Lesson plan
Midhinge
In statistics, the midhinge ( ) is the average of the first and third quartiles and is thus a measure of location. Equivalently, it is the 25% trimmed mid-range or 25% midsummary; it is an L-estimator. The midhinge is defined as \begin{align} \operatorname{MH}(X) &= \overline{Q_{1, 3}(X)} \\ &= \frac{Q_1(X) + Q_3(X)}{2} \\ &= \frac{P_{25}(X) + P_{75}(X)}{2} \\ &= M_{25}(X). \end{align} The midhinge is related to the interquartile range ( ), the difference of the third and first quartiles (i.e. ), which is a measure of statistical dispersion. The two are complementary in sense that if one knows the midhinge and the , one can find the first and third quartiles. The use of the term hinge for the lower or upper quartiles derives from John Tukey's work on exploratory data analysis in the late 1970s, and midhinge is a fairly modern term dating from around that time. The midhinge is slightly simpler to calculate than the trimean ( ), which originated in the same context and equals the average of the median ( ) and the midhinge: \begin{align} \operatorname{MH}(X) &= 2 \operatorname{TM}(X) - \operatorname{med}(X) \\ &= 2\; \frac{Q_1 + 2Q_2 + Q_3}{4} - Q_2. \end{align}
Article summary
In statistics, the midhinge ( ) is the average of the first and third quartiles and is thus a measure of location. Equivalently, it is the 25% trimmed mid-range or 25% midsummary; it is an L-estimator. The midhinge is defined as \begin{align} \operatorname{MH}(X) &= \overline{Q_{1, 3}(X)} \\ &= \frac{Q_1(X) + Q_3(X)}{2} \\ &= \frac{P_{25}(X) + P_{75}(X)}{2} \\ &= M_{25}(X). \end{align} The midhinge is related to the interquartile range ( ), the difference of the third and first quartiles (i.e. ), which is a measure of statistical dispersion. The two are complementary in sense that if one knows the midhinge and the , one can find the first and third quartiles. The use of the term hinge for the lower or upper quartiles derives from John Tukey's work on exploratory data analysis in the late 1970s, and midhinge is a fairly modern term dating from around that time. The midhinge is slightly simpler to calculate than the trimean ( ), which originated in the same context and equals the average of the median ( ) and the midhinge: \begin{align} \operatorname{MH}(X) &= 2 \operatorname{TM}(X) - \operatorname{med}(X) \\ &= 2\; \frac{Q_1 + 2Q_2 + Q_3}{4} - Q_2. \end{align}
Key claims
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.