What is the interquartile range (IQR)?

IQR = Q3 − Q1, where Q1 is the 25th percentile and Q3 is the 75th. The IQR contains the middle 50% of data. It's resistant to outliers, making it useful for identifying unusual values (outlier if > Q3+1.5×IQR or < Q1−1.5×IQR).

What does skewness mean?

Skewness measures asymmetry. Positive skew: a long tail to the right (mean > median). Negative skew: long tail to the left (mean < median). Zero skew: symmetric distribution (like a normal distribution).

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About Descriptive Statistics

Descriptive statistics summarize and describe the features of a dataset. Measures of central tendency (mean, median, mode) tell you where data is centered, while measures of dispersion (variance, standard deviation, IQR) tell you how spread out the data is.

Quartiles and the IQR

The interquartile range (IQR = Q3 − Q1) captures the middle 50% of the data and is resistant to outliers. Q1 is the 25th percentile and Q3 is the 75th percentile. Values more than 1.5 × IQR below Q1 or above Q3 are typically considered outliers.

Skewness

Pearson's second skewness coefficient is 3 × (mean − median) / standard deviation. A value near 0 indicates a symmetric distribution; positive values indicate right skew (tail on the right), and negative values indicate left skew (tail on the left).

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For a related calculation, use Mean, Median, Mode, Range Calculator to calculate mean, median, mode, and range with step-by-step working. Great for students. Alternatively, use Standard Deviation Calculator to calculate population and sample standard deviation, variance, mean, and full descriptive stats from a dataset.

For the underlying method, read Understanding Standard Deviation and Why It Matters or Matrix Operations Explained Simply: Addition, Multiplication, and the Determinant.