If the mean of a set of numbers is 4, what is the value of X if the entries are 1, 5, 7, 2, 2, and X?

To determine the correct value of ( X ) in the dataset where the mean is given as 4, we start by recalling the formula for the mean, which is the sum of all entries divided by the number of entries.

First, we identify the entries in the dataset: 1, 5, 7, 2, 2, and ( X ). There are 6 entries in total. To find the mean, we set up the equation:

[

\text{Mean} = \frac{\text{Sum of entries}}{\text{Number of entries}}

]

Substituting in the known values:

[

4 = \frac{1 + 5 + 7 + 2 + 2 + X}{6}

]

Next, we compute the sum of the known numbers:

[

1 + 5 + 7 + 2 + 2 = 17

]

Now we substitute this sum back into the equation:

[

4 = \frac{17 + X}{6}

]

To eliminate the fraction, we multiply both sides by 6:

[

24 = 17 + X

]

Now, we isolate ( X ) by subtracting 17