Biased and unbiased Estimators

Example: If a population contains 1,000 items with an average value of "u" and you randomly pick many samples. If each sample contains 10 items with an average value of "ai" [e.g. kg in weight], then you plot the values of "ai" and it should give you
a normal distribution with an average value = "u". The sample mean is an unbiased estimator of the population mean.

However, instead of using the sample mean, you have decided to use the lowest weight in a sample of 10 items as the "mean" of that sample, and you plot the "mean" of many samples, you will find the curve plotted is not a normal distribution, And, accordingly, the "mean" of the "means" of the skewed curve would no longer equal to the mean of the population. The sample mean of this skewed distribution is an biased estimator of the population mean.

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