Here is a list of numbers. 9
7
5
10
5
3
a) Work out the median.
Josh picks at random one of the numbers.
b) What is the probability that he picks an even number?
?
8
Basil has five numbered cards.
Two of the numbers are hidden.
49 ?
The mode of the five numbers is 8
The mean of the five numbers is 6
c) Work out the two hidden numbers.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.