If the mean of the data 5, 7, 10, 14, x, 25, 32, 19 is x, what is the value of x?

To find the value of x, we need to set up an equation based on the information given in the problem.

The mean (or average) of a set of numbers is calculated by adding all the numbers together and then dividing by the count of numbers.

In this case, the mean of the data is given as x, and the data includes the numbers 5, 7, 10, 14, x, 25, 32, and 19.

So, we can set up the equation as follows:

(5 + 7 + 10 + 14 + x + 25 + 32 + 19) / 8 = x

Adding the numbers together gives:

(112 + x) / 8 = x

Multiplying both sides of the equation by 8 to get rid of the denominator on the left side gives:

112 + x = 8x

Subtracting x from both sides to isolate the variable gives:

112 = 7x

Finally, dividing both sides by 7 to solve for x gives:

x = 112 / 7

So, x = 16.