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 five cars; nineteen generally sell six cars; twelve generally sell seven cars; nine generally sell eight cars; eleven generally sell nine cars. Calculate the following. (Round your answer to two decimal places.)

Question

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 five cars; nineteen generally sell six cars; twelve generally sell seven cars; nine generally sell eight cars; eleven generally sell nine cars. Calculate the following. (Round your answer to two decimal places.)

sample mean = x
x = cars

Answer 1

To calculate the sample mean, we need to find the average number of cars sold by the car salespersons.

Step 1: Multiply the number of cars sold by the frequency of each category.
For the given data:
5 cars: 14 salespersons
6 cars: 19 salespersons
7 cars: 12 salespersons
8 cars: 9 salespersons
9 cars: 11 salespersons

To find the total number of cars sold, we multiply the number of cars by the frequency:
(5 cars * 14 salespersons) + (6 cars * 19 salespersons) + (7 cars * 12 salespersons) + (8 cars * 9 salespersons) + (9 cars * 11 salespersons)

Step 2: Add up the products from Step 1 to get the sum of all the cars sold.

Step 3: Divide the sum from Step 2 by the total number of car salespersons to get the sample mean.

Let's calculate it:

(5 cars * 14 salespersons) + (6 cars * 19 salespersons) + (7 cars * 12 salespersons) + (8 cars * 9 salespersons) + (9 cars * 11 salespersons) = 70 cars + 114 cars + 84 cars + 72 cars + 99 cars = 439 cars

sample mean (x) = 439 cars / (14 salespersons + 19 salespersons + 12 salespersons + 9 salespersons + 11 salespersons) = 439 cars / 65 salespersons ≈ 6.76 cars (rounded to two decimal places)

Therefore, the sample mean for the number of cars generally sold by car salespersons is approximately 6.76 cars.

Answer 2

To calculate the sample mean (x), we need to multiply the number of cars sold by the number of salespersons for each category, sum them up, and then divide by the total number of salespersons.

The calculation is as follows:

(14 * 5) + (19 * 6) + (12 * 7) + (9 * 8) + (11 * 9) = 70 + 114 + 84 + 72 + 99 = 439

Next, we divide the sum by the total number of salespersons:

x = 439 / 65

Using a calculator, we find that x is approximately 6.75 (rounded to two decimal places).

Therefore, the sample mean (x) for the number of cars sold in one week is 6.75 cars.

Answer 3

Step 1: Make a frequency distribution table. I will refer to each of the values (number of cars) as x(i) and each of the frequencies as f(i)

Step 2: Finding the mean:

Mean = Σ( x(i)*f(i) ) / (Total number of salespersons)