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A Mean Tetrahedron

Can you number the vertices, edges and faces of a tetrahedron so that the number on each edge is the mean of the numbers on the adjacent vertices and the mean of the numbers on the adjacent faces?

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Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was thinking of.

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Converging Means

Take any two positive numbers. Calculate the arithmetic and geometric means. Repeat the calculations to generate a sequence of arithmetic means and geometric means. Make a note of what happens to the two sequences.

Bat Wings

Stage: 3 Challenge Level: Challenge Level:1

There are different ways of working out the average of a set of numbers. This problem looks at using the mean. The mean is worked out by adding up the set of numbers and dividing the answer by how many numbers there are.

For example, the mean of the numbers 2, 3, 4, and 5 is (2+3+4+5)/4 = 3.5

Three students had collected some data for a project about bats. Each had collected a different set of readings for the wingspan of some bats. Unfortunately, each student had lost one measurement.

Two of the students had already added up their data and worked out their individual means and the overall mean was also known. The known information is summarised below:

Student A had collected 5 measurements, the others had each collected 6.

Student Data set (wingspans in cm) Mean (cm)

A 12 10 16 14 - 15   13
B 13 12 - 12 14 17 16 14
C 11 14 15 - 11 13 12 -

The overall mean from the combined data = 13.35 cm Using the above information can you complete the table?