# Which of the following statistics are unbiased estimators of population​ paramet

Which of the following statistics are unbiased estimators of population​ parameters?
Choose the correct answer below. Select all that apply.
A) Choose the correct answer below. Select all that apply.
B) Sample variance used to estimate a population variance.
C) Sample proportion used to estimate a population proportion.
D) Sample mean used to estimate a population mean.
E) Sample range used to estimate a population range.
F) Sample standard deviation used to estimate a population standard deviation
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Step 1
Concept and reason
Estimator: It is a rule that tells you how to calculate the estimate based on the sample.
Parameter space: The set of all possible value is called parameter space.
Unbiasedness: An estimator is said to be an unbiased estimator of $\gamma \left(\theta \right)$ if $E\left({T}_{n}\right)=\gamma \left(\theta \right)$ for all $\theta \in \mathrm{\Theta }$
Baisedness: An estimator is said to be an unbiased estimator of $\gamma \left(\theta \right)$ if $E\left({T}_{n}\right)\ne \gamma \left(\theta \right)$ for all $\theta \in \mathrm{\Theta }$
Fundamentals
The formula for sample mean is,
$\stackrel{―}{x}=\frac{\sum x}{n}$
The formula for sample variance is,
${s}^{2}=\frac{1}{n}\sum _{i=1}^{n}{\left({x}_{i}-\stackrel{―}{x}\right)}^{2}$
${S}^{2}=\frac{1}{n-1}\sum _{i=1}^{n}{\left({x}_{i}-\stackrel{―}{x}\right)}^{2}$
The formula for standard deviation is,
$s={\sqrt{s}}^{2}$
Step 2
From the known information sample median, ranges and standard deviation are biased estimators.
The sample mean, variance and the proportion are unbiased estimators of population parameters.
Step 2
From the known information and $E\left({s}^{2}\right)={\sigma }^{2}$. So, the unbiased estimators are sample mean, variance and the proportion.
Sample variance used to estimate a population variance.
Sample proportion used to estimate a population proportion.
Sample mean used to estimate a population mean.
The sample variance is an unbiased estimator of population variance. The sample proportion is an unbiased estimate of the population proportion and the sample mean is an unbiased estimate of the population mean.