Part 1: Consider the four identical spheres below, each with a mass of 2.00 g.

Calculate the average mass of a sphere in this sample.
Part 2: Now consider a sample that consists of four spheres, each with a different mass: blue mass is 2.00 g, red mass is 1.75 g, green mass is 3.00 g, and yellow mass is 1.25 g.

a. Calculate the average mass of a sphere in this sample.
b. How does the average mass for a sphere in this sample compare with the average mass of the sample that consisted just of the blue spheres? How can such different samples have their averages turn out the way they did?
Part 3: Consider two jars. One jar contains 100 blue spheres, and the other jar contains 25 each of red, blue, green, and yellow colors mixed together.
a. If you were to remove 50 blue spheres from the jar containing just the blue spheres, what would be total mass of spheres left in the jar?
b. If you were to remove 50 spheres from the jar containing the mixture (assume you get a representative distribution of colors), what would be the total mass of spheres left in the jar?
c. In the case of the mixture of spheres, does the average mass of the spheres necessarily represent the mass of an individual sphere in the sample?
d. If you had 80.0 grams of spheres from the blue sample, how many spheres would you have?
e. If you had 60.0 grams of spheres from the mixed-color sample, how many spheres would you have? What assumption did you make about your sample when performing this calculation?
Part 4: Consider a sample that consists of three green spheres and one blue sphere. The green mass is 3.00 g, and the blue mass is 1.00 g.

a. Calculate the fractional abundance of each sphere in the sample.
b. Use the fractional abundance to calculate the average mass of the spheres in this sample.
c. How are the ideas developed in this Concept Exploration related to the atomic masses of the elements?