Btec Level 5 Hnd Diploma In Business Unit 42 - Statistics For Management.pdf

ASSIGNMENT 2 FRONT SHEET

QualificationBTEC Level 5 HND Diploma in Business

Unit number and titleUnit 42 - Statistics for Management

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TABLE CONTENT

I Introduction: 4

II Apply Statistical Methods in Business Planning 4

1 Measuring the Variability in Business Processes or Quality Management 4

2 Probability distributions and application to business operations and processes 5

III Communicate findings using appropriate charts/tables 15

1 Different types of visual representations for variables in the dataset 15

I Introduction:

The demand of analyzing and evaluation the business data is increasing day by day in recovering aftercovid-19 era As the role of a Research Analyst of SSI Securities Corporation, which is one of the topfinancial investments in Viet Nam in recent 20 years, by applying statistical methods to make businessreports of some Vietnamese companies’ business planning and operations management with aim toprovide the necessary data and point out the risk, the trends or opportunities, and so on for meet thedemand of recovery business planning after covid-19 as well as demonstrate effective of applyingstatistical techniques in analyzing data business Specially, this report will focus on sample data businessincluding Garments (a4a=18), Whosales (a4a=51) and Retail (a4a =52) with basing on combininginferential statistics, regression technique and descriptive statistics method to access and export the exactresult for stakeholders In addition, this report will divide in two parts, with firstly that apply statisticsmethods in business planning and the rest of this report will present relation to universal information andthe application of different variables and different charts and tables.

II Apply Statistical Methods in Business Planning

1 Measuring the Variability in Business Processes or Quality Management

Figure 1: The chart of measuring the variability of hours operating in a week

The graph illustrates the distribution of weekly working hours among companies operating in theGarments, Whosales, and Retail sectors in all regions covered by the VES dataset In general, it is rare tofind companies operating fewer than 40 hours per week, with the focus being mainly on the range of 40 toalmost 60 hours per week, especially between 40 and 60 hours Additionally, there are some companiesthat work over 100 hours per week in these industries.

2 Probability distributions and application to business operations and processes.2.1 Poisson Distribution

- Theory:

A Poisson distribution is a discrete probability distribution, which means it predicts the likelihoodof a discrete (countable) outcome The discrete result of a Poisson distribution is the number oftimes an event occurs, denoted by k( Turney, 2022).

The Poisson distribution is used to forecast or explain the number of events that occur within acertain time or space interval "Events" can range from disease outbreaks to client purchases tometeor strikes The interval can be any quantity of time or space, for example, 10 days or 5 squareinches (Turney, 2022).

- Example:

Figure2: PoissonDistributionGraph (Turney,2022).

A Poisson distribution can be shown as a probability mass function graph A function thatcharacterizes a discrete probability distribution is known as a probability mass function The peakof the distribution—the mode—represents the most likely number of events.

 When is not an integer, the mode is the nearest integer less than.

 There are two possibilities when is an integer: and 1.

 When is small, the distribution is significantly longer on the right side of its peak than onthe left (i.e., it is highly skewed to the right).

- Application:

The Poisson distribution, a probability distribution model, is widely used in various fields ofbusiness to describe the random occurrence of events (Hayes, 2023) It is commonly applied inscenarios where the number of events happening in a given time interval is of interest, such as

accident rates, phone calls, or website traffic In finance, the Poisson distribution can be utilized toanalyze the number of losses a business might experience, helping to estimate the probability ofdefault or loan risk In addition, it can also be used to model patterns in customer arrival rates,which assists in optimizing staffing and reducing customer wait times Overall, the Poissondistribution is a valuable tool for businesses to quantify the probability of events occurring, leadingto more informed and accurate decision-making processes (Hayes, 2023)

2.2 Normal distribution

- Theory and Example:

Normal distribution, also called Gaussian distribution, is a fundamental concept in statistics(Britannica, 2023) It is a distribution in which the data is symmetrically distributed aroundthe mean, and the data points are evenly distributed on both sides of the mean value Thenormal distribution is often used as a model for many naturally occurring phenomena, suchas biological variables or socio-economic phenomena It has a bell-shaped curve with thehighest frequency at the mean value and gradually decreasing towards the tails Thestandard deviation of the data in a normal distribution helps to measure the spread of thedata points from the mean value (Britannica, 2023).

