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The reason the standard deviation of a distribution of means is smaller than the standard deviation of the population from which it was derived is actually quite logical. Keep in mind that standard deviation is the square root of variance. Variance is quite simply an expression of the variation among values in the population. Each of the means within the distribution of means is comprised of a sample of values taken randomly from the population. While it is possible for a random sample of multiple values to have come from one extreme or the other of the population distribution, it is unlikely. Generally, each sample will consist of some values on the lower end of the distribution, some from the higher end, and most from near the middle. In most cases, the values (both extremes and middle values) within each sample will balance out and average out to somewhere toward the middle of the population distribution. So the mean of each sample is likely to be close to the mean of the population and unlikely to be extreme in either direction. Because the majority of the means in a distribution of means will fall closer to the population mean than many of the individual values in the population, there is less variation among the distribution of means than among individual values in the population from which it was derived. Because there is less variation, the variance is lower, and thus, the square root of the variance - the standard deviation of the distribution of means - is less than the standard deviation of the population from which it was derived.
For data sets having a normal, bell-shaped distribution, the following properties apply: About 68% of all values fall within 1 standard deviation of the mean About 95% of all values fall within 2 standard deviation of the mean About 99.7% of all values fall within 3 standard deviation of the mean.
The Empirical Rule states that 68% of the data falls within 1 standard deviation from the mean. Since 1000 data values are given, take .68*1000 and you have 680 values are within 1 standard deviation from the mean.
A standard distribution regards 95% of all data being within 2-standard deviations of either side. Similarly, within one standard deviation either way is 68% of all data. This creates a bell curve distribution. An abnormal distribution would be erratic and not follow such a statistical structure of representation.
Individual digits within a number have place values, not whole numbers.
34.1% of the data values fall between (mean-1sd) and the mean.
The reason the standard deviation of a distribution of means is smaller than the standard deviation of the population from which it was derived is actually quite logical. Keep in mind that standard deviation is the square root of variance. Variance is quite simply an expression of the variation among values in the population. Each of the means within the distribution of means is comprised of a sample of values taken randomly from the population. While it is possible for a random sample of multiple values to have come from one extreme or the other of the population distribution, it is unlikely. Generally, each sample will consist of some values on the lower end of the distribution, some from the higher end, and most from near the middle. In most cases, the values (both extremes and middle values) within each sample will balance out and average out to somewhere toward the middle of the population distribution. So the mean of each sample is likely to be close to the mean of the population and unlikely to be extreme in either direction. Because the majority of the means in a distribution of means will fall closer to the population mean than many of the individual values in the population, there is less variation among the distribution of means than among individual values in the population from which it was derived. Because there is less variation, the variance is lower, and thus, the square root of the variance - the standard deviation of the distribution of means - is less than the standard deviation of the population from which it was derived.
For data sets having a normal, bell-shaped distribution, the following properties apply: About 68% of all values fall within 1 standard deviation of the mean About 95% of all values fall within 2 standard deviation of the mean About 99.7% of all values fall within 3 standard deviation of the mean.
The Empirical Rule states that 68% of the data falls within 1 standard deviation from the mean. Since 1000 data values are given, take .68*1000 and you have 680 values are within 1 standard deviation from the mean.
For data sets having a normal distribution, the following properties depend on the mean and the standard deviation. This is known as the Empirical rule. About 68% of all values fall within 1 standard deviation of the mean About 95% of all values fall within 2 standard deviation of the mean About 99.7% of all values fall within 3 standard deviation of the mean. So given any value and given the mean and standard deviation, one can say right away where that value is compared to 60, 95 and 99 percent of the other values. The mean of the any distribution is a measure of centrality, but in case of the normal distribution, it is equal to the mode and median of the distribtion. The standard deviation is a measure of data dispersion or variability. In the case of the normal distribution, the mean and the standard deviation are the two parameters of the distribution, therefore they completely define the distribution. See: http://en.wikipedia.org/wiki/Normal_distribution
A Gaussian distribution is the "official" term for the Normal distribution. This is a probability density function, of the exponential family, defined by the two parameters, its mean and variance. A population is said to be normally distributed if the values that a variable of interest can take have a normal or Gaussian distribution within that population.
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.
Whichever location has higher property values will charge higher prices to cover the cost of the building.
A normal distribution is symmetric and when looked at on a graph, the graph looks like a bell shaped curve. Approximately 95 percent of its values should lie within two standard deviations of the mean. Frequency of the data lies mostly in the middle of the curve.
A biodistribution is the distribution of compounds within a biological system or within an organism.
Population distribution refers to the patterns that a population creates as they spread within an area. A sampling distribution is a representative, random sample of that population.
advantages: -very informative when examining how values are changing within the data set. -shows the running total of frequencies from the lowest interval up. disadvantages: -difficult to compare the frequencies between each data group. by Mr. Hsia