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Questions and Answers
What is the formula for calculating the mean of a dataset?
What is the formula for calculating the mean of a dataset?
What is a characteristic of the median that makes it a better representation of the 'typical' value than the mean?
What is a characteristic of the median that makes it a better representation of the 'typical' value than the mean?
What is a situation where the mode would be a more suitable measure of central tendency than the mean or median?
What is a situation where the mode would be a more suitable measure of central tendency than the mean or median?
What is a characteristic of the mean that makes it sensitive to outliers?
What is a characteristic of the mean that makes it sensitive to outliers?
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What is the definition of the mode?
What is the definition of the mode?
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When is the median a better representation of the 'typical' value than the mean?
When is the median a better representation of the 'typical' value than the mean?
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What is a key difference between the mean and the median?
What is a key difference between the mean and the median?
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Study Notes
Measures of Central Tendency
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, as one extreme value can greatly affect the mean
- Used when data is normally distributed and there are no extreme outliers
Median
- Middle value in a dataset when arranged in order
- If there are an odd number of values, the middle value is the median
- If there are an even number of values, the median is the average of the two middle values
- Less sensitive to outliers compared to the mean
- Used when data is not normally distributed or has outliers
Mode
- Most frequently occurring value in a dataset
- A dataset can have multiple modes (bimodal or multimodal) or no mode at all
- Not affected by outliers, as it is based on frequency of occurrence
- Used when the goal is to identify the most common value, rather than a "typical" value
Key Differences
- The mean is sensitive to outliers, while the median and mode are more robust
- The median is a better representation of the "typical" value when data is not normally distributed
- The mode is used when identifying the most common value is the goal, rather than a measure 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 using the formula: μ = (Σx) / n
- Sensitive to outliers, as one extreme value can greatly affect the mean
- Suitable for normally distributed data with no extreme outliers
Median
- Middle value in a dataset when arranged in order
- For odd number of values, the middle value is the median
- For even number of values, the median is the average of the two middle values
- Less sensitive to outliers compared to the mean
- Suitable for non-normally distributed data or data with outliers
Mode
- Most frequently occurring value in a dataset
- A dataset can be unimodal (one mode), bimodal (two modes), multimodal (more than two modes), or have no mode at all
- Not affected by outliers, as it is based on frequency of occurrence
- Used when identifying the most common value is the primary goal
Key Differences
- Mean is sensitive to outliers, while median and mode are more robust
- Median better represents the "typical" value when data is not normally distributed
- Mode is used for identifying the most common value, not for measuring central tendency
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Description
Learn about the measures of central tendency, including the mean and median, their formulas, and when to use them in data analysis.
