BPP University Business Mathematics Coursework: Comprehensive Analysis

This document presents a comprehensive solution to a Business Mathematics coursework, addressing various aspects of data analysis and statistical methods. The assignment covers time series analysis, including moving averages and decomposition models, applied to sales data. It also involves cluster, stacked, and pie charts to analyze employment status based on academic streams. Furthermore, the solution includes frequency tables, histograms, and calculations of mean, median, mode, and standard deviation to compare exam scores. Finally, regression analysis, scatter plots, and correlation coefficients are utilized to examine the relationship between house size and sales price, providing insights into market trends. This resource offers detailed explanations and interpretations, making it a valuable tool for students studying business mathematics.

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Business mathematic
coursework

Contents
QUESTION 1..................................................................................................................................1
a)..................................................................................................................................................1
b)..................................................................................................................................................1
c)..................................................................................................................................................2
QUESTION 2..................................................................................................................................3
a)..................................................................................................................................................3
b)..................................................................................................................................................3
c)..................................................................................................................................................4
d)..................................................................................................................................................4
QUESTION 3..................................................................................................................................4
a)..................................................................................................................................................4
b)..................................................................................................................................................5
c)..................................................................................................................................................6
d)..................................................................................................................................................6
QUESTION 4..................................................................................................................................7
a)..................................................................................................................................................7
b)..................................................................................................................................................7
c)..................................................................................................................................................8
d)..................................................................................................................................................8
e)..................................................................................................................................................8
f)...................................................................................................................................................8

QUESTION 1
a)
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
Daily frozen yogurt Sales
b)
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
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
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
Moving averages
1

Day 1
Day 3
Day 5
Day 7
Day 9
Day 11
Day 13
Day 15
Day 17
Day 19
Day 21
Day 23
Day 25
Day 27
0
200
400
600
800
1000
1200
1400
Moving averages
Series1
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 1 data and insert 2 decimal points.
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.
2

QUESTION 2
a)
Accountancy
Business
0 20 40 60 80 100 120 140 160 180
170
57
28
27
Cluster chart
Unemployed Temporary Permanent
Employment Status
Stream
b)
Permanent
Temporary
Unemployed
0 50 100 150 200 250
Stacked chart
Accountancy Business
Stream
Employment Status
3

c)
73%
18%
9%
Pie chart
Permanent Temporary Unemployed
d)
Clustered bar chart – A clustered chart is prepared for the purpose of analysis, from which
insights are gained that people who have education qualification of accounting are more
employed at the positions with permanent positions. Another insight which has been gained is
that people with business stream qualification have lower rate of unemployment.
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)
Marks Interval Exam 1 Exam 2
1 01-10 0 0
4

2 11-20 0 0
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)
Histogram for Exam 1
01-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-
100
0
2
4
6
8
10
12
14
16
Exam 1
Marks Interval
Score
Histogram for Exam 2
5

01-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-
100
0
2
4
6
8
10
12
Exam 2
Marks Interval
Score
c)
Mean 75 81
Median 75 82
Mode 65 94
SD 15.7
11.423
7
d)
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 has 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.
6

QUESTION 4
a)
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.
meters 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)
The concept of correlation determines the relationship between two different variables
from which one is independent variable and another is independent variable. In the current
scenario the dependent variable is sales price and the independent variable is house size. Using
Microsoft Excel application the correlation Coefficient is determined. The formula which has
been used is “=CORREL” and the value of correlation coefficient is 0.93.
7

c)
Using the Microsoft application of Excel, scatter plot graph is used to determine the
regression equation that can be utilised to estimate the average price of a house. The regression
equation is:
y = 0.57x+48.024
d)
(i)
This represents a significant positive relationship between sale price and house size.
(ii)
The slope of regression equation shows the relationship between two variables which is
linear. In the current scenario, regression equation shows that with increasing size of house, the
sale price of house will also increase.
(iii)
The intercept of the regression equation represents the constant relationship between the
two variables. In the present context, if the regression equation would have shown intercept, then
the house of price would not be affected with the size of the house.
e)
f)
8

By predicting the average sale price of the houses of 200 and 300 square meter, it has been
observed that which the increasing size of the house property, the value of that house also
increases.
9