Measures of Central Tendency Quiz

Measures of Central Tendency

Mean

• Also known as the average
• Calculated by summing all values and dividing by the number of values
• Sensitive to outliers, which can greatly affect the result
• Example: 1, 2, 3, 4, 5; Mean = (1 + 2 + 3 + 4 + 5) / 5 = 3

Median

• 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 affected by outliers compared to the mean
• Example: 1, 2, 3, 4, 5; Median = 3

Mode

• Most frequently occurring value in a dataset
• A dataset can have multiple modes (bimodal or multimodal) or no mode at all
• Example: 1, 2, 2, 3, 4, 4, 4; Mode = 4

Measures of Dispersion

Range

• Difference between the largest and smallest values in a dataset
• Simple to calculate but sensitive to outliers
• Example: 1, 2, 3, 4, 5; Range = 5 - 1 = 4

Variance

• Average of the squared differences between each value and the mean
• Measures the spread of a dataset
• Larger variance indicates a more spread out dataset
• Example: 1, 2, 3, 4, 5; Variance = ((1-3)^2 + (2-3)^2 + ... + (5-3)^2) / 5

Measures of Central Tendency

Mean

• The average value of a dataset
• Calculated by summing all values and dividing by the number of values
• Sensitive to outliers, which can greatly affect the result
• Example calculation: 1, 2, 3, 4, 5; Mean = (1 + 2 + 3 + 4 + 5) / 5 = 3

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 affected by outliers compared to the mean
• Example calculation: 1, 2, 3, 4, 5; Median = 3
• Used when the data is not normally distributed or when outliers are present

Mode

• The most frequently occurring value in a dataset
• A dataset can have multiple modes (bimodal or multimodal) or no mode at all
• Example calculation: 1, 2, 2, 3, 4, 4, 4; Mode = 4
• Used when the dataset is categorical or nominal

Measures of Dispersion

Range

• The difference between the largest and smallest values in a dataset
• Simple to calculate but sensitive to outliers
• Example calculation: 1, 2, 3, 4, 5; Range = 5 - 1 = 4
• Used to understand the spread of the data

Variance

• The average of the squared differences between each value and the mean
• Measures the spread of a dataset
• Larger variance indicates a more spread out dataset
• Example calculation: 1, 2, 3, 4, 5; Variance = ((1-3)^2 + (2-3)^2 +...+ (5-3)^2) / 5