Application Of Statistics: Techniques And Probability Laws

Identify a need for the application of statistics

1 Identify a problem requiring a statistical application

2 Define the problem

3 Determine data currently available for analysis

4 Determine information required from outcome

Prepare to solve statistical problem

1 Determine statistical techniques to be applied

2 Identify and gain access to appropriate computational devices

3 Collect required input data

4 Analyse collected data for suitability and completeness

5 Take appropriate action to address any deficiencies found

Solve statistical problem

1 Apply appropriate techniques to collected data

2 Check answer by appropriate means

3 Interpret answer to determine information required by problem definition

Communicate outcomes

1 Communicate outcome to relevant stakeholders by appropriate means

2 Explain outcome to stakeholders, as appropriate

3 Check outcome has addressed problem

When defining a problem, there are a number of questions that should be asked, and these include:

What indicators are there that there is a problem?

What are the symptoms?

When do these occur?

What is happening when they do occur?

What departments appear to be involved or affected?

Why is this happening?  (if this is known)

Identify a need for the application of statistics

Discrete and continuous data

Discrete Data is data that is able to be placed into a category and based on counts or instances of the particular items in that category. Within discrete data only whole counts are possible, and values cannot be subdivided.  For example the number of people in a class. While, Continuous data can take on any value and can be measured on a scale or continuum.  Continuous data is able to be sub-dived into fine increments in order to represent the precision that is required in order to complete the task that statistical analysis is to be conducted for.

Methods suitable to use when presenting data

1. Frequency distribution tables

Frequency usually tells one how regular   something occurs. The frequency of an observation tells one how many times the given observation occurs in the given data. For instance list of numbers, the frequency of the number 9 is 5 because it appears 5 times.

1,2,3,9,4,6,9,8,5,9,9,1,0,6,1,0,9

The frequency distribution  tables  they either show the  categorical  variables  which are also referred to as  qualitative  variables  or  quantitative variables which are also referred to as  numeric variables .Categorical variables refers to  variables which are in categories such as  brand of food  and the quantitative  variables are numbers. Usually the frequency distribution tables gives one a snapshot of the data which permits one to find the patterns (Brown, 2016, p. 284).

1. Histograms

A histogram is  a plot  which enables one to discover ,l and display the  underlying  frequency  distribution  of a set of data .The histogram allow one to inspect  data for its underlying   distribution  for example  normal distribution , skewness, outliers among other Below  is an example of a histogram and the set of data from which it was constructed.

1. Ogives

An ogive which is also referred to as  cumulative frequency polygon, is a category of  frequency polygon which  displays the cumulative frequencies. Usually on the y-axis of an ogive cumulative frequencies are plotted  and  along the x-xis the    class boundaries are plotted, the ogive is very similar to an  histogram, the key difference between them is that instead of the rectangles  the ogive graph has a one point  marking which shows where the  top right  of the rectangle would have been. The figure below shows an example of an ogive (Barlow, 2016, p. 26).

Arithmetic mean

Arithmetic mean is also referred to as mean. The average of a given set of data is referred to as arithmetic mean, or just the mean of the given set of data. The arithmetic mean of a set of numbers is usually obtained by taking the sum of the data and then dividing by the number   of the total values in the set .The figure show the common formula which is used to calculate the arithmetic mean.

Discrete and continuous data

Whereby the ∑ is referred to as sigma and stands for summation (Tom, 2014, p. 328).

Median

The median refers to the middle value of a set of numbers. In order to obtain a median one is required list the numbers from the largest to the smallest or vice versa. One has to rewrite the list before obtaining the median.

Mode

The mode of a set of data is the value which appears most often. Usually it is the X value at its probability mass function takes its maximum value. In a set of data the mode is the value with the highest probability of being sampled. The mode is not necessary unique   to a given set of discrete distribution, this is because the probability mass function may take the same maximum value at many points (Agarwal, 2017, p. 32).

Standard deviation

Standard deviation is the average of the variance.  Variance is the difference between all of the data sets and the mean figure.

Range

The range of a data set is the space, distance or amount between the smallest and largest figure.

Interquartile range

The interquartile range is the two middle sections of the data in the second quarter and third quarter. When we apply all of these equations to a set of data, we can work out the profile of the most average figure in a set of data. This can be used to see the typical behaviour of a person in our target market.

Probability laws

The following are the Probability laws;

1. Law of large numbers
2. Law of subtraction

• Law of addition

1. Law of multiplication

Probability distributions (binomial, and normal)

Probability distributions refers to the function which describes the like hood of obtaining the possible values   that a random variable can assume i.e.  The values of the variables which vary based on the underlying probability distribution.

The normal distribution refers to the continues distribution  which exists in many natural  processes in this case ‘ continuous’   simply means that  between  any two set of data  another value would be found while the binomial distribution is discrete and not continuous (Rumsey, 2015, p. 23).

The random walk method

A random walk method is a mathematical object which is a stochastic or random formula that explains a path of successive random steps across a range of mathematical integers.   The random walk method randomises the direction that the steps will be taken in within the range of the formula.

The Monte Carlo method

Monte Carlo methods are complex equations that are used to project the probability of complex random real-life based scenarios through the application of risk factors and other factors that impact on the random events occurring.

Methods suitable to use when presenting data

Statistical inference

1. Large and small samples
2. Larger sample sizes are considered to be more statistically accurate due to the fact that there are more sets of data in order to analyse, but depending on the method of sampling in some cases a smaller but more refined sample size has the potential to be more accurate.
3. Sample size

The sample size is the percentage of the complete data available that will be collected and analysed as a part of the statistical analysis; it is important to make sure that large sample size is used when possible in order to make sure that there is a lot of information to analyse.  When sample size is a large variance that is caused by anomalies will be reduced due to the sheer number of other results, when in a small sample size one varied count could result in skewed research (Griffiths, 2017, p. 193).

