A new car with a $19,700 list price can be bought for different prices from different dealers. In one city the car can be bought for $18,900 from 2 dealers, for $17,500 from 1 dealer, for $17800 from 3 dealers, for $18,300 from 2 dealers, and for $18,200 from 2 dealers. What are the mean and standard deviation of this sample of car prices? Round your answer to two decimal places wherever applicable.

Question

A new car with a $19,700 list price can be bought for different prices from different dealers. In one city the car can be bought for $18,900 from 2 dealers, for $17,500 from 1 dealer, for $17800 from 3 dealers, for $18,300 from 2 dealers, and for $18,200 from 2 dealers. What are the mean and standard deviation of this sample of car prices? Round your answer to two decimal places wherever applicable. ​

Quizplus · Accepted Answer

To find the mean, we need to add up all the prices and divide by the total number of dealers:

Mean = (2 x 18,900 + 1 x 17,500 + 3 x 17,800 + 2 x 18,300 + 2 x 18,200) / 10
Mean = 18,060

To find the standard deviation, we need to find the variance first:

Variance = [(18,900 - 18,060)^2 x 2 + (17,500 - 18,060)^2 + (17,800 - 18,060)^2 x 3 + (18,300 - 18,060)^2 x 2 + (18,200 - 18,060)^2 x 2] / 10
Variance = 124,322

Then, we can calculate the standard deviation by taking the square root of the variance:

Standard deviation = sqrt(124,322)
Standard deviation = 352.53

Therefore, the mean is $18,060 and the standard deviation is $352.53, which is only provided as an option in choice C.

A New Car with a $19,700 List Price Can Be