Certainly! Let's solve this step-by-step:
1. Understand the problem:
- We have a data set consisting of 4 whole numbers.
- The mean of the data set is given to be 67.
- Three of the data values are provided: 56, 63, and 70.
- We need to find the fourth data value.
2. Recall the formula for the mean:
The mean (average) of a set of numbers is defined as the sum of the numbers divided by the count of numbers.
[tex]\[
\text{Mean} = \frac{\text{Sum of all data values}}{\text{Number of data values}}
\][/tex]
3. Set up the equation using the given mean:
[tex]\[
67 = \frac{\text{Sum of all data values}}{4}
\][/tex]
4. Express the sum of all data values:
Since the mean is 67 and there are 4 data values, we can rewrite the equation to find the sum of all data values:
[tex]\[
\text{Sum of all data values} = 67 \times 4
\][/tex]
[tex]\[
\text{Sum of all data values} = 268
\][/tex]
5. Calculate the sum of the known data values:
We know three of the data values: 56, 63, and 70. Let's sum them:
[tex]\[
56 + 63 + 70 = 189
\][/tex]
6. Find the fourth data value:
The sum of all four data values is 268, and we have already calculated the sum of the first three data values as 189. The fourth data value can be found by subtracting the sum of the known data values from the total sum:
[tex]\[
\text{Fourth data value} = 268 - 189
\][/tex]
[tex]\[
\text{Fourth data value} = 79
\][/tex]
So, the fourth data value is [tex]\( 79 \)[/tex].
