Question

Suppose that you convert the class’s heights from inches to centimeters ($1inch=2.54cm$). Describe the effect this will have on the shape, center, and spread of the distribution.

Short answer

Centre and spread are affected but shape would not be changed

Step-by-step solution

Step 1. Given

Step 2. Concept

The following Minitab computer output validates the outcome: When each observation in distribution is standardized, the resultant set of z-scores has a mean of $0$ and a standard deviation of $1$

Step 3. Explanation

The change in height was from $1$ inch to $2.54$ centimeters. Height was modified from one centimeter to $2.54$ inches based on the information provided. Multiplication has an effect on the center and spread, therefore spread and center would be multiplied by $2.54$. The form would not be altered.