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The empirical rule is 68 - 95 - 99.7. 68% is the area for +/- 1 standard deviation (SD) from the mean, 95% is the area for +/- 2 SD from the mean; and 99.7% is the area for +/- 3 SD from the mean.
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State the main reason for using the empirical rule rather than chebyshevs theorem?
The empirical rule can only be used for a normal distribution, so I will assume you are referring to a normal distribution. Chebyshev's theorem can be used for any distribution. The empirical rule is more accurate than Chebyshev's theorem for a normal distribution. For 2 standard deviations (sd) from the mean, the empirical rule says 95% of the data are within that, and Chebyshev's theorem says 1 - 1/2^2 = 1 - 1/4 = 3/4 or 75% of the data are within that. From the standard normal distribution chart, the answer for 2 sd from the mean is 95.44% So, as you can see the empirical rule is more accurate.
Is standard deviation the arithmetic mean of the squared deviations from the means?
No. Standard deviation is the square root of the mean of the squared deviations from the mean. Also, if the mean of the data is determined by the same process as the deviation from the mean, then you loose one degree of freedom, and the divisor in the calculation should be N-1, instead of just N.
What is the formula to determine the standard deviation of the resulting normal distribution when adding two normal distributions with different means and standard deviations?
s= bracket n over sigma i (xi-x-)^2 all over n-1 closed bracket ^ 1/2
What do you do if you get a number that is not on the Normal Distribution table as it is too high so above 3?
Suspect you've made a mistake in your calculations.Looking at the Normal curve, the area under it between the mean and 3.09 standard deviations is [approx] 0.4990, ie the probability that the data could exceed 3.09 standard deviations from the mean is 2 x (0.5-0.4990) = 0.002 = 0.2% [using a half-tail table], ie it is quite unlikely that a data point is much further away from the mean than the tables' limit of 3.09.Beyond 3[.09] standard deviations away from the mean, the area under the curve changes very little in the first 4 dp, so [most] tables are going to not be of much help anyway - when 4 standard deviations away are reached, it is almost all the distribution and rounds to 1.So if you are looking at a point greater than 3 standard deviations away from the mean it is either a very unusual event that has caused it, or (more likely) you've made a mistake in your calculations.
What is the probability of randomly selecting values more then 2.57 standard deviations away from the mean in either a positive or negative direction in a normal distribution?
1% total 0.5% in either direction
What are the differences between the Emperical Rule and Chebyshev's Theorem?
The Empirical Rule applies solely to the NORMAL distribution, while Chebyshev's Theorem (Chebyshev's Inequality, Tchebysheff's Inequality, Bienaymé-Chebyshev Inequality) deals with ALL (well, rather, REAL-WORLD) distributions. The Empirical Rule is stronger than Chebyshev's Inequality, but applies to fewer cases. The Empirical Rule: - Applies to normal distributions. - About 68% of the values lie within one standard deviation of the mean. - About 95% of the values lie within two standard deviations of the mean. - About 99.7% of the values lie within three standard deviations of the mean. - For more precise values or values for another interval, use a normalcdf function on a calculator or integrate e^(-(x - mu)^2/(2*(sigma^2))) / (sigma*sqrt(2*pi)) along the desired interval (where mu is the population mean and sigma is the population standard deviation). Chebyshev's Theorem/Inequality: - Applies to all (real-world) distributions. - No more than 1/(k^2) of the values are more than k standard deviations away from the mean. This yields the following in comparison to the Empirical Rule: - No more than [all] of the values are more than 1 standard deviation away from the mean. - No more than 1/4 of the values are more than 2 standard deviations away from the mean. - No more than 1/9 of the values are more than 3 standard deviations away from the mean. - This is weaker than the Empirical Rule for the case of the normal distribution, but can be applied to all (real-world) distributions. For example, for a normal distribution, Chebyshev's Inequality states that at most 1/4 of the values are beyond 2 standard deviations from the mean, which means that at least 75% are within 2 standard deviations of the mean. The Empirical Rule makes the much stronger statement that about 95% of the values are within 2 standard deviations of the mean. However, for a distribution that has significant skew or other attributes that do not match the normal distribution, one can use Chebyshev's Inequality, but not the Empirical Rule. - Chebyshev's Inequality is a "fall-back" for distributions that cannot be modeled by approximations with more specific rules and provisions, such as the Empirical Rule.
State the main reason for using the empirical rule rather than chebyshevs theorem?
