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What else can I help you with?
Does the empirical rule work for any data set?
No.The empirical rule is a good estimate of the spread of the data given the mean and standard deviation of a data set that follows the normal distribution.If you you have a data set with 10 values, perhaps all 10 the same, you clearly cannot use the empirical rule.
What does one standard deviation mean?
Standard deviation is a measure of variation from the mean of a data set. 1 standard deviation from the mean (which is usually + and - from mean) contains 68% of the data.
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.
In research how to define standard deviation?
Standard deviation shows how much variation there is from the "average" (mean). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
What are importance of mean and standard deviation in the use of normal distribution?
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
Does the empirical rule work for any data set?
No.The empirical rule is a good estimate of the spread of the data given the mean and standard deviation of a data set that follows the normal distribution.If you you have a data set with 10 values, perhaps all 10 the same, you clearly cannot use the empirical rule.
When a data set is normally distributed about how much of the data fall within one standard deviation of the mean?
In a normally distributed data set, approximately 68% of the data falls within one standard deviation of the mean. This is part of the empirical rule, which states that about 68% of the data lies within one standard deviation, about 95% within two standard deviations, and about 99.7% within three standard deviations.
What percentage of the data falls within 3 standard deviation of the mean?
Approximately 99.7% of the data falls within 3 standard deviations of the mean in a normal distribution. This is known as the empirical rule or the 68-95-99.7 rule, which describes how data is distributed in a bell-shaped curve. Specifically, about 68% of the data falls within 1 standard deviation, and about 95% falls within 2 standard deviations of the mean.
A set of 1000 values has a normal distribution the mean of the data is 120 and the standard deviation is 20 how many values are within one standard deviaiton from 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.
How does the bell curve relates to the empirical rule?
The bell curve, also known as the normal distribution, is a symmetrical probability distribution that follows the empirical rule. The empirical rule states that for approximately 68% of the data, it lies within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations when data follows a normal distribution. This relationship allows us to make predictions about data distribution based on these rules.
Is empirical rule a characteristic of a normal distribution?
Yes, the empirical rule, also known as the 68-95-99.7 rule, is a characteristic of a normal distribution. It states that approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and around 99.7% lies within three standard deviations. This rule helps in understanding the spread and variability of data in a normally distributed dataset.
In a normal distribution what percentage of the data falls within 2 standard deviation of the mean?
In a normal distribution, approximately 95% of the data falls within 2 standard deviations of the mean. This is part of the empirical rule, which states that about 68% of the data is within 1 standard deviation, and about 99.7% is within 3 standard deviations. Therefore, the range within 2 standard deviations captures a significant majority of the data points.
A What is empirical rule?
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.
When a data set is normally distributed about how much of the data fall within two standard deviations of the mean?
In a normally distributed data set, approximately 95% of the data falls within two standard deviations of the mean. This is part of the empirical rule, which states that about 68% of the data falls within one standard deviation and about 99.7% falls within three standard deviations. Therefore, two standard deviations capture a significant majority of the data points.
What is standard deviation used for?
Standard deviation is a measure of the spread of data.
If the standard deviation is small the data is more dispersed?
No, if the standard deviation is small the data is less dispersed.
In a standard normal distribution 95 of the data is within plus - standard deviations of the mean.?
In a standard normal distribution, approximately 95% of the data falls within two standard deviations (±2σ) of the mean (μ). This means that if you take the mean and add or subtract two times the standard deviation, you capture the vast majority of the data points. This property is a key aspect of the empirical rule, which describes how data is spread in a normal distribution.
