Define, and give examples of biased and unbiased statistics, and give one example of how to remove bias from a statistic
What will be an ideal response?
Ans: A statistic is unbiased when the mean of its sampling distribution (its expected value) equals the parameter it estimates. The sample mean is an unbiased statistic. When the mean of a statistic’s distribution does not equal the parameter it estimates, the statistic is biased. The sample variance, computed as the average squared deviation from the mean, is a biased statistic. Its expected value is , which underestimates ?2. To correct this bias we could multiply the biased statistic by , or simply compute the variance by dividing the sum of squares ( ) by .
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