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Basic Statistics & Data Analysis

Statistics is the methodology used to interpret and draw conclusions from collected data. It provides methods for designing research studies, summarizing and exploring data, and making predictions about phenomena represented by the data. A population is the set of all individuals of interest, while a sample is a subset of individuals from the population used for measurements. Parameters describe characteristics of the entire population, while statistics describe characteristics of a sample and can be used to infer parameters. Basic descriptive statistics used to summarize samples include the mean, standard deviation, and variance, which measure central tendency, spread, and how far data points are from the mean, respectively. The goal of statistical data analysis is to gain understanding from data through defined steps.

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Basic Statistics and Data Analysis
What is Statistics ? “ Statistics is the methodology which scientists and mathematicians have developed for interpreting and drawing conclusions from collected data ”
Statistical methods can be used to find answers to the questions like: • What kind and how much data need to be collected? • How should we organize and summarize the data? • How can we analyze the data and draw conclusions from it? • How can we assess the strength of the conclusions and evaluate their uncertainty?
Statistics provides methods for : 1. Design: Planning and carrying out research studies. 2. Description: Summarizing and exploring data. 3. Inference: Making predictions and generalizing about phenomena represented by the data.
Population and Sample Population can be characterized as the set of individual persons or objects in which an investigator is primarily interested during his or her research problem often only a set of individuals of that population are observed for measurements such a set of individuals constitutes a sample.
Parameters and Statistics  A parameter is an unknown numerical summary of the population.  A statistics is a known numerical summary of the sample which can be used to make inference about parameters.  A statistic describes a sample, while a parameter describes the population from which the sample was taken.
Basic Descriptive Statistics  Mean: The mean (also know as average), is obtained by dividing the sum of observed values by the number of observations.  Standard Deviation: The standard deviation gives an idea of how close the entire set of data is to the average value. Data sets with a small standard deviation have tightly grouped. Data sets with large standard deviations have data spread out over a wide range of values.  Variance: Measures how far a set of numbers is spread out. A variance of zero indicates that all the values are identical. Variance is always non-negative, a small variance indicates that the data points tend to be very close to the mean (Average value), while a high variance indicates that the data points are very spread out around the mean.
Statistical data analysis The goal of statistics is to gain understanding from data. Any data analysis should contain following steps:
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