Measures of Central Tendency

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
• Can be skewed by extreme values

Median

• Middle value in a dataset when arranged in order
• If there are an even number of values, the median is the average of the two middle values
• Less sensitive to outliers than the mean

Mode

• Most frequently occurring value in a dataset
• Can be multiple modes if there are multiple values with the same frequency
• Not affected by outliers

Measures of Dispersion

Range

• Difference between the largest and smallest values in a dataset
• Simple to calculate, but sensitive to outliers

Interquartile Range (IQR)

• Difference between the 75th percentile (Q3) and 25th percentile (Q1)
• Less sensitive to outliers than the range

Variance

• Average of the squared differences between each value and the mean
• Sensitive to outliers

Standard Deviation

• Square root of the variance
• Also sensitive to outliers

Coefficient of Variation (CV)

• Ratio of the standard deviation to the mean
• Useful for comparing variability between datasets with different units or scales

Measures of Central Tendency

• The mean is also known as the arithmetic mean and is calculated by summing all values and dividing by the number of values.
• The mean is sensitive to outliers, which can skew the result.
• The median is the middle value in a dataset when arranged in order, and if there are an even number of values, it is the average of the two middle values.
• The median is less sensitive to outliers than the mean.
• The mode is the most frequently occurring value in a dataset, and there can be multiple modes if there are multiple values with the same frequency.
• The mode is not affected by outliers.

Measures of Dispersion

• The range is the difference between the largest and smallest values in a dataset, and is simple to calculate, but sensitive to outliers.
• The Interquartile Range (IQR) is the difference between the 75th percentile (Q3) and 25th percentile (Q1), and is less sensitive to outliers than the range.
• Variance is the average of the squared differences between each value and the mean, and is sensitive to outliers.
• Standard Deviation is the square root of the variance, and is also sensitive to outliers.
• The Coefficient of Variation (CV) is the ratio of the standard deviation to the mean, and is useful for comparing variability between datasets with different units or scales.