Certainly! To determine the mean of the dataset [tex]\[3, 7, 9, 13, 5\][/tex], we need to follow these steps:
1. Sum the data values: Add all the numbers in the dataset together.
[tex]\[
3 + 7 + 9 + 13 + 5
\][/tex]
2. Calculate the total sum:
[tex]\[
3 + 7 = 10
\][/tex]
[tex]\[
10 + 9 = 19
\][/tex]
[tex]\[
19 + 13 = 32
\][/tex]
[tex]\[
32 + 5 = 37
\][/tex]
So, the total sum of the dataset is 37.
3. Count the number of data values: There are 5 values in the dataset.
4. Divide the total sum by the number of data values: To find the mean, we divide the total sum by the number of values.
[tex]\[
\bar{x} = \frac{\text{total sum}}{\text{number of values}}
\][/tex]
[tex]\[
\bar{x} = \frac{37}{5}
\][/tex]
5. Perform the division:
[tex]\[
\frac{37}{5} = 7.4
\][/tex]
Therefore, the mean of the dataset [tex]\[3, 7, 9, 13, 5\][/tex] is [tex]\(\boxed{7.4}\)[/tex].
