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• For example consider the data points: $$50$$, $$55$$, $$55$$, $$55$$, $$62$$, $$65$$, $$78$$, $$99$$.
• To find the first quartile, take the bottom half of the data: $$50$$, $$55$$, $$55$$, $$55$$, and find the middle value. The middle value is between $$55$$ and $$55$$, therefore, the first quartile is $$55$$.
• To find the third quartile, take the top half of the data: $$62$$, $$65$$, $$78$$, $$99$$, and find the middle value. The middle value is between $$65$$ and $$78$$, so the third quartile is $$71.5$$.
• Therefore the interquartile range, IQR is $$71.5 - 55 = 16.5$$.