Aparameteris a number that describes a population and a statistic is a number that describes a sample. In general,statisticsare used to estimate parameters. Some statistics give better estimates than others. For example, there is a value for the true proportion of U.S. adults that approve of the President. This value is a parameter, and would be estimated because it is difficult to measure since populations are large. It is too costly to ask all U.S. registered voters if they approve of the President. A statistician will take a sample, say of 1000 U.S. voters, and calculate the proportion of the sample - called the sample proportion. This value should be close to the parameter of interest, the true proportion of U.S. adults that approve of the President. Will every sample of 1,000 U.S. voters have the same value for the sample proportion? No! The value of the statistic (the sample proportion will vary so the sample mean is said have a sampling distribution. The sampling distribution can be plotted with a histogram.

Four different statistics have been proposed as estimators of a population parameter. To investigate the behavior of these estimators, 500 random samples are selected from a known population and each statistic is calculated for each sample. The true value of the population parameter is 75. The graphs below show the distribution of values for each statistic.

Which of statistics, A, B, C, or D would be a better estimator of the population parameter? Explain your choice.

Statistic A Statistic B 50 75 100 50 75 100 Statistic C Statistic D 50 75 100 50 75 100