Statistics Measures of Central Tendency

Measures of Central Tendency

• Mean, median, and mode are single values used to represent the center of a dataset.
• Mean, also known as arithmetic mean, is calculated by summing all values and dividing by the total number of values.
• It's most stable and used to compare other measures like standard deviation and skewness.
• Mean is affected by extreme values.
• Median is the middlemost value when the data is arranged in order.
• It is not influenced by extreme values, making it a reliable measure for skewed data.
• Mode is the value that appears most frequently in a dataset.
• It can be unimodal (one mode), bimodal (two modes), trimodal (three modes), or multimodal (more than two modes).
• It is not affected by outliers and may not exist in some datasets.

Measures of Dispersion/Variability

• Measures of dispersion indicate the spread or variability of data points around the central tendency.
• A smaller dispersion signifies data points are close to the center, while a larger dispersion indicates data points are spread over a larger range.
• Range is the difference between the highest and lowest values in a distribution.
• It's sensitive to extreme values, making it less reliable than other measures.
• Standard deviation (SD) is a commonly used and reliable measure of variability.
• It represents the average deviation of data points from the mean.
• A smaller SD implies data points are close to the mean, while a larger SD indicates greater spread.
• Variance is the square of the standard deviation.
• It measures the average squared deviations from the mean.

Z-score

• The z-score indicates how many standard deviations a data point is away from the mean.
• A positive z-score implies the data point is above the mean, while a negative z-score indicates it’s below the mean.

Types of Data

• Data refers to raw, factual information used for analysis.
• Primary data is collected firsthand by the researcher, such as national census data.
• Secondary data is collected by others, such as data from online sources.
• Population represents all individuals of interest in a study.
• Sample is a subset of individuals selected from a population to represent the population in a study.

Types of Variables

• Variables are characteristics that change or differ among individuals.
• Qualitative variables are categorical and cannot be meaningfully ordered or ranked, such as gender.
• Quantitative variables are measurable using a number scale, allowing for ranking or ordering, such as height.

Types of Quantitative Variables

• Discrete variables are obtained by counting, such as the number of children.
• Continuous variables are obtained by measuring, such as temperature.

Levels of Measurement

• Nominal level is used for naming and categorization only and cannot be ordered or computed. Examples include gender, nationality, and civil status.
• Ordinal level allows for ranking or ordering but doesn’t provide information about the size of difference between ranks. Examples include year level, level of satisfaction, and educational qualification.
• Interval level represents values with known sizes or distances, but zero doesn’t indicate an absence of the characteristic. Examples include temperature in Celsius or Fahrenheit and test scores.
• Ratio level possesses all characteristics of the interval scale and has a true zero point, indicating an absence of the characteristic. Examples include height, weight, age, and monetary savings.

Explore the key concepts of central tendency including mean, median, and mode. Understand how these measures represent data and their roles in data analysis. Learn about the impact of extreme values and discover the significance of measures of dispersion.