FUNDAMENTALS OF STATISTICS
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Fundamentals of Statistics
Statistics is the science of collecting, recording, analysis and interpretation of data. The aim of this process is usually to spearhead informed conclusions, which are important in the decision making process. Statistical data is useful in almost all scientific fields, including medical trials for drugs, disease surveillance and control, marketing and advertising strategies as well as demographic measures of given populations. Data analysis is therefore of fundamental implication in science. Rules of statistics also form an integral part of mathematics and the derivations of this specific subject. This paper describes the elementary precepts of statistics with regard to types of data, methodology, analysis of data and its interpretation
Statistics is a process rather than one-step procedure. The conventional procedure involves a series of processes whose result is the findings, which the researcher reports for further interpretation. In its initial stage, the scientist or mathematician identifies the problem or a gap in knowledge that exists in a given field. Once this occurs, the researcher chooses the population sample from which to collect data. Descriptive analytical procedures are then carried out to define the characteristics of the variables and the findings from this analysis are applied in the solution of the research problem (Holcomb, 2016).
Analysis of data gives more meaning to the raw facts. Analytical methods involve calculation of measures of central tendency, determination of data skewedness and calculation of dispersion. Measures of central tendency are mean, mode and median. The mean is gives an average of the number of occurrence of events. Mean is calculated by dividing the total value of the data entries by the cumulative frequency of these values. A centrally placed mean is gives a symmetrical picture of distribution while a mean far off the central value gives an asymmetrical distribution which can be skewed to the left or to the right depending on the value frequency. Median is the central value of data in a given variable while mode is the value that exists with the most frequency in a data table. Measures of dispersion include variance and standard deviation. Variance shows the deviation of the data from the mean (Mulholland & Jones, 2013).
A variable refers to any characteristic of an entity or individual. It can be either quantitative or categorical. Nominal variables are categorical variables that do not have any inherent order or ranking for example names like of gender. The value may be numerical but have no numerical value for example I, II. The only operation that can be attributed to this variable is enumeration. Ordinal variables are those that the statistician can arrange in an order for example good, better, best. They can be compared for equality but we are unable to know how much greater or less (Petrozzi, 2013).
In interval variables, differences between the values are meaningful but not anchored. Examples are temperature and calendar dates. The only calculations that can be done on these values are addition and subtraction. In ratio presentation of data, variables possess properties of non-arbitrary zero point and interval for example age and weight. Distribution of a variable tells us what values the variable has and how often it takes those values. Distribution can be unimodal, bimodal or symmetric. Unimodal distribution has a single peak while bimodal has two peaks. In symmetric distribution the left and right, half are like mirror images (Mulholland & Jones, 2013).
In conclusion, statistics use a central value for a given set of observations and to what level that central value represents the whole set of data. Measures of central tendency include the mean, the mode and the median. In the calculation of the mean, all observations are summed and then the sum divided by the number of observations. The median refers to the middle value when all the observations are ordered in a sequence. The mode refers to the value that occurs the most in frequency in a given set of observations.
Holcomb, Z. C. (2016). Fundamentals of descriptive statistics. Routledge.
Mulholland, H., & Jones, C. R. (2013). Fundamentals of statistics. Springer.
Petrozzi, S. (2013). Fundamentals of Statistics. Practical Instrumental Analysis: Methods, Quality Assurance and Laboratory Management, 17-51.