Introduction To Quantitative Method: What Is STAT

Introduction To Quantitative Method Need To Know What Is Stats

Introduction To Quantitative Method Need To Know What Is Stats

- INTRODUCTION TO QUANTITATIVE METHOD - NEED TO KNOW - =: what is stats, descriptive stats, inferential stats, population, sample, parameter and statistics, confidence and significance levels, you need to know: what is variable, types of data, relative frequency and using it to create pie charts, developing histograms , shapes of histograms, stem-and-leaf plot, cumulative relative frequency, developing an ogive, scatter diagrams, you need to know: mean, median, mode, range, variance, standard deviation, empirical rule, coefficient of variation, percentiles, quartiles, inter quartile range, box plots, geometric mean. please see attachtment

Paper For Above instruction

Quantitative methods form the backbone of scientific research and data analysis across diverse disciplines, providing essential tools for understanding and interpreting numerical data. To effectively employ these methods, one must grasp fundamental statistical concepts and techniques, starting with the basics of what statistics entails. Statistics, broadly, is the discipline that deals with collecting, analyzing, interpreting, presenting, and organizing data. It bifurcates into descriptive statistics, which summarizes data characteristics, and inferential statistics, which makes predictions or generalizations about a population based on sample data.

Understanding the core components like population and sample is critical; while the population encompasses the entire set of observations or data points that are of interest, the sample is a subset drawn from the population, used in analyses to infer properties of the larger group. Parameters are characteristics of populations (like population mean or variance), whereas statistics are characteristics calculated from samples (sample mean or variance). Confidence levels and significance levels quantify the reliability and statistical significance of inferences made thus ensuring the robustness of conclusions.

Fundamental to statistical analysis is the concept of variables and data types. Variables are attributes or characteristics that can vary across observations. Data can be classified as nominal, ordinal, interval, or ratio, depending on measurement levels. Relative frequency represents how often an event occurs concerning the total number of observations, and it facilitates the creation of visual representations such as pie charts that depict proportions of categories within data sets. Developing histograms involves plotting data ranges against their frequencies, which helps in visualizing data distribution shapes such as symmetric, skewed, or uniform histograms. The shape of a histogram can reveal underlying patterns or skewness in data, essential for choosing appropriate statistical tests.

Additional tools like stem-and-leaf plots provide detailed views of data distribution, preserving individual data points while displaying the shape. Cumulative relative frequency tables enable the development of ogives, which are cumulative frequency graphs useful for determining medians and quartiles. Scatter diagrams are instrumental in analyzing relationships between two quantitative variables, revealing correlations or patterns.

Measures of central tendency—mean, median, and mode—are essential for summarizing data. The mean, or average, is sensitive to outliers, whereas median provides a central value robust to skewed data. The mode identifies the most frequently occurring value(s). Variance and standard deviation measure data dispersion, quantifying how spread out observations are around the mean. The empirical rule states that, for a normal distribution, approximately 68% of data falls within one standard deviation, 95% within two, and 99.7% within three. The coefficient of variation expresses the standard deviation as a percentage of the mean, allowing for comparisons across different datasets.

Percentiles and quartiles divide data into sections, assisting in understanding the distribution's spread. The interquartile range (IQR), the difference between the third and first quartiles, indicates the middle 50% of data, and is often visualized using box plots. The geometric mean is used for data involving rates or ratios, especially with multiplicative relationships. Collectively, these statistical tools and measures form a robust framework for analyzing and interpreting quantitative data, enabling informed decision-making and research conclusions.

References

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• Weiss, N. A. (2012). Introductory Statistics (9th ed.). Pearson Education.
• Ott, R. L., & Longnecker, M. (2010). An Introduction to Statistical Methods and Data Analysis (6th ed.). Brooks/Cole.
• Triola, M. F. (2018). Elementary Statistics (13th ed.). Pearson.
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• Fisher, R. A. (1925). Statistical Methods for Research Workers. Oliver and Boyd.
• Agresti, A., & Franklin, C. (2017). Statistics: The Art and Science of Learning from Data (4th ed.). Pearson.