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
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).
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.
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.
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;
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.
Statistical inference
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).
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.
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
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.
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
Questions used to define the problem
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
Types of computational devices used in analysing statistics
Methods of data collection
Requirements for analysing statistical data
For the data to be analysed effectively I will require different computational tools.
Deficiencies encountered in data collection
Discuss the types of actions that could be taken to deal with deficiencies identified
Validating data sources what might you determine by applying appropriate techniques to collected data?
What process will you need to follow to interpret the answer so you can determine the information required by problem definition?
Provide three tips that could be applied to providing clear explanation to stakeholders.
What will you need to consider when checking that the outcome has addressed 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,.
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