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Matilda was curious if sample interquartile range (IQR) was an unbiased estima- tor of population IQR. She placed ping pong balls numbered from 0 to 32 in a drum and mixed them well. Note that the IQR of the population is 16. She then took a random sample of 5 balls and calculated the IQR of the sample. She replaced the balls and repeated this process for a total of 50 trials. Her results are summarized in the dotplot below, where each dot represents the sample IQR from a sample of 5 balls.

Matilda was curious if sample interquartile range (IQR) was an unbiased estima- tor of population IQR. She placed ping pong balls numbered from 0 to 32 in a drum and mixed them well. Note that the IQR of the population is 16. She then took a random sample of 5 balls and calculated the IQR of the sample. She replaced the balls and repeated this process for a total of 50 trials. Her results are summarized in the dotplot below, where each dot represents the sample IQR from a sample of 5 balls.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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Matilda was curious if sample interquartile range (IQR) was an unbiased estima- tor of population IQR. She placed ping pong balls numbered from 0 to 32 in a drum and mixed them well. Note that the IQR of the population is 16. She then took a random sample of 5 balls and calculated the IQR of the sample. She replaced the balls and repeated this process for a total of 50 trials. Her results are summarized in the dotplot below, where each dot represents the sample IQR from a sample of 5 balls. H|| 5 10 15 25 Sample IQR Based on these results, does sample IQR appear to be a biased or unbiased estimator of population IQR? Explain briefly. 20
Transcribed Image Text:Matilda was curious if sample interquartile range (IQR) was an unbiased estima- tor of population IQR. She placed ping pong balls numbered from 0 to 32 in a drum and mixed them well. Note that the IQR of the population is 16. She then took a random sample of 5 balls and calculated the IQR of the sample. She replaced the balls and repeated this process for a total of 50 trials. Her results are summarized in the dotplot below, where each dot represents the sample IQR from a sample of 5 balls. H|| 5 10 15 25 Sample IQR Based on these results, does sample IQR appear to be a biased or unbiased estimator of population IQR? Explain briefly. 20
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