FC301 Statistics: Investigation Report on Business Demography

This statistical investigation report examines the relationship between business births and deaths in the UK mining support service activities from 2014 to 2019. The report utilizes secondary data from Business demography UK and employs quantitative methods, including descriptive statistics, line and bar graphs, correlation, and regression analysis to identify if the birth of new enterprises affects the death of existing ones. The analysis reveals a positive correlation, indicating that an increase in new businesses is associated with an increase in business closures. The report includes detailed calculations, graphical representations, and a discussion of the trends observed, concluding that competition between new and existing enterprises is a significant factor in the sector.

Statistics

Table of Contents
Introduction......................................................................................................................................3
Methodology....................................................................................................................................3
Calculations and graphs...................................................................................................................3
Analysis of data...............................................................................................................................9
Conclusion.....................................................................................................................................10
References......................................................................................................................................10

Introduction
This written statistical investigation report is based on finding an association between births and
deaths from the year 2014 to 2019 (6 years) in mining support service activities in UK. There are
two independent variables taken: Birth and Death; where birth shows new startups established,
and death indicates shut down of existing business during selected years. The main motive of this
report is to identify whether birth of new enterprises is responsible for death of existing
enterprise or not. As normally in this competitive world, new startups grab the market of existing
enterprises by its exciting schemes and innovative services. Thus, in this investigation, it will be
analyzed whether startups are responsible for shutdown of business or not.
Methodology
For this investigation report, quantitative approach has been applied by collecting qualitative
data from Business demography UK. The source of data collection can be categorized as
secondary because it is collected from survey already conducted by some other organization.
Both variables are from common source, and to analyze these variables excel tool has been used.
Statistical tools used for analyzing the data includes: descriptive statistics, line graph, bar graph,
correlation relation and regression model analysis.
Calculations and graphs
Part 1
Analyses of variable Birth of new enterprises
(a) Descriptive analysis
Births
Mean
88.3333333
3
Standard Error
6.00925212
6
Median 85
Mode 80
Standard Deviation
14.7196014
4

Sample Variance
216.666666
7
Kurtosis -0.8591716
Skewness 0.41807152
Range 40
Minimum 70
Maximum 110
Sum 530
Count 6
(b) On an average 88 new births have been recorded from 2014 to 2019. The range is 40; this
indicates there is not much difference between maximum and minimum in these 6 years. The
standard deviation is 14.71, which means mean is deviated either by extending or contracting
from 88 new births. The mode is 80; this indicates maximum births recorded are 80 new births in
the year 2015 and 2019.
Part 2
Analysis of Deaths of existing enterprises
(a) Descriptive analysis
Deaths
Mean 65
Standard Error
8.66025403
8
Median 62.5
Mode 65
Standard Deviation
21.2132034
4
Sample Variance 450
Kurtosis 3.32962963
Skewness
1.64991582
3
Range 60
Minimum 45
Maximum 105
Sum 390
Count 6

(b) The above descriptive analysis shows that on an average 65 deaths of enterprises have been
recorded from 2014 to 2015. The mean of deaths are lower than births, this indicates firms in the
sector of mining support service activities are increasing; as births are more than deaths. The
standard deviation is 21.21 which are higher than births; this indicates uncertainty of deaths is
comparatively higher than births. The higher range of deaths is the indicator of more room for
deviation. The minimum deaths noticed are 45, while highest deaths noticed within selected
years are 105. The sum total of deaths in these 6 years is lesser than sum total of births.
Part 3
Comparison
(a) Line graph
2014 2015 2016 2017 2018 2019
0
20
40
60
80
100
120
Births
Deaths
(b) The above line chart shows that lines of both births and deaths never collide with each other,
this means that births and deaths never been equal from 2014 to 2019. Also, before 2018, both
trend lines seems to be behave opposite to each other; as when birth line was diminishing, death
line started increasing and vice a versa. But after 2018, both line starts moving in the same
direction.

