Certainly! Let's go through a detailed step-by-step solution regarding the data provided in the table:
### Step 1: Listing the Data
First, let's list the given data for [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 3 & 3 & 7 & 9 & 10 \\
\hline
y & 9 & 15 & 21 & 22 & 30 \\
\hline
\end{array}
\][/tex]
### Step 2: Calculating the Mean of [tex]\( x \)[/tex]
To find the mean of the [tex]\( x \)[/tex] values, you need to sum all the [tex]\( x \)[/tex] values and then divide by the number of values.
[tex]\[
x = [3, 3, 7, 9, 10]
\][/tex]
Sum of [tex]\( x \)[/tex]:
[tex]\[
3 + 3 + 7 + 9 + 10 = 32
\][/tex]
Number of elements in [tex]\( x \)[/tex] is 5. The mean [tex]\( \bar{x} \)[/tex] is calculated as:
[tex]\[
\bar{x} = \frac{\text{sum of } x}{\text{number of elements in } x} = \frac{32}{5} = 6.4
\][/tex]
### Step 3: Calculating the Mean of [tex]\( y \)[/tex]
Similarly, to find the mean of the [tex]\( y \)[/tex] values, you sum all the [tex]\( y \)[/tex] values and then divide by the number of values.
[tex]\[
y = [9, 15, 21, 22, 30]
\][/tex]
Sum of [tex]\( y \)[/tex]:
[tex]\[
9 + 15 + 21 + 22 + 30 = 97
\][/tex]
Number of elements in [tex]\( y \)[/tex] is 5. The mean [tex]\( \bar{y} \)[/tex] is calculated as:
[tex]\[
\bar{y} = \frac{\text{sum of } y}{\text{number of elements in } y} = \frac{97}{5} = 19.4
\][/tex]
### Final Results
- The data set [tex]\( x \)[/tex] is: [tex]\([3, 3, 7, 9, 10]\)[/tex]
- The data set [tex]\( y \)[/tex] is: [tex]\([9, 15, 21, 22, 30]\)[/tex]
- The mean of [tex]\( x \)[/tex] values ([tex]\( \bar{x} \)[/tex]) is: [tex]\( 6.4 \)[/tex]
- The mean of [tex]\( y \)[/tex] values ([tex]\( \bar{y} \)[/tex]) is: [tex]\( 19.4 \)[/tex]
Thus, we achieve the following numerical results:
[tex]\[
([3, 3, 7, 9, 10], [9, 15, 21, 22, 30], 6.4, 19.4)
\][/tex]
This is the detailed step-by-step solution for calculating the means of the given datasets.
