The data set has five values. If listed from lowest to highest, it looks like this { 4, , 8, , 14 }

Find the missing four values if the following is true:

The range of the data is 10
The mode is 8 (and there's only one mode)
The mean is 9 (<- how do i find this)

{4, 8, 8, 11, 14}

Step-by-step explanation:

The range is 10. This criteria is already met as 14-4=10. This means that we cannot have any numbers smaller than 4 or larger than 14.

The mode is 8 (And there is only one mode). The mode is the numbers that occurs the most. For there to be only one mode, there has to be at least 2 8's in this data set.

Currently, our data set is {4, 8, 8, ?, 14}

The mean is 9. Firstly, let us go over what the mean is. The mean is the average of all of the numbers in the set. To find this, you add up all of the elements in the set and divide it by the number of elements that you added.

This means that the equation that we would use to find the mean is

Now, we just need to solve for x to find the last element

final answer is : )

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.