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Questions and Answers
What is the purpose of quantiles?
What is the purpose of quantiles?
- To divide a dataset into equal parts or segments (correct)
- To calculate the range of a dataset
- To measure the spread of data around the mean
- To find the average of squared differences between data points and the mean
Which quantile is the value below which 25% of the data falls?
Which quantile is the value below which 25% of the data falls?
- 25th percentile (P25) (correct)
- Median (Q2)
- Third quartile (Q3)
- First quartile (Q1)
What is the range of a dataset?
What is the range of a dataset?
- Half of the difference between the third quartile (Q3) and the first quartile (Q1)
- The square root of the variance
- The sum of absolute differences between each data point and the mean
- The difference between the highest and lowest values (correct)
Which measure quantifies the average deviation of data points from the mean?
Which measure quantifies the average deviation of data points from the mean?
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What does the standard deviation (σ) measure?
What does the standard deviation (σ) measure?
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What is the variance (σ²)?
What is the variance (σ²)?
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Which quantile is the median of the lower half of the data?
Which quantile is the median of the lower half of the data?
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What is the quantile deviation (QD)?
What is the quantile deviation (QD)?
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Study Notes
Quantiles
- Divide a dataset into equal parts or segments
- Median (Q2): the middle value when data is sorted, splitting data into two halves
- Quartiles (Q1 and Q3): divide data into four equal parts, with Q1 being the median of the lower half and Q3 being the median of the upper half
- Percentiles: divide data into 100 equal parts, with each percentile (e.g., 25th percentile, P25) representing the value below which a certain percentage of data falls
Range
- The difference between the highest and lowest values in a dataset
- Provides a simple measure of variability
Quantile Deviation
- Half of the difference between the third quartile (Q3) and the first quartile (Q1)
- Measures the spread of data around the median
Mean Deviation
- Quantifies the average deviation of data points from the mean (average)
- Calculated as the sum of absolute differences between each data point and the mean, divided by the total number of data points
Standard Deviation
- Measures the dispersion or spread of data around the mean
- The square root of the variance
Variance
- Represents the average of squared differences between data points and the mean
- Symbolized as σ²
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