Statistics Homework: Descriptive Statistics and Data Analysis

This assignment presents a comprehensive analysis of statistical concepts. It begins with ungrouped and grouped descriptive statistics, calculating measures like mean, standard deviation, and frequency distributions. The assignment then explores data types, networking analysis, and correlation between variables, including sales revenue and average order value. Regression analysis is performed, and expected values are calculated for different ventures. The second part of the assignment applies the high-low method in costing, calculates break-even points, and analyzes the advantages and disadvantages of break-even analysis. The document uses tables, formulas, and plots to explain the statistical concepts.

Coursework

Table of Contents
PART 1............................................................................................................................................3
Task 1: Ungrouped Descriptive statistics....................................................................................3
Task 2 grouped Descriptive statistics..........................................................................................3
Task 3 Data type.........................................................................................................................4
Task 4 Networking......................................................................................................................5
Task 5 Relationship.....................................................................................................................7
Task 6 Expected values...............................................................................................................9
Task 7..........................................................................................................................................9
Part 2..............................................................................................................................................10
REFERENCES..............................................................................................................................12

PART 1
Task 1: Ungrouped Descriptive statistics
a. Calculate the count and standard deviation using the table given
Expenditure (£) on Stand
Mixers
Mean 224.00
Standard Error 6.58
Median 224.00
Mode 224.00
Standard Deviation 75.00
Sample Variance 5625.09
Kurtosis -0.49
Skewness -0.32
Range 301.00
Minimum 68.00
Maximum 369.00
Sum
29120.0
0
Count 130.00
Coefficient of
Variation 33.5%
b. If mean, mode and median are same then the distribution is considered as normal one. It
means there is an equality on both the side. It is considered as truly normal distribution.
This also implies that the data appears at equal frequency in the observation table. While
the standard deviation implies that there is deviation between the values and mean by 75.
Task 2 grouped Descriptive statistics
a.
Expenditure (£) Frequency
Frequency
(%)
Under 100 14 11.54
100 and under 200 35 37.69
200 and under 300 65 86.92
300 and over 16 100

Total: 130 236.1538462
Expenditure (£)
Frequency
(f) midpoint (x) fx (x-mean) (x-mean)2 f(x-mean)2
Under 100 14 50 700 17.5 306.25 4287.5
100 and under 200 35 150 5250 -117.5 13806.25 483218.75
200 and under 300 65 250 16250 -217.5 47306.25 3074906.25
300 and over 16 350 5600 -317.5 100806.25 1612900
Total: 130 800 27800 -635 162225 5175312.5
Mean 32.5
Variance 54075
Standard Deviation 116.076
Where mean is average total frequency with the number of observation. Variance and standard
deviation is the deviation from the mean value of the observation.
B) In order to be under 25% the customer needed are 14 which fall in the range of 100-85.
Task 3 Data type
For better understanding the customer profile various aspect need to be understood to make the
research useful. When studies are performed data need to be extracted from the people,
publication and other source. Both the type of data is useful for the study however there is major
difference between the these are:
Cross-sectional data- here, the observation is related to many variables at specific point of time.
in this data about the customer will be collected for particular duration but under this many
aspects about the customer can be analysed.
Time series data- It the information about a single variable at different point of time. In this
scenario it is customer behaviour in regard to trend in different years.

Task 4 Networking

B
0 5 5
5 3 8
8 5 13

c. Diffrence between critical and non critical activities.
(a) As the name suggest those process or action which is unavoidable, importnant and are to
be finished on priority basis are considred as critical activities. While the non critrical
activities rae those which can be delayed during a project. Critical aactivities have
beginging and end point. Here in the scenerio the project non-critical activities are B, D,
F, G, and H.
Task 5 Relationship
Sales
Revenue
(£'000)
Total
Costs
(£'000)
Average Order
Value
(£)
Gross
Profit
(£'000)
Sales Revenue
(£'000) 1
Total Costs (£'000) 0.546350669 1
Average Order
Value (£) 0.973533731 0.466050155 1
Gross Profit (£'000) 0.42291345 0.842573515 0.333656281 1

