To determine the mean number of languages spoken per person, follow these steps:
1. Identify the data provided:
- Number of languages spoken: [tex]\(1, 2, 3\)[/tex]
- Corresponding frequencies: [tex]\(9, 8, 3\)[/tex]
2. Calculate the total number of people:
To find the total number of people surveyed, sum the frequencies:
[tex]\[
9 + 8 + 3 = 20
\][/tex]
So, there are [tex]\(20\)[/tex] people in total.
3. Calculate the total number of languages spoken:
To find the total number of languages spoken by all people, multiply each number of languages by its corresponding frequency and then sum these products:
[tex]\[
(1 \times 9) + (2 \times 8) + (3 \times 3) = 9 + 16 + 9 = 34
\][/tex]
4. Calculate the mean number of languages spoken per person:
The mean is found by dividing the total number of languages spoken by the total number of people:
[tex]\[
\text{Mean number of languages spoken} = \frac{\text{Total number of languages spoken}}{\text{Total number of people}} = \frac{34}{20} = 1.7
\][/tex]
So, the mean number of languages spoken per person is [tex]\(1.7\)[/tex].
