Learn the concept of dispersion, range, IQR, outliers, and box and whisker plots.
Want a deeper conceptual understanding? Try our interactive lesson! (Plus Only)
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Practice exam-style quartiles and box & whisker plots problems
Range is the difference between a dataset's minimum and maximum values.
Though range may give a sense of the dispersion of a set, outliers will always have a strong effect on range since they pull the minimum or maximum values far from the rest of the data.
Quartiles are conceptually similar to the median, except that there are three of them: ​Q1​,Q2​​ and ​Q3​, dividing the sorted dataset into 4 equal-size parts.
​Q2​​ is the median, dividing the datapoints in two.
​Q1​​ is halfway between the first value and the median, at position
​Q3​​ is halfway between the median and the last value, at position
Note: you will not need to find quartiles by hand on IB exams.
The interquartile range, denoted ​IQR, is the difference between the third and first quartile:
A value ​x​ in a dataset is said to be an outlier if ​x<Q1​−1.5×IQR​ or ​x>Q1​+1.5×IQR.
A box-and-whisker plot visually summarizes data by splitting it into quarters. The box shows the middle 50% of your data (from Q1 to Q3), and the line inside marks the median. The whiskers extend to show the spread of data, excluding outliers, which are marked with a cross.
- Minimum: smallest value (left whisker end)
- Lower Quartile (Q1): median of lower half (25% mark)
- Median (Q2): middle value of data set
- Upper Quartile (Q3): median of upper half (75% mark)
- Maximum: largest value (right whisker end)
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