Question

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)

Answer 1

Answer:

{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

$\frac{4+8+8+x+14}{5} =9$

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

$\frac{4+8+8+x+14}{5} =9\\\\4+8+8+x+14=45\\\\x+34=45\\\\x=11$