Range and Interquartile Range

Pre-Algebra · Axiom Academy

LESSON Range and Interquartile Range Two ways to measure how spread out data is — the full reach, and the middle 50% that ignores the extremes. The simplest measure of spread is the range — subtract the smallest value from the largest. It answers "how wide is the whole dataset?" in a single number. Dataset: 65, 72, 78, 81, 85, 89, 95 So the range = 95 - 65 = 30 points: the scores reach across 30 points end to end. 2. Quartiles and the IQR: The Middle 50% To measure spread without the extremes, first sort the data , then split it into four equal parts with three cut points called quartiles . The IQR is the distance between the outer two. Q_1 — the median of the lower half (the 25th percentile) Q_2 — the median of all the data (the 50th percentile) Q_3 — the median of the upper half (the 75th percentile) The middle value is Q_2 = 81 . Take the median of each half around it: lower half 65, 72, 78 gives Q_1 = 72 ; upper half 85, 89, 95 gives Q_3 = 89 . So the IQR = 89 - 72 = 17 points — the middle 50% of scores span just 17 points, far less than the full range of 30. 3. The Box Plot: Spread You Can See A box-and-whisker plot draws all five key numbers on one axis. The box itself is the IQR , and the whiskers reach out to the extremes — so range and IQR appear side by side in a single picture. Reach from the minimum to Q_1 , and from Q_3 to the maximum — their full span is the range. Spans Q_1 to Q_3 . Its width is the IQR — the middle 50% of the data.

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