Tag Archives: median

Mean and Median

What is the number of distinct real numbers that have the property that the median of the five numbers is equal to their mean? Source: NCTM Mathematics Teacher, November 2006 SOLUTION Suppose is the smallest number. We order the five … Continue reading

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Inscribed Circle of Equilateral Triangle

The circumference of a circle circumscribing an equilateral triangle is units. Find the number of square units in the area of the circle inscribed in the same triangle. Source: NCTM Mathematics Teacher, February 2006 SOLUTION In equilateral triangle , angle … Continue reading

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Median of a Trapezoid

The trapezoid has and . The three congruent sides have lengths . Find the length of the median in terms of . Source: NCTM Mathematics Teacher 2008 SOLUTION Triangle is a triangle with hypotenuse equal . Likewise Median of trapezoid … Continue reading

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Mean of 41

A set of seven different positive integers has a median of and a mean of . What is the greatest possible value of one of the seven positive integers? Source: mathcontest.olemiss.edu 11/18/2013 SOLUTION First guess and check Median  Mean too … Continue reading

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Three Tangent Circles

Three mutually tangent circles of radius one are surrounded by a larger circle that is simultaneously tangent to all three. What is the radius of the larger circle? Source: http://www.mathcircles.org SOLUTION The centers of the three mutually tangent circles form … Continue reading

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Mean, Median, Mode, and Range

The mean, median, unique mode, and range of a collection of eight counting numbers are each 8. What is the largest number that can be in this collection? Source: mathcontest.olemiss.edu 10/23/2006 SOLUTION First solution Let’s try a simple solution and … Continue reading

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Median to 16

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.  You are given a triangle with side lengths of 11 cm, 13 cm, and 16 cm.  Determine the length of the … Continue reading

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