Answered: Flavia wanted to know if the first…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Flavia wanted to know if the first sample quartile (or Q1) was an unbiased estimator of the first population quartile. She started with a large population of normally distributed grades, the first quartile of which was Q = 70. She then took a random sample of 6 tests and calculated the first quartile of the sample. She replaced those exams and repeated this process a total of 50 times. Her results are summarized in the dot plot below, where each point represents the first sample quartile of a sample of 6 exams. Based on these results, does the first sample quartile appear to be a biased or unbiased estimator of the first population quartile? Track; the first population quartile is 70.

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The first sample quartile appears to be a biased estimator since it consistently underestimated
the first population quartile
The first sample quartile appears to be a biased estimator since it consistently overestimated
the first population quartile
The first sample quartile appears to be an unbiased estimator of the first population quartile.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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