1. Statistical significance

Statistical significance is the probability   that the difference in the conversion rates between a given variation and a given baseline is not due to the random chance.

1. Short cut methods

The shortcut method on  the set of data  having a distribution and  an initial state  is the sequence  of the random  variables  whose increments are  independent , identically  distributed  random  variables  with the common  distribution

Linear regression

Linear regression refers to the basic and often used type of predictive analysis .the overall concept of regression is to examine two things

1. Does a given set of  predictor variables  doo a good  work in predicting  an outcome
2. Which of the given variable in particular is significant predictor of the outcome variable(Bulmer, 2014, p. 461).

Correlation

Correlation refers to a statistical technique which has the ability to show if and how strongly pairs of variables are related with one another.

One way, two way and multiple

In statistics , the two-way of analysing a variance  is an extension of the one-way  which  examines  the influence  of the two different  categorical  independent  variables  on one   continuous  dependent variable.

Factorial experiments

The factorial experiments includes the simultaneously more than one factor   each at two or more levels.

Failure time distributions

This is the measure of how much reliable a component is or how reliable a given set of data is.

Reliability and life testing

In this case reliability and life testing refers to the probability which a given system will be able to perform for a given period of time. The reliability function is hence the same probability expressed as a function of the time period.

PRART 2: PRACTICAL ACTIVITY

Identify a problem requiring a statistical application, and define and document this problem

Lifecycle analysis of technology items

Determine, and record, the data currently available for analysis

Determine the information required from the outcome, and document this

To assess environmental impact that all assorted with different products

To evaluate the potential impacts that are associated with the given products

Determine the statistical techniques to be applied. Document these techniques.

Arithmetic mean

Sampling

Analysing

Identify, and gain access to, the appropriate computational devices

Computers

Data processors

Collect the required input data. Provide the data collected.

Analyse the collected data for suitability and completeness, taking action to address any deficiencies found. Document the analysis, including action taken to address deficiencies.

Deficiencies encountered in data collection

Errors

Sample size

Variation in samples

Validation of source

Actions taken to deal with deficiencies identified

Further data collection activities

Discarding and replacing data

Checking data for errors

Using appropriate means, communicate the outcome to the relevant stakeholders, explaining the outcomes, as appropriate

Reading all results

Understanding relationships

Investigating causation and correlation

Assessing the results

Coming to conclusions

PART 3: Questions

Methods used to identify problems which require statistical application

1. consultation
2. conducting a  risk profiling

Questions used to define the problem

• What indicators are there that there is a problem?
• What are the symptoms?
• When do these occur?
• What is happening when they do occur?

Types of data analysis

Inters for example 1

Double for example precision floating point value 

Char for example a single character

Void for example valueless

Float for example a number with a fractional part

Type of information that will required for the outcome

• Correlation
• Causation
• Amount
• Type

Types of computational devices used in analysing statistics

• Computers
• Processing systems
• Data processors

Methods of data collection

• Surveys
• Collection from output data
• Research
• Meetings
• Error log analysis

Requirements for analysing statistical data

For the data to be analysed effectively I will require different computational tools.

Deficiencies encountered in data collection

• Errors
• Sample size
• Variation in samples
• Validation of source
• Mishandling data
• Missing data

Discuss the types of actions that could be taken to deal with deficiencies identified

• Further data collection activities
• Discarding and replacing data
• Checking data for errors

Validating data sources what might you determine by applying appropriate techniques to collected data?

• The answers to certain problems
• The relationship between two or more different factors
• Why events have occurred
• The probability of an event occurring

What process will you need to follow to interpret the answer so you can determine the information required by problem definition?

• Reading all results
• Understanding relationships
• Investigating causation and correlation
• Assessing the results

Provide three tips that could be applied to providing clear explanation to stakeholders.

• What methods were used to collect data
• Data integrity methods
• What methods were used to analyses the data
• Statistical methods overview

What will you need to consider when checking that the outcome has addressed problem?

• Reasons why a problem has occurred
• Extent and breadth of the problem
• Factors that are contributing to the problem
• Possible actions that could be taken in relation to resolving the problem

References

Agarwal, L., 2017. Basic Statistics. 3rd ed. Chicago: New Age Internationa.

Barlow, J., 2016. Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences. 1st ed. London: John Wiley & Sons.

Brown, B., 2016. Dealing With Statistics: What You Need To Know: What you need to know. 4th ed. London: McGraw-Hill Education.

Bulmer, M. G., 2014. Principles of Statistics. 6th ed. London: Courier Corporation.

Griffiths, D., 2017. Head First Statistics. 5th ed. Chicago: O'Reilly Germany,.

Rumsey, D. J., 2015. Statistics For Dummies. 3rd ed. Chicago: John Wiley & Sons.

Tom, L., 2014. U-Statistics: Theory and Practice. 2nd ed. London: CRC Press, .

Wasserman, L., 2013. All of Statistics: A Concise Course in Statistical Inference. 3rd ed. London: Springer Science & Business Media.

White, G., 2016. Statistics of the State of Georgia: Including an Account of Its Natural, Civil, and Ecclesiastical History ; Together with a Particular Description of Each County, Notices of the Manners and Customs of Its Aboriginal Tribes, and a Correct Map of the State. 4th ed. Texas: W. Thorne Williams,.