Solve the below problem:
Q: Two types of wire, a 12 ½-gauge low-carbon wire and a thinner 14-gauge high-tensile wire, both used in barbed-wire fencing, are tested to see which wire is stronger. Data on the breaking strengths, in pounds, of both types of wire are given below. 12 ½-gauge, low-carbon wire: 455 455 495 490 410 470 475 450 480 460 480 445 435 405 450 500 435 430 460 480 14-gauge, high-tensile wire: 780 780 775 770 780 780 790 780 770 780 780 785 800 775 760 770 800 780 790 790
a. Make comparative boxplots for the breaking strengths of the types of wire. Would you describe the shapes of the distributions as symmetric or skewed?
b. Determine the mean breaking strengths for the two types of wire. Which type of wire has the larger mean breaking strength?
c. The two types of wires have different properties that affect the consistency of the wire's breaking strength. Find the standard deviation of breaking strengths for each type of wire. Which wire has the more variable breaking strength?