Question

Used cars, cheap! A used-car salesman has 28 cars in his inventory, with prices ranging from \(11,500 to \)25,000. For a Labor Day sale, he reduces the price of each car by $500. What effect will this reduction have on each of the following characteristics of the resulting distribution of price?

a. Shape

b. Mean and median

c. Standard deviation and interquartile range (IQR)

Short answer

Part (a) No change.

Part (b) Mean = It will be decreased by $\$500$

Median = No effect

Part (c) No change in standard deviation.

No change in the interquartile range.

Step-by-step solution

Part (a) Step 1: Given information

A used-car vendor had $28$ vehicles in stock, ranging in price from $\$11,500$ to $\$25,000$ He lowers the price of each car by $\$500$ for a Labor Day sale.

Part (a) Step 2: Explanation

Here, changes are being made to the car prices of each car, with each car's price being reduced by $\$500$ Changes in the car price of all cars indicate a change in origin, although the structure of the distribution is unaffected by the change in origin.

Part (b) Step 1: Explanation

Changes are being made to the car prices of each car, with each car's price being reduced by $\$500$ Changes in the price of all cars indicate a change in origin, and when there is a change in origin, it also indicates an increase or drop by the same amount, thus the mean will reduce by $\$500$, but the median will remain same. The data's median continues to be the data's middle term.

Part (c) Step 1: Explanation

Changes are being made to the car prices of each car, with each car's price being reduced by $\$500$ Changes in the price of all cars indicate a change in origin, and when there is a change in origin, the measures of dispersion such as standard and interquartile range have no influence.