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Questions and Answers
What is the average of the squared differences between each value and the mean?
What is the average of the squared differences between each value and the mean?
What is the most frequently occurring value in a dataset?
What is the most frequently occurring value in a dataset?
What is the ratio of the standard deviation to the mean?
What is the ratio of the standard deviation to the mean?
What is the middle value in a dataset when arranged in order?
What is the middle value in a dataset when arranged in order?
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What is the difference between the largest and smallest values in a dataset?
What is the difference between the largest and smallest values in a dataset?
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What is calculated by summing all values and dividing by the number of values?
What is calculated by summing all values and dividing by the number of values?
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What is the difference between the 75th percentile (Q3) and 25th percentile (Q1)?
What is the difference between the 75th percentile (Q3) and 25th percentile (Q1)?
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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
- 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.
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Description
This quiz covers the different measures of central tendency, including the mean, median, and mode, and their characteristics in statistics.
