# How can I calculate ± estimate based on sample set?

Say I have a completely random sample of 25M weights of a population of 100M. Say the average weight of the 25M random sample is 150lbs with a standard deviation of 45lbs. How can I be more precise in describing the average weight of the larger 100M population?

In other words, help me make this sentence more precise:

The average weight of this 100M population is 150lbs.


This isn't entirely precise because I didn't measure all 100M. Please help me use more precise language to describe the results of this data.

• How was this sample obtained? – Glen_b May 25 '16 at 16:52
• @Glen_b assume the sample set is random. This is a fictional scenario. I'm trying to understand how to be more precise with making estimates on similar sets of data. If the randomness is in question, they all stood in a long line and a fair four sided die was rolled for each in turn. If a 1 was rolled, they were weighed and recorded. The others were teleported to an alternate universe with similar gravitational forces. – Ryan May 25 '16 at 18:03
• Heh. "A completely random sample" suffices, thanks; it's necessary to be clear about the kind of sampling to be able to answer the question properly. If you edit your question at some point it would be best to edit that information into the question. – Glen_b May 25 '16 at 23:53
• The only issue here (that hasn't been extensively discussed in other threads) is whether to account for the fact that this sample is an appreciable fraction of the population (by applying a "finite population correction"). Is that your concern, or do you only care about how to express whatever standard error of estimate you have computed? – whuber May 26 '16 at 15:05
• @whuber, Yes, the comments so far indicate it doesn't matter if the finite population is 100B, 100M or 25M. How does the % of the finite population sampled influence precision, and how would you report the above findings in one readable sentence? – Ryan May 27 '16 at 16:07