To find the mean number of languages spoken per person, follow these steps:
### Step 1: Understand the Data
The table provides the number of languages spoken and the frequency of people who speak that number of languages.
| Number of languages | Frequency |
|---------------------|-----------|
| 1 | 7 |
| 2 | 8 |
| 3 | 5 |
### Step 2: Calculate the Total Number of People
To find the total number of people, sum the frequencies.
[tex]\[
\text{Total number of people} = 7 + 8 + 5 = 20
\][/tex]
### Step 3: Calculate the Total Number of Languages Spoken
To find the total number of languages spoken, multiply each number of languages by its corresponding frequency and sum these products.
[tex]\[
\text{Total number of languages spoken} = (1 \times 7) + (2 \times 8) + (3 \times 5)
\][/tex]
Calculate each term:
[tex]\[
1 \times 7 = 7
\][/tex]
[tex]\[
2 \times 8 = 16
\][/tex]
[tex]\[
3 \times 5 = 15
\][/tex]
Now sum these values:
[tex]\[
7 + 16 + 15 = 38
\][/tex]
### Step 4: Calculate the Mean Number of Languages Spoken Per Person
To find the mean, divide the total number of languages spoken by the total number of people.
[tex]\[
\text{Mean number of languages spoken per person} = \frac{\text{Total number of languages spoken}}{\text{Total number of people}} = \frac{38}{20} = 1.9
\][/tex]
Therefore, the mean number of languages spoken per person is [tex]\(1.9\)[/tex].
