Is the mean of the squares of two numbers greater than, or less
than, the square of their means?
Choose any two numbers. Call them a and b. Work out the arithmetic mean and the geometric mean. Which is bigger? Repeat for other pairs of numbers. What do you notice?
There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?
. . . like Samantha's here, from
I knew that to find the mean, you add up the numbers, and divide
by the quantity of numbers.
If the first two numbers had a mean of four, then they had to
add up to eight, because eight divided by two is four.
If the first three numbers had a mean of nine, they had to add
up to 27 because 27/3 is 9.
The third number then had to be 19, because 27 - 8 = 19
The sum of the four numbers had to be 60, since 60/4 = 15.
The third number had to be 33 because 60 - 27 = 33.
The answer to the problem is 2, 6, 19, 33.
Easy really! Well done Samantha.