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CIE A Level Maths: Probability & Statistics 2复习笔记1.2.1 Unbiased Estimates
Category:
A-level课程
,
教材笔记
,
福利干货
Date: 2022年8月18日 下午2:55
Unbiased Estimates
What is an unbiased estimator of a population parameter?
An
estimator
is a
statistic
that is used to estimate a
population parameter
When a sample is used with the estimator, the value that it produces is called an
estimate
An estimator is called
unbiased
if the
expected value
of the estimator is
equal
to the
population parameter
An estimate from an unbiased estimator is called an unbiased estimate
This means that the
mean
of the
unbiased estimates
will get
closer
to the
population parameter
as more samples are taken
What are the unbiased estimates for the mean and variance of a population?
If you had the data for a
whole population
you could find the
actual population mean
and
variance
using
Is there an unbiased estimate for the standard deviation?
Unfortunately square rooting an unbiased variance
does not
result in an unbiased standard deviation
There is
not a formula
for an unbiased estimate for the
standard deviation
that works for all populations
Therefore it is better to just work with the variance and not the standard deviation
If you need an estimate for the standard deviation then you can use:
This
won’t be unbiased
but it will be a good estimate
How do I calculate unbiased estimates?
Worked Example
Exam Tip
Always check whether you need to divide by n or n-1 by looking carefully at the wording in the question.
转载自savemyexams
Previous post: CIE A Level Maths: Probability & Statistics 2复习笔记1.1.1 Sampling & Data Collection
Next post: CIE A Level Maths: Probability & Statistics 2复习笔记1.2.2 Distribution of Sample Means
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