Statistics: Measures of Central Tendency

Measures of Central Tendency

Measures of central tendency are statistical values that describe the middle or average value of a dataset.

Types of Measures of Central Tendency

1. Mean

• Also known as the arithmetic mean
• Calculated by summing all values and dividing by the number of values
• Sensitive to outliers and skewed data
• Example: The average score of a class

2. Median

• The middle value in a dataset when it is arranged in order
• If the dataset has an even number of values, the median is the average of the two middle values
• Less sensitive to outliers and skewed data compared to the mean
• Example: The middle score of a class

3. Mode

• The most frequently occurring value in a dataset
• A dataset can have multiple modes or no mode at all
• Useful for categorical data
• Example: The most common eye color in a population

Characteristics of Measures of Central Tendency

• Sensitivity to outliers: The mean is sensitive to outliers, while the median and mode are more resistant.
• Skewness: The mean is affected by skewed data, while the median and mode are more robust.
• Data type: The mean is suitable for continuous data, while the median and mode are suitable for categorical data.

Importance of Measures of Central Tendency

• Summary statistic: Measures of central tendency provide a summary statistic for a dataset.
• Comparing datasets: Measures of central tendency allow for comparisons between datasets.
• Understanding data: Measures of central tendency help to understand the characteristics of a dataset.

Measures of Central Tendency

• Measures of central tendency describe the middle or average value of a dataset.

Types of Measures of Central Tendency

Mean

• Also known as the arithmetic mean.
• Calculated by summing all values and dividing by the number of values.
• Sensitive to outliers and skewed data.
• Example: The average score of a class.

Median

• The middle value in a dataset when it is arranged in order.
• If the dataset has an even number of values, the median is the average of the two middle values.
• Less sensitive to outliers and skewed data compared to the mean.
• Example: The middle score of a class.

Mode

• The most frequently occurring value in a dataset.
• A dataset can have multiple modes or no mode at all.
• Useful for categorical data.
• Example: The most common eye color in a population.

Characteristics of Measures of Central Tendency

Sensitivity to Outliers

• The mean is sensitive to outliers.
• The median and mode are more resistant to outliers.

Skewness

• The mean is affected by skewed data.
• The median and mode are more robust to skewed data.

Data Type

• The mean is suitable for continuous data.
• The median and mode are suitable for categorical data.

Importance of Measures of Central Tendency

Summary Statistic

• Measures of central tendency provide a summary statistic for a dataset.

Comparing Datasets

• Measures of central tendency allow for comparisons between datasets.

Understanding Data

• Measures of central tendency help to understand the characteristics of a dataset.

Learn about the different types of measures of central tendency, including mean, median, and mode, and how to calculate them.