Question

Which biased estimator will have a reduced bias based on an increased sample size? mean median standard deviation range

Answer 1

The answer is: [C]: standard deviation ..
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Explanation:
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However, note that the mean of a sample from a normal population (that is, a type of "standard deviation" known as "standard deviation from a sample mean", is an "unbiased estimator" of the "population mean".

We shall represent the "sample mean" as:  x̅  ; 
               (pronounced: "x-bar"; that is; "ex-bar"); this is the usual symbol                                                                                                              used; 

We shall represent the sample size as "n" ;
                                                 (This is the usual variable used; note that
                                                                                "n" is a numeric value).
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The standard deviant from the sample mean:

(n *  x̅)  / (n + 1) is a "biased estimator of the mean" that becomes "unbiased" as the sample size increases; since as "n" increases in values; the value of the entire entire expression becomes smaller (i.e the standard deviation becomes smaller.
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