The mean is the scale parameter, and the standard deviation is the location parameter The meandecides where the curve's apex is located Increasing the mean shifts the curve to the right, whilereducing it shifts the curve to the left The standard deviation either stretches or compresses thecurve A narrow curve is produced by a small standard deviation, whereas a wide curve isproduced by a big standard deviation.

- Application:

Table1:Probability normaldistributionchart ofdays ofinventoryin Garments,Non-metallicmineralproductsandRetailindustry

The result of Probability normal distribution ratio of the number of days of inventory (d16) was0,011425026, in which, it was calculated as the mean, and the Standard Deviation of thepopulation in the normal area was equal to the sample mean and the SD in the data set Therefore,the probability for businesses to have less than 6 days of inventory is very low In addition, thenumber of companies with inventory is relatively small, estimated to be around 28 out of all thebusinesses in Garments, Non-metallic mineral products and Retail industry examined.

3 Inferential statistics3.1 One Sample T-test

- Theory:

The one-sample t-test is a statistical hypothesis test used to determine whether an unknownpopulation mean is different from a specific value (SAS, 2016).

- Example:

Figure4:One-sampleT-test example (Gerald,2018)

To compare a sample mean to a specific value, use the one-sample t-test The sample mean and thepresumed population mean can be compared using a one-sample t-test to see whether there is asignificant difference between the two One-sample t-tests are employed, for instance, to comparethe sample mean and sample midpoint of the test variable or to ascertain if a sample of

observations might have been produced by a process with a certain mean (Gerald, 2018)

- Application for assigned dataset:

Step1: Write null and alternative hypothesis

Let μ the average sales operating in a week of firms in the garment, whosale and retail andwholesale industries in VietNam in 2019 It will be tested on the hypothesis different from 54 saleswith the significance level of 5%.

Ho: μ = 54 (null hypothesis)

Hα: μ ≠ 54 (altenative hypothesis - need to test)

Step2: Find P-value

Assume null hypothesis is true ( μ= 54), the report calculates the probabilities from the numbersspecified from the survey of enterprises.

Table2:The tableofOne-sampleT-test

Step 3: Conclusion

From the calculated date from the above table, it can be seen that P-value=0.0000000036477< 0,05.This demonstrates that Ha accepted 95% confidence that the average hours operating in a week offirms (Medium size) is not different from 54 hours The Ha is rejected.

3.2 Two Sample T-test

- Application for assigned dataset:

Step1: Write null and alternative hypothesis

Let �,µ be the average hours operating in a week of millions micro and medium firms in the

Garments, Non-metallic mineral products and Retail industry in Viet Nam in 2015 It will be testedon the hypothesis: different in two types of company (Micro company and Medium firms) with thesignificance level of 5%

Ho: �1=µ2(nullhypothesis)Hα:�1≠µ2(alternativehypothesis)

Step2: Find P-value by Jamovi

Table 3:Thetableof firmdatasetin termTwo-sampleT-test

Step 3: Conclusion

From the calculation of from above table, it is clearly seen that P-value = 0,867 > 0,05 Therefore,The Hypothesis Hα is rejected and is not sufficient evidence 95% confident that the averageweekly hours of operation in the Garments, Non-metallic mineral products and Retail industry aredifferent for micro and medium enterprises.

3.3 Regression

- Theory:

Regression is a statistical method used in finance, investing, and other disciplines that attempts todetermine the strength and character of the relationship between one dependent variable (usuallydenoted by Y) and a series of other variables (known as independent variables) (Beers, 2023).

- Example:

Figure6:EstimatedRegression Equation(Beers,2023).

The height coefficient in the regression equation is 106.5 This coefficient represents the meanincrease of weight in kilograms for every additional one meter in height If your height increasesby 1 meter, the average weight increases by 106.5 kilograms.

The regression line on the graph visually displays the same information If you move to the rightalong the x-axis by one meter, the line increases by 106.5 kilograms Keep in mind that it is onlysafe to interpret regression results within the observation space of your data In this case, the height

and weight data were collected from middle-school girls and range from 1.3 m to 1.7 m.Consequently, we can’t shift along the line by a full meter for these data.

