Descriptive Statistics Chapter

Descriptive Statistics

• Goal: To describe and summarize the basic features of a dataset
• Types of Descriptive Statistics:
  • Measures of Central Tendency
  • Measures of Variability

Measures of Central Tendency

• Describe the middle or average value of a dataset
• Three main types:
  1. Mean
  2. Median
  3. Mode

Mean

• Also known as the arithmetic mean
• Calculated by summing all values and dividing by the number of values
• Formula: μ = (Σx) / n
• Sensitive to outliers
• Can be skewed by extremely large or small values

Median

• Middle value in a dataset when arranged in order
• If dataset has an even number of values, the median is the average of the two middle values
• Less affected by outliers compared to the mean
• More robust for skewed datasets

Mode

• Most frequently occurring value in a dataset
• Can have multiple modes (bimodal, multimodal)
• Not affected by extreme values, but may not be representative of the dataset as a whole
• Often used for categorical or nominal data

Descriptive Statistics

• Descriptive statistics aim to describe and summarize the basic features of a dataset
• It involves calculating and interpreting numerical values to understand the characteristics of a dataset

Measures of Central Tendency

• Measures of central tendency describe the middle or average value of a dataset
• There are three main types of measures of central tendency: mean, median, and mode

Mean

• The mean is also known as the arithmetic mean
• It is calculated by summing all values and dividing by the number of values (μ = (Σx) / n)
• The mean is sensitive to outliers and can be skewed by extremely large or small values
• This means that a single extreme value can greatly affect the mean, making it less representative of the dataset

Median

• The median is the middle value in a dataset when arranged in order
• If the dataset has an even number of values, the median is the average of the two middle values
• The median is less affected by outliers compared to the mean, making it a more robust measure for skewed datasets
• It is often used when the dataset contains outliers or is not normally distributed

Mode

• The mode is the most frequently occurring value in a dataset
• A dataset can have multiple modes (bimodal, multimodal), and this is often the case for categorical or nominal data
• The mode is not affected by extreme values, but it may not be representative of the dataset as a whole
• It is often used in conjunction with other measures of central tendency to get a more complete picture of the dataset