Certainly! Let's compute the mean of the given values with their respective frequencies, step by step.
Firstly, we have the values and their corresponding frequencies:
Values: [tex]\(1, 2, 3, 4, 5\)[/tex]
Frequencies: [tex]\(7, 1, 3, 2, 2\)[/tex]
To find the mean, we need to follow these steps:
1. Calculate the sum of the products of each value and its frequency:
- For value [tex]\(1\)[/tex] with frequency [tex]\(7\)[/tex]: [tex]\(1 \times 7 = 7\)[/tex]
- For value [tex]\(2\)[/tex] with frequency [tex]\(1\)[/tex]: [tex]\(2 \times 1 = 2\)[/tex]
- For value [tex]\(3\)[/tex] with frequency [tex]\(3\)[/tex]: [tex]\(3 \times 3 = 9\)[/tex]
- For value [tex]\(4\)[/tex] with frequency [tex]\(2\)[/tex]: [tex]\(4 \times 2 = 8\)[/tex]
- For value [tex]\(5\)[/tex] with frequency [tex]\(2\)[/tex]: [tex]\(5 \times 2 = 10\)[/tex]
Adding these products together:
[tex]\[
7 + 2 + 9 + 8 + 10 = 36
\][/tex]
2. Calculate the total number of observations by summing the frequencies:
[tex]\[
7 + 1 + 3 + 2 + 2 = 15
\][/tex]
3. Calculate the mean by dividing the sum of the products by the total number of observations:
[tex]\[
\text{Mean} = \frac{36}{15} = 2.4
\][/tex]
Since the mean is already calculated to the nearest tenth, there is no additional rounding needed.
Hence, the mean of the given data is [tex]\(2.4\)[/tex].
