.................................................7
d) Commentary............................................................................................................................7
QUESTION 4..................................................................................................................................8
a) Plotting a scatter diagram........................................................................................................8
b) Calculating the correlation coefficient....................................................................................8
c) Determining the regression equation.......................................................................................9
d) Explaining the following.........................................................................................................9
e) Using your regression equation...............................................................................................9
f) Commentary...........................................................................................................................10

QUESTION 1
a) Plotting the data over time
Mon Tue Wed Thu Fri Sat Sun
Week 1 218 224 319 489 553 678 492
Week 2 289 260 431 660 777 915 613
Week 3 370 313 556 831 960 1152 759
Week 4 443 374 660 1004 1153 1388 904
b) Seven-point moving averages
Mon Tue Wed Thu Fri Sat Sun
Week 1 218 224 319 489 553 678 492
Week 2 289 260 431 660 777 915 613
Week 3 370 313 556 831 960 1152 759
Week 4 443 374 660 1004 1153 1388 904
Moving averages
Week 1 #N/A 221 271.5 404 521 615.5 585
Week 2 #N/A 274.5 345.5 545.5 718.5 846 764
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Week 3 #N/A 341.5 434.5 693.5 895.5 1056 955.5
Week 4 #N/A 408.5 517 832 1078.5 1270.5 1146
2

Moving averages are calculated in Excel following below steps:
 Use data analysis function in Data tab.
 Select Moving averages option from the drop down list.
 Select the Week 1 data and insert 2 decimal point.
 Repeat it for every week data.
c) Decomposition model
By computing the seven point moving averages, it has been ascertained that multiplicative
decomposition model should have been used here. Multiplicative model shows non stable
frequencies which means sales over the weeks are fluctuating and showing increasing and
decreasing trend. As it can be seen in above developed graphs, the sales over weeks are first
increasing and then reducing which implies that in this case there is a multiplicative model.
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QUESTION 2
a) Clustered bar chart
b) Stacked bar chart
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c) Pie chart
d) Interpretations
Clustered bar chart – From the developed cluster bar chart, it is analysed that the students
which have completed their graduation with the stream of accounting are maximum employed at
permanent positions. Students of business stream are less unemployed than the students of
accountancy stream.
Stacked bar chart – From the developed stacked chart, it is evidently seen that the survey is
conducted for accounting and business streams. In both the streams, maximum students have
permanent employment status, some students are a temporary position at their job posts and only
few students are unemployed.
Pie chart – In case of the pie chart, it has been seen that the maximum of students is
employed at permanent position comprising a total of 227 students. Apart from this, 55 students
are at temporary job positions and 28 students are unemployed which combines students of both
streams i.e., business and accounting.
QUESTION 3
a) Suitable frequency table using an interval of 10
Marks Interval Exam 1 Exam 2
1 01-10 0 0
2 11-20 0 0
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3 21-30 0 0
4 31-40 1 0
5 41-50 1 0
6 51-60 3 1
7 61-70 14 5
8 71-80 2 10
9 81-90 9 11
10 91-100 10 11
Total 40 38
b) Plotting a histogram
Histogram for Exam 1
Histogram for Exam 2
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c) Calculation of Mean, Median, Mode and Standard deviation
Mean mark 75.675 81.6579
Median 75.5 82.5
Mode 65 94
Standard deviation 15.722575 11.4237
d) Commentary
As mentioned in the case scenario, test results of Exam 1 are required to be compared with
Exam 2. After developing the frequency tables for each exam, it is observed that a total of 40
students attended Exam 1 but the reduced and only 38 students attended Exam 2. This variation
of students implies that 2 students were dropped from the course due to low attendance. It is also
found from the frequency table that in Exam 2, there are more students who have scored good
marks as the scores between the range of 71-80 is attained by only 2 students in exam 1 but in
exam 2, a total of 10 students have scored this mark.
From the “c” part of the analysis, it has been analysed that the average or mean mark in
Exam 1 was 75.67 but it increased in Exam 2 as 81.65. Along with this in the case of exam 1, the
mode ascertained as 65 which means maximum number of students have acquired the mark of 65
but this increased to 94 in case of Exam 2 which provides a clear evidence that the new
attendance policy implemented by tutor is effective.
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QUESTION 4
a) Plotting a scatter diagram
House Size
(square meters) 230 110 200 170 150 210 240 130 190 250
Sales Price
(thousands of
pounds) 180.0 98.1 173.1 136.5 141.0 165.9 193.5 127.8 163.5 172.5
From the above scatter diagram, it has been seen that with every increasing square meter
of a house size, its price increases. Above scatter diagram suggests that the house size of 240 sq.
meter is most demanded as the cost for 240 sq. meter house is 193500 pounds which is even
higher than the house of 250 sq. meter.
b) Calculating the correlation coefficient
Correlation coefficient is the statistical measure which states the relationship between two
variables. In context of given data, relationship between sales price and house size is determine
using Excel formula of “=CORREL” by which value of relationship is gained as 0.93
Correlation coefficient 0.93786
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