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What are the differences between mean and median?
Mean: Average value, sensitive to outliers | Median: Middle value, resistant to outliers
What are the differences between standard deviation and IQR?
Standard Deviation: Measures spread around the mean, best for symmetric data | IQR: Measures spread of middle 50%, best for skewed data
What are the differences between unimodal and bimodal distributions?
Unimodal: Has one peak, indicating one mode | Bimodal: Has two peaks, indicating two modes
What are the differences between symmetric and skewed distributions?
Symmetric: Data evenly distributed around the center, mean ≈ median | Skewed: Data concentrated on one side, mean ≠ median
What are the differences between range and IQR?
Range: Max - Min, sensitive to outliers | IQR: Q3 - Q1, resistant to outliers
What are the differences between right-skewed and left-skewed distributions?
Right-skewed: Tail longer on the right, mean > median | Left-skewed: Tail longer on the left, mean < median
Explain the concept of symmetry in a distribution.
A distribution is symmetric if it can be folded in half, and both sides look like mirror images. Symmetrical data often has the mean and median close together.
Explain the concept of skewness in a distribution.
Skewness refers to the asymmetry of a distribution. A right-skewed distribution has a longer tail on the right, while a left-skewed distribution has a longer tail on the left. Skewness affects the relationship between the mean and median.
Explain the concept of standard deviation.
Standard deviation measures the typical distance of data points from the mean. It indicates how spread out the data is around the average value. Best for symmetric distributions.
Explain why the median is resistant to outliers.
The median is the middle value in a dataset. Outliers, being extreme values, do not affect the position of the middle value as much as they affect the mean, which is calculated using all values.
Explain why it is important to investigate outliers.
Outliers might be valid but unusual data points. Discarding them without investigation may lead to a loss of important information or a misunderstanding of the data.
Explain the importance of context when describing a distribution.
Relating your answer back to what the data represents provides a meaningful interpretation of the distribution. It connects the statistical description to the real-world scenario.
What is a symmetric distribution?
A distribution where both sides look like mirror images when folded in half.
What is a right-skewed distribution?
A distribution with a tail longer on the right side; mean > median.
What is a left-skewed distribution?
A distribution with a tail longer on the left side; mean < median.
What is a mode in a distribution?
The most frequent value(s) in a dataset, represented by peak(s) in a histogram.
What are outliers?
Values that are significantly higher or lower than the rest of the data.
What is the range of a dataset?
Maximum value minus the minimum value.
What is the Interquartile Range (IQR)?
The range of the middle 50% of the data (Q3 - Q1).