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Questions and Answers
What is the mean of the dataset: 1, 2, 3, 4, 5?
What is the mean of the dataset: 1, 2, 3, 4, 5?
Which measure of central tendency is most affected by outliers?
Which measure of central tendency is most affected by outliers?
What is the mode of the dataset: 1, 2, 2, 3, 4, 4, 4?
What is the mode of the dataset: 1, 2, 2, 3, 4, 4, 4?
What is the range of the dataset: 1, 2, 3, 4, 5?
What is the range of the dataset: 1, 2, 3, 4, 5?
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What does a larger variance indicate about a dataset?
What does a larger variance indicate about a dataset?
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Which measure of central tendency is the middle value in a dataset when it is arranged in order?
Which measure of central tendency is the middle value in a dataset when it is arranged in order?
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Study Notes
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
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Description
Test your understanding of measures of central tendency, including mean and median, with this quiz. Learn how to calculate and interpret these statistical measures.
