Understanding Sample Median as an Estimator

Alejandro conducted an experiment to determine if the sample median is an unbiased estimator of the population median. He used 33 ping pong balls numbered 0 to 32, repeatedly taking random samples of five balls, calculating their median, and plotting the results. After 50 trials, he analyzed the dot plot to approximate the sampling distribution. By comparing the distribution to the true population median, he concluded that the sample median appears to be an unbiased estimator, as the distribution was not skewed significantly above or below the true median.

What was Alejandro curious about in his experiment?

• If the sample range is an unbiased estimator of the population range

• If the sample mode is an unbiased estimator of the population mode

• If the sample median is an unbiased estimator of the population median

• If the sample mean is an unbiased estimator of the population mean

How many ping pong balls did Alejandro use in his experiment?

• 50

• 32

• 33

• 16

What was the size of each sample Alejandro took?

• 15 balls

• 10 balls

• 5 balls

• 3 balls

How many trials did Alejandro conduct in his experiment?

• 10

• 50

• 20

• 100

What does each dot in the dot plot represent?

• A sample range

• A sample median

• A sample mode

• A sample mean

What is the purpose of the dot plot in Alejandro's experiment?

• To show the distribution of sample ranges

• To show the distribution of sample modes

• To show the distribution of sample medians

• To show the distribution of sample means

What would indicate a biased estimator in the sampling distribution?

• A distribution skewed to one side

• A distribution with equal peaks

• A perfectly symmetrical distribution

• A distribution with no variation

What is the true population median in Alejandro's experiment?

• 32

• 16

• 10

• 20

What conclusion does Alejandro reach about the sample median?

• It is a biased estimator of the population median

• It is an unbiased estimator of the population median

• It is an unreliable estimator of the population median

• It is a perfect estimator of the population median

What does an unbiased estimator imply about the sample statistics?

• They have no relation to the population parameter

• They are skewed away from the population parameter

• They are symmetrically distributed around the population parameter

• They are always equal to the population parameter