Introduction Measures of dispersion, also referred to as measures of variability, are statistical tools used to describe the extent to which data points in a dataset deviate from a central value. They provide insights into the distribution and consistency of data, helping to evaluate the spread of observations. Common measures of dispersion include the range,…
Mode:The mode refers to the value that appears most frequently in a given dataset. A dataset may be: Example: In the dataset {2, 3, 3, 4, 5, 5, 5, 6}, the mode is 5, as it occurs three times—more than any other value. Median and Quartiles:The median represents the middle value that divides a dataset…
Measures of central tendency, such as the arithmetic mean (AM), combined arithmetic mean, geometric mean (GM), and harmonic mean (HM) are all measures of central tendency, each used in different contexts. AM is the simple average. Combined AM calculates the average of combined datasets. GM is used for rates of change or when data is…
Skewness and kurtosis are important statistical measures that help describe the shape and characteristics of a data distribution. While skewness refers to the asymmetry of the distribution, kurtosis pertains to the “tailedness” or the peakedness of the distribution curve. Skewness Definition:Skewness quantifies the degree of asymmetry in a distribution relative to its mean. It helps…
Introduction In statistics, measures of central tendency and dispersion are essential tools used to describe and summarize the characteristics of a dataset. Measures such as the mean, median, and mode provide insights into the central location or ‘average’ value, while measures like range, variance, and standard deviation indicate the degree of spread or variability within…
The Central Limit Theorem (CLT) is a foundational principle in statistics that underpins many statistical methods and inferential techniques. It states that, regardless of the shape of the original population distribution, the distribution of sample means will approximate a normal distribution as the sample size increases. In essence, if multiple random samples are drawn from…
Interval Estimation of the Mean and Proportion from Large Samples Introduction Interval estimation is a fundamental concept in inferential statistics, particularly useful when working with large samples. Instead of providing a single value (point estimate) for a population parameter such as the mean or proportion, interval estimation provides a range of values—called a confidence interval—that…
IntroductionSampling from a non-normal population involves selecting data from a population whose distribution deviates from the classical bell-shaped curve of the normal distribution. Such deviations may result from skewness, the presence of outliers, or irregular patterns in data distribution. Although many statistical methods assume normality, several techniques—including the Central Limit Theorem—allow researchers to perform valid…
IntroductionA normal distribution is a fundamental concept in statistics, characterized by a symmetric, bell-shaped curve centered around the mean. In such a distribution, data points are more likely to occur near the mean than at the extremes. This symmetry implies that most values cluster around the average, with fewer observations appearing as one moves further…
IntroductionA sampling distribution is a probability distribution of a given statistic derived from all possible random samples of a fixed size drawn from a specific population. It serves as a fundamental concept in inferential statistics, enabling researchers to analyze how a statistic behaves across different samples and make well-informed generalizations about the population. 1. What…
