标题: Reading 7: Statistical Concepts and Market Returns-LOS h习题 [打印本页]
作者: bmaggie 时间: 2010-4-9 15:00 标题: [2010]Session 2:-Reading 7: Statistical Concepts and Market Returns-LOS h习题
Session 2: Quantitative Methods: Basic Concepts
Reading 7: Statistical Concepts and Market Returns
LOS h: Calculate and interpret the proportion of observations falling within a specified number of standard deviations of the mean using Chebyshev's inequality.
Assume a sample of beer prices is negatively skewed. Approximately what percentage of the distribution lies within plus or minus 2.40 standard deviations of the mean?
作者: bmaggie 时间: 2010-4-9 15:00
Assume a sample of beer prices is negatively skewed. Approximately what percentage of the distribution lies within plus or minus 2.40 standard deviations of the mean?
Use Chebyshev’s Inequality to calculate this answer. Chebyshev’s Inequality states that for any set of observations, the proportion of observations that lie within k standard deviations of the mean is at least 1 – 1/k2. We can use Chebyshev’s Inequality to measure the minimum amount of dispersion whether the distribution is normal or skewed. Here, 1 – (1 / 2.42) = 1 ? 0.17361 = 0.82639, or 82.6%.
作者: bmaggie 时间: 2010-4-9 15:01
In a skewed distribution, what is the minimum proportion of observations between +/- two standard deviations from the mean?
作者: bmaggie 时间: 2010-4-9 15:01
In a skewed distribution, what is the minimum proportion of observations between +/- two standard deviations from the mean?
For any distribution we can use Chebyshev’s Inequality, which states that the proportion of observations within k standard deviations of the mean is at least 1 – (1 / k2).
1 – (1 / 22) = 0.75, or 75%.
Note that for a normal distribution, 95% of observations will fall between +/- 2 standard deviations of the mean.
作者: bmaggie 时间: 2010-4-9 15:01
Regardless of the shape of a distribution, according to Chebyshev’s Inequality, what is the minimum percentage of observations that will lie within +/– two standard deviations of the mean?
作者: bmaggie 时间: 2010-4-9 15:01
Regardless of the shape of a distribution, according to Chebyshev’s Inequality, what is the minimum percentage of observations that will lie within +/– two standard deviations of the mean?
According to Chebyshev’s Inequality, for any distribution, the minimum percentage of observations that lie within k standard deviations of the distribution mean is equal to:
1 – (1 / k2), with k equal to the number of standard deviations. If k = 2, then the percentage of distributions is equal to 1 – (1 / 4) = 75%.
作者: bmaggie 时间: 2010-4-9 15:01
In a skewed distribution, what is the minimum amount of observations that will fall between +/- 1.5 standard deviations from the mean?
作者: bmaggie 时间: 2010-4-9 15:02
In a skewed distribution, what is the minimum amount of observations that will fall between +/- 1.5 standard deviations from the mean?
Because the distribution is skewed, we must use Chebyshev’s Inequality, which states that the proportion of observations within k standard deviations of the mean is at least 1 – (1 / k2).
1 – (1 / 1.52) = 0.5555, or 56%.
作者: bmaggie 时间: 2010-4-9 15:02
According to Chebyshev’s Inequality, for any distribution, what is the minimum percentage of observations that lie within three standard deviations of the mean?
作者: bmaggie 时间: 2010-4-9 15:02
According to Chebyshev’s Inequality, for any distribution, what is the minimum percentage of observations that lie within three standard deviations of the mean?
According to Chebyshev’s Inequality, for any distribution, the minimum percentage of observations that lie within k standard deviations of the distribution mean is equal to: 1 – (1 / k2). If k = 3, then the percentage of distributions is equal to 1 – (1 / 9) = 89%.
作者: zaestau 时间: 2010-4-26 18:22
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作者: kison 时间: 2010-8-24 21:11
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