- Application for assigned dataset:

Step1: Write null and alternative hypothesis

This analysis will examinate the relationship between sales and hours operating in 2015 by ES(with >95% confidence level)

Ho: There is no significant relation between sales and hours of operationHα: There is a positive relation between sales and hours of operation

Step 2: Assume Ho is true, find P-value:

Table4:The tableoffirmdatasetin termofRegression technique

Step 3: Conclusion

Basing on the information of the regression table, it can be seen that P-value = 0,014 < 0,05 Thisdemonstrate that the Hα is enough 95% confident that there is a relationship between operatinghour and sales This hypothesis Hα is accepted.

III Communicate findings using appropriate charts/tables

1 Different types of visual representations for variables in the dataset1.1 Frequency tables

A frequency table is a statistical tool used to organize and summarize data by categorizing it intodistinct groups or intervals and displaying the frequency or count of occurrences in each category.It provides a clear and concise summary of the data distribution, making it easier to identifypatterns, trends, and outliers (Splashlearn, 2022).

The advantages of frequency tables include their simplicity and ease of interpretation They offer astructured format that presents information in an organized manner, facilitating quickcomprehension and analysis Frequency tables allow for easy comparison between categories,making it straightforward to identify the most common or rare occurrences They are particularlyuseful for handling large datasets by condensing the information into manageable categories,which simplifies the presentation and analysis process (Splashlearn, 2022).

However, frequency tables also have some limitations They can oversimplify complex datasets,potentially losing granularity by aggregating data into categories This aggregation can lead toinformation loss, as individual data points are not explicitly represented Additionally, frequencytables may not provide detailed insights into the relationships or distributions within each category.As a result, they might not be suitable for more sophisticated analyses that require a deeperunderstanding of individual data points or complex data structures (Splashlearn, 2022).

Table5: Frequencydistributionof industry

1.2 Simple tables

A simple table is a visual representation of data that organizes information into rows and columns,presenting it in a structured and easily readable format It is a widely used method for organizingand presenting data in various fields and contexts The advantages of simple tables include theirsimplicity and ease of understanding They provide a clear and concise way to display data,allowing for quick comparisons and identification of patterns or trends Simple tables make iteasier to locate specific information and enable efficient data analysis They are also flexible andcan be customized to suit specific needs or preferences However, simple tables may becomecumbersome and difficult to read when handling large datasets or when the information is highlydetailed They may require additional effort to update or modify if the data changes Furthermore,simple tables may not effectively represent complex relationships or hierarchies within the data,limiting their usefulness in certain analytical or presentation scenarios.

Example:

Table6:Table ofQuantitative datafortheA4A (Regions)

The table provides quantitative information for the sample's l1 (number of employees) variable.First, according to Talor (2023), the mean represents average and that it is the sum of a collectionof data divided by the sum of all the data The mean for this data set shows a corporation having anaverage of 214,136 employees Secondly, the median is the midpoint of the data set when it issorted ascendingly, and the median employee count is 24 Taylor (2023) defines mode as the valuethat occurs most often in the set data, so 5 represents the most number of employees appearing outof 324 companies According to Bhandari (2022), the range is the difference between the highest

and lowest value for a specific variable in a sample It is calculated by subtracting the minimumfrom the largest value The range represents the variance of the data, for this data set, the numberof employees disparate across companies is 8996 Finally, Bhandari (2022) defines the standarddeviation as the average amount of variation in your data set It demonstrates how different eachscore's average is from the mean With increasing standard deviation, the data collection becomesmore diverse This sample's standard deviation is 845,7793 Overall, these descriptive statisticsgive a thorough account of the workforce, reflecting both the dataset's central tendency and itsvariability.

1.3 Pie charts

A pie chart is a circular graphical representation that displays data as slices, with each slicerepresenting a different category or proportion of the whole It is commonly used to showcase thedistribution or composition of a dataset (Byjus, 2019) The advantages of pie charts include theirability to provide a visual representation of proportions, making it easy to compare and understandrelative sizes They are particularly useful for highlighting the dominant or significant categorieswithin a dataset However, pie charts can be limited in displaying precise numerical values and areless effective for comparing multiple datasets or categories (Byjus, 2019) They may also becomecluttered and difficult to interpret when dealing with too many slices or small proportions, leadingto potential misinterpretation or confusion.

Example: