Question:
My fifth grade class is working on a statistics project and they want to
know why one must have 95% of the data before we can determine the margin of
error. We need to know the way to find the margin of error like 5%. We
watched Newton's Apple and they talked about margin of error and bias.
Replies:
I do not think I know enough from your question to answer it with certainty.
In common sampling surveys for instance, it is not required that you have
95% of the data. In polls where there are only two choices for responses
(yes or no ... for or against) a sample of about 1000 persons from very
large populations (e.g. USA) is a very small percent of the "data" and yet
it is enough to get results with a margin of error that is less than 5%. I
am using what I think is the common meaning of "margin of error"; that is, a
measure of uncertainty for a statistic computed from the data. A common
example might appear as a statement such as "60% of those polled favored
candidate A versus candidate B. The poll has a margin of error of + or -
4%." In this case, the data yield the 60% statistic. The size of the
sample, etc. (in other words, the design of the poll which is usually not
stated to the public), is used to guarantee in theory that there is a high
probability that if we could afford to get all the data, the true percentage
for it would be between 56% and 64%. Some topics to research include design
of experiments, statistics for polls, confidence intervals (where you may
find that a few of my previous statements are oversimplified or even
inadequate but the situation is too complicated to fit in a small space and
with out more advanced study.
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