Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell four cars; nineteen generally sell five cars; twelve generally sell six cars; nine generally sell seven cars; eleven generally sell eight cars. Calculate the following. (Enter an exact number as an integer, fraction, or decimal.)

Given the data from the survey of 65 car salespersons, we need to calculate several statistics from the given information. Here's the summary of the dataGiven the data from the survey of 65 car salespersons, we need to calculate several statistics from the given information. Here's the summary of the 

- 14 people sell 4 cars
- 19 people sell 5 cars
- 12 people sell 6 cars
- 9 people sell 7 cars
- 11 people sell 8 cars

We can calculate various statistics like the mean, median, mode, variance, and standard deviation. Let’s begin with the mean.

### 1. **Mean Calculation**
The formula for the mean (\( \mu \)) is:

\[
\mu = \frac{\sum (x \times f)}{\sum f}
\]

Where:
- \( x \) is the number of cars sold.
- \( f \) is the frequency of that number of cars sold.

So, the sum of the product of each number of cars sold and its frequency is:

\[
\text{Sum of } x \times f = (4 \times 14) + (5 \times 19) + (6 \times 12) + (7 \times 9) + (8 \times 11)
\]

And the sum of the frequencies is 65 (since there are 65 respondents).

Let me calculate the mean.The mean number of cars sold by the car salespersons is approximately \( 5.75 \).

Would you like me to calculate other statistics such as the median, mode, variance, or standard deviation?

Here are some follow-up questions:
1. How is the median of this data calculated?
2. What does the mode tell us about the data?
3. How can we compute the standard deviation for this dataset?
4. What is the interpretation of the variance in this context?
5. How does the distribution of car sales impact these statistics?

**Tip**: The mean gives an overall average, but other statistics like the median and mode can provide additional insights into the dataset.

Learn how to calculate the mean number of cars sold by 65 randomly selected car salespersons based on the frequency of cars sold per week. This solution covers key statistics concepts, including the calculation of the mean using frequency distribution. Suitable for high school students in Grades 9-12.

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