Weighted Average
Purpose: This activity will illustrate how to find the average weight of a item in a sample without having to weigh every object in the sample.  The average mass of a washer in a sample will be determined by finding the mass of just one representative item of each type and determining the % of that item within the population.

Time required: 1 day.

Group Size: Students should work in groups of 2

Materials Needed Per group:
• A set of washers in a film canister. The set will contain washers of three different sizes. The composition of the canisters will vary from group to group.
Prior Knowledge: Students need to be able to calculate a weighted average.
Avg. mass = Σ(mass of washer × relative abundance)
Procedure:
1. Obtain a film canister with washers.
2. Find the mass of one large washer, one medium sized washer, and one small washer. Record the masses.
3. Determine the percentage of each type of washer. Record  the percentages.

 Small washer Medium washer Large washer Mass of ONE washer % of washers
Analysis: Part I
Calculate the average mass of the washers in the sample.

Average mass = (mass of a small washer x percentage of small washers) + (mass of a medium washer x percentage of medium washers) + (mass of a large water x percentage of large washers)

NOTE:  The percentages must be converted to decimal format!
Analysis: Part II
Find the average mass of a washer by weighing all of the washers in the sample and dividing by the total number of washers.

 Mass of all washers Total # of washers

Average massmass of all washers/total # of washers × 100

Using the result from part one as the experimental value and the result from part two as the theoretical value, calculate the % error.
% error = (T-E)/T × 100

E Saylor

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