Bachelor Level
1. A spinner labeled 8-14 was spun 20 times. The data are recorded below. What is the
mean absolute deviation of the data set below?
Spinner 1
8
9
10 11 12 13 14
Result

it has to be a.

the answer for this question is 38

9 x 8 divided by (5-3)=36

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.