# Introduction to Statistics and Data Analysis | Probability & Statistics for Engineers & Scientists | Walpole | Problem 1.4

In a study conducted by the Department of Mechanical Engineering at Virginia Tech, the steel rods supplied by two different companies were compared. Ten sample springs were made out of the steel rods supplied by each company and a measure of flexibility was recorded for each. The data are as follows:

 Company A: Company B: 9.3 8.8 6.8 8.7 8.5 6.7 8 6.5 9.2 7 11 9.8 9.9 10.2 10.1 9.7 11 11.1 10.2 9.6

(a) Calculate the sample mean and median for the data for the two companies.

(b) Plot the data for the two companies on the same line and give your impression.

## Solution:

Part (a)

The mean and median of Company A are  $\displaystyle \overline{x}_A=7.950\:and\:\widetilde{x}_A=8.250$, respectively.

The mean and median of Company B are  $\displaystyle \overline{x}_B=10.260\:and\:\widetilde{x}_B=10.150$, respectively.

Part (b)

A dot plot is shown below

In the ﬁgure, “×” represents company A and “◦” represents company B. The steel rods made by company B show more ﬂexibility.