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

Answer:

x = 6.75 cars

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 65

14 people generally sell 5 cars

19 generally sell 6 cars

12 generally sell 7 cars

9 generally sell 8 cars

11 generally sell 9 cars

We have to calculate the sample mean.

Formula:

$\text{Weighted mean} = \displaystyle\frac{\sum w_ix_i}{\sum w_i}\\\\\sum w_ix_i = 14(5) + 19(6) + 12(7) + 9(8) + 11(9) = 439\\\\\sum w_i = 14 + 19 + 12 + 9 + 11 = 65\\\\\text{Weighted mean} = \frac{439}{65} = 6.75$

Thus, the weighted sample mean is 6.75 cars.