The empirical rule can only be used for a normal distribution, so I will assume you are referring to a normal distribution. Chebyshev's theorem can be used for any distribution. The empirical rule is more accurate than Chebyshev's theorem for a normal distribution. For 2 standard deviations (sd) from the mean, the empirical rule says 95% of the data are within that, and Chebyshev's theorem says 1 - 1/2^2 = 1 - 1/4 = 3/4 or 75% of the data are within that. From the standard normal distribution chart, the answer for 2 sd from the mean is 95.44% So, as you can see the empirical rule is more accurate.
What is the 68-95-99.7 rule?
The 68-95-99.7 rule, or empirical rule, says this:for a normal distribution almost all values lie within 3 standard deviations of the mean.this means that approximately 68% of the values lie within 1 standard deviation of the mean (or between the mean minus 1 times the standard deviation, and the mean plus 1 times the standard deviation). In statistical notation, this is represented as: μ ± σ.And approximately 95% of the values lie within 2 standard deviations of the mean (or between the mean minus 2 times the standard deviation, and the mean plus 2 times the standard deviation). The statistical notation for this is: μ ± 2σ.Almost all (actually, 99.7%) of the values lie within 3 standard deviations of the mean (or between the mean minus 3 times the standard deviation and the mean plus 3 times the standard deviation). Statisticians use the following notation to represent this: μ ± 3σ.(www.wikipedia.org)
What is the measures that fall beyond three standard deviations of the mean called?
You may be referring to the statistical term 'outlier(s)'. Also, there is a rule in statistics called the '68-95-99 Rule'. It states that in a normally distributed dataset approximately 68% of the observations will be within plus/minus one standard deviation of the mean, 95% within plus/minus two standard deviations, and 99% within plus/minus three standard deviations. So if your data follow the classic bell-shaped curve, roughly 1% of the measures should fall beyond three standard deviations of the mean.
How many standard deviations is 99?
You cannot have a standard deviation for 1 number.
What is the difference between Chebyshevs inequality and empirical rule in terms of skewness?
Chebyshev's inequality: The fraction of any data set lying within K standard deviations is always at least 1-1/K^2 where K is any positive number greater than 1. It does not assume that any distribution. Now, there is the empirical rule of bell shaped curves or the 68-95-99.7 rule, which states that for a bell shaped curve: 68% of all values should fall within 1 standard deviation, 95% of all values should fall within 2 standard deviations and 99.7% of all values should fall within 3 standard deviation. If we suspect that our data is not bell shaped, but right or left skewed, the above rule can not be applied. I note that one test of skewness is Pearson's index of skewness, I= 3(mean of data - median of data)/(std deviation) If I is greater or equal to 1000 or I is less than 1, the data can be considered significantly skewed. I hope this answers your question. I used the textbook Elementary Statistics by Triola for the information on Pearson's index. If this answer is insufficient, please resubmit and be a bit more definitive on what you mean by empirical rule.
What is chebychev's rule?
Chebyshev's rule, also known as Chebyshev's inequality, is a statistical theorem that describes the proportion of values that fall within a certain number of standard deviations from the mean in any distribution. It states that for any set of data, regardless of the shape of the distribution, at least (1 - 1/k^2) where k is greater than 1, of the data values will fall within k standard deviations of the mean.
What percentage of a normal distribution is within 2 standard deviations of the mean?
I believe the standard deviations are measured from the median, not the mean.1 Standard Deviation is 34% each side of median, so that is 68% total.2 Standard Deviations is 48% each side of median, so that is 96% total.
How can you find the percentage of empirical rule?
The number of potholes inThe number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has a bell-shaped distribution. This distribution has a mean of 61 and a standard deviation of 9. Using the empirical rule (as presented in the book), what is the approximate percentage of 1-mile long roadways with potholes numbering between 34 and 70? any given 1 mile stretch of freeway pavement in Pennsylvania has a bell-shaped distribution. This distribution has a mean of 61 and a standard deviation of 9. Using the empirical rule (as presented in the book), what is the approximate percentage of 1-mile long roadways with potholes numbering between 34 and 70?
A z-score of plus 1.6 represents a value which is how many standard deviations above the mean?
1
The mean number is 14 with a standard deviation of 2.5 How many standard deviations is 16.50 from the mean?
16.5 is 1 standard deviation from the mean. If you add the mean of 14 to the 1 standard deviation of 2.5, the result is 16.5.
What does standard deviation help you find?
Standard deviation helps you identify the relative level of variation from the mean or equation approximating the relationship in the data set. In a normal distribution 1 standard deviation left or right of the mean = 68.2% of the data 2 standard deviations left or right of the mean = 95.4% of the data 3 standard deviations left or right of the mean = 99.6% of the data
