![]() Well, scientists have a method, and we go into the details, or more details, in other videos, called mass, sometimes it's So let's say that we have some mystery substance here, and we know that it's a pure element, and we need to figure out what it is. But weighted averages are necessary for things which do have unequal representations like atomic mass or GPA. So arithmetic averages are good for finding averages of things which are equally possible like dice rolls or coin tosses. So if I had an element with isotopes of those masses and abundances, in real life we'll see the 5.88 number since most of the mass of the sample is coming from the 6 and 5 isotopes and relatively little from the 3 isotope. The weighted average is much closer to 6 because there so much of 6 compared to the other numbers. An athematic average would be 4.67, but a weighted average would be 5.88. ![]() If I use your example and assign random abundances to the numbers, say 90% for 6, 9% for 5, and 1% for 3 we can see the differences in using arithmetic compared to a weighted average. And of course they are not, some isotopes are more stable than others leading to wildly different abundances often.Īnd the whole point of an average atomic mass to determine how much mass there would be in a pure sample of a single element. ![]() The issue with using an arithmetic mean for calculating something like average atomic mass is that it assumes that all the masses of the isotopes are present in nature in equally abundant amounts. The kind of mean you're describing is called an arithmetic mean.
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