b) Correlation defines the relationship between two variables irrespective of their dependency.
The above Metrix defines that average total order and sales revue is highly correlated. That
means that if one moves the other variable variable moves in the same direction. For determine
the gross profit sales revenue that is because if the upper turnover depicts a higher gross profit
and vice versa.
c)
D) a correlation value lies between -1 to 1, in the current scenario there is high correction
between the sales revenue. In the current model the coefficient of determination is 95% that
means that it very well fit in the equation constructed.
E) regression equation is
Scatter plot between Sales Revenue (£'000) and Average order value
120.00
100.00
80.00 f(x) = 0.03 x + 10.68
R² = 0.95
60.00 Average Order Value (£)
Linear (Average Order Value (£))
40.00
20.00
0.00
0 500 1000 1500 2000 2500 3000
Average Order Value (£)

In case of sales this equation can be moulded as
Y= 0.0309x+10.676
Task 6 Expected values
a.
1. Venture A
Coefficient of variation = standard deviation / Expected value
= 30.08/700
=0.6745
2. Venture B
Coefficient of variation = 13.32/400
=0.3393
b. A higher variation shows a greater risk that means the low variation project must be selected.
In the present case second option B produces a lower variation hence it must be exercised.
Task 7
From this project I got learn various statistical skills and analysis techniques which can be
implement and utilised in the real life situation. From different task perform help me gain

meaningful insights. In this project what I find the most challenging was finding sources
that can help me confirm that what I was performing was accurate or not. From this project I
learnt a lot of strategies I would like to learn more about marketing technique and tool that
can help improve my task.
Part 2
a. High low method in costing is split technique for determine the element of fixed and
variable cost. This helps in determination of the product price, the formula for calculation
is
Variable cost per unit= Maximum activity cost- Minimum activity cost / uppermost unit-
lowermost unit
= 400000-195000/34000-14000
=10.25per unit
In order to find out the fixed cost presence following method can be used:
14502 units will incur a cost of 10.25-euro variable cost
since, Total cost = Fixed + variable cost
fixed cost = 195000-148645.5
=50000
b. Break even is the point where the firm incurs no loss no profit, for finding the t-shirt units
that need to sold by Andeera Ltd. To break even is:
Breakeven point = Fixed cost / contribution
=50000/ (15-10)
= 10000 units
So in order to break even the firm need to sell 10000 units.

c. In order to achieve a desired profit of 60000 firm need to sell
= desired profit+ fixed cost / contribution
=110000/5
=22000 units
d. Margin of safety = Total sales – BEP sales
=22000-10000
=12000 units
e. Advantage of break-even analysis-
This helps to calculate the losses and profit earned by an organisation at distinct stages of
revenue and manufacturing (Winda, 2018)
It is used to predict feasible result of differences in revenue cost.
It is beneficial to correlate the link between fixed and variable costs.
Disadvantages of break-even analysis-
In this analysis it is suppose that the sales price is stable at all the stages of return which is not
real.
it is supposed in this analysis that the goods manufactured and sold at the similar time which is
not practical.
It takes a lot of time to prepare the manufacturing chart.

REFERENCES
Books and Journals
Winda, S.N., 2018. Analisis Break Even Point (BEP) Sebagai Alat Perencanaan Laba
Perusahaan Pada PT. Madubaru PG/PS Madukismo (Doctoral dissertation, Universitas
Teknologi Yogyakarta).
Fraser‐Mackenzie, P.A., Ma, T., Sung, M.C. and Johnson, J.E., 2019. Let's Call it Quits: Break‐
Even Effects in the Decision to Stop Taking Risks. Risk analysis, 39(7), pp.1560-1581.
Kvam, P., Vidakovic, B. and Kim, S.J., 2022. Nonparametric Statistics with Applications to
Science and Engineering with R. John Wiley & Sons.
Rasch, D. and Schott, D., 2018. Mathematical statistics. John Wiley & Sons.
Rumsey, D.J., 2021. Statistics II for dummies. John Wiley & Sons.