(c) Bar graph
2014 2015 2016 2017 2018 2019
0
20
40
60
80
100
120
Births (X)
Deaths (Y)
(d) From the above graph it can be analyzed that both births and deaths were very closed in the
year 2016 and 2019, while there was huge gap between both variables in the year 2014. An
increasing trend can be seen in deaths from 2017, which is expected to be further increase in the
year 2020 based on past trend.
Part 4
Correlation analysis

Year Births (X) Deaths (Y)
2014 100 45
2015 80 60
2016 70 65
2017 90 50
2018 80 65
2019 110 105
X - Mx Y - My (X - Mx)2 (Y - My)2 (X - Mx)(Y - My)
11.667 -20 136.111 400 -233.333
-8.333 -5 69.444 25 41.667
-18.333 0 336.111 0 0
1.667 -15 2.778 225 -25
-8.333 0 69.444 0 0
21.667 40 469.444 1600 866.667
Mx: 88.333 My: 65.000 Sum: 1083.33 Sum: 2250 Sum: 650
X Values
∑ = 530
Mean = 88.333
∑(X - Mx)2 = SSx = 1083.333
Y Values

∑ = 390
Mean = 65
∑(Y - My)2 = SSy = 2250
X and Y Combined
N = 6
∑(X - Mx)(Y - My) = 650
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = 650 / √((1083.333)(2250)) = 0.4163
Although technically a positive correlation, the relationship between your variables is weak (the
nearer the value is to zero, the weaker the relationship). The value of R2, the coefficient of
determination, is 0.1733. Thus, this indicates that any increase in births of new enterprise also
slightly increase deaths with small proportion.
Part 4
Regression analysis
Regression Statistics
Multiple R 0.728789995
R Square 0.531134856
Adjusted R Square 0.374846475
Standard Error 16.63221076
Observations 5
ANOVA
df SS MS F
Significance
F
Regression 1 940.1086957
940.108
7
3.39842
8 0.162473941
Residual 3 829.8913043
276.630
4
Total 4 1770

Coefficients Standard Error t Stat P-value Lower 95%
Intercept
-
17.93478261 47.74090735 -0.37567
0.73215
3 -169.867657
Births 1.010869565 0.54834775
1.84348
3
0.16247
4 -0.73421771
X - Mx Y - My (X - Mx)2 (X - Mx)(Y - My)
11.6667 -20 136.1111 -233.3333
-8.3333 -5 69.4444 41.6667
-18.3333 0 336.1111 0
1.6667 -15 2.7778 -25
-8.3333 0 69.4444 0
21.6667 40 469.4444 866.6667
SS: 1083.3333 SP: 650
Sum of X = 530
Sum of Y = 390
Mean X = 88.3333
Mean Y = 65
Sum of squares (SSX) = 1083.3333
Sum of products (SP) = 650
Regression Equation = ŷ = bX + a
b = SP/SSX = 650/1083.33 = 0.6

a = MY - bMX = 65 - (0.6*88.33) = 12
ŷ = 0.6X + 12
The critical value of F is lesser than F value; this indicates that there is association between both
variables. The regression equation has positive coefficient value, which means there is positive
relationship between both variables. This means any increase in births of new enterprise also
increases the deaths of existing enterprises.
Analysis of data
The above result clearly indicates that births have direct association with deaths of existing
enterprises. But before 2018, both variables act as opposite to each other. This indicates that
before 2018, any decline in births was due to insufficient revenue in mining service activities
sector; due to which new enterprises didn’t enter into the market and existing enterprises start
exiting the market. This trend continuous till 2016, after that Birth line shown improvement by
increase in the births of new enterprises; while decline in deaths of existing companies. This
indicates favorable market environment in mining service sector. But after 2018, both trend line
moves towards same direction, this is the indication of competition between new and existing
enterprises. As with the increase in new enterprises existing enterprises start leaving the market.
Conclusion
Based on above analysis, it can be concluded that today there is huge competition between new
and existing enterprises in the sector of mining service activities. This can be proved by positive
relationship shown in statistical tools: correlation and regression model. The positive relation is
the indicator of direct impact of births on deaths. With increase in entry of new business in
mining sector, the existing enterprises lose their market and finally shut down their business or
shift to any other sector.

References
Business demography UK - Annual data on births, deaths and survivals of businesses in the UK,
by geographical area. Available at:
https://www.ons.gov.uk/businessindustryandtrade/business/activitysizeandlocation/datasets/
businessdemographyreferencetable [Accessed on 22nd February 2021]