Based on the table, were you able to show that the sample mean is unbiased?Based on the table, were you able to show that the sample variance is unbiased?Determine the mean of all sample medians. Based on your result, is the sample median an unbiased estimator of the population mean?Determine the mean of all sample medians. Based on your result, is the sample median an unbiased estimator of the population mean? Yı, Yar Yay8, 10, 47.3333#N/A9.33338, 10, 57.66678#N/A6.333338, 10, 109.333310101.333348, 4,5.66675#N/A4.33338, 4, 107.33338#N/A9.33338, 5,107.66678#N/A6.3333710, 4, 56.33335#N/A10.333310, 4, 108.0000101012.0000910, 5, 108.333310108.3333104, 5, 106.333351010.3333Total73.99977. 9992.5.

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College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.5: Counting Principles

Problem 41SE: A cell phone company offers 6 different voice packages and 8 different data packages. Of those, 3...

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Question

Based on the table, were you able to show that the sample mean is unbiased?
Based on the table, were you able to show that the sample variance is unbiased?
Determine the mean of all sample medians. Based on your result, is the sample median an unbiased estimator of the population mean?
Determine the mean of all sample medians. Based on your result, is the sample median an unbiased estimator of the population mean?

Yı, Yar Ya
y
8, 10, 4
7.3333
#N/A
9.3333
8, 10, 5
7.6667
8
#N/A
6.3333
3
8, 10, 10
9.3333
10
10
1.3333
4
8, 4,
5.6667
5
#N/A
4.3333
8, 4, 10
7.3333
8
#N/A
9.3333
8, 5,
10
7.6667
8
#N/A
6.3333
7
10, 4, 5
6.3333
5
#N/A
10.3333
10, 4, 10
8.0000
10
10
12.0000
9
10, 5, 10
8.3333
10
10
8.3333
10
4, 5, 10
6.3333
5
10
10.3333
Total
73.999
77. 999
2.
5.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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