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What are all the values that a standard deviation can possibly take?
Any real value >= 0.
What is the standard deviation of a set data in which all the data values are the same?
It is 0.
Can a standard deviation be 0?
Yes. For this to happen, the values would all have to be the same.
What is the relationship between the mean and standard deviation in statistics?
The 'standard deviation' in statistics or probability is a measure of how spread out the numbers are. It mathematical terms, it is the square root of the mean of the squared deviations of all the numbers in the data set from the mean of that set. It is approximately equal to the average deviation from the mean. If you have a set of values with low standard deviation, it means that in general, most of the values are close to the mean. A high standard deviation means that the values in general, differ a lot from the mean. The variance is the standard deviation squared. That is to say, the standard deviation is the square root of the variance. To calculate the variance, we simply take each number in the set and subtract it from the mean. Next square that value and do the same for each number in the set. Lastly, take the mean of all the squares. The mean of the squared deviation from the mean is the variance. The square root of the variance is the standard deviation. If you take the following data series for example, the mean for all of them is '3'. 3, 3, 3, 3, 3, 3 all the values are 3, they're the same as the mean. The standard deviation is zero. This is because the difference from the mean is zero in each case, and after squaring and then taking the mean, the variance is zero. Last, the square root of zero is zero so the standard deviation is zero. Of note is that since you are squaring the deviations from the mean, the variance and hence the standard deviation can never be negative. 1, 3, 3, 3, 3, 5 - most of the values are the same as the mean. This has a low standard deviation. In this case, the standard deviation is very small since most of the difference from the mean are small. 1, 1, 1, 5, 5, 5 - all the values are two higher or two lower than the mean. This series has the highest standard deviation.
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
Why we calculate standard deviation and quartile deviation?
we calculate standard deviation to find the avg of the difference of all values from mean.,
What are all the values that a standard deviation s can possibly take?
Any non-negative value.
What are all the values that a standard deviation can possibly take?
Any real value >= 0.
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.
What is the standard deviation of a set data in which all the data values are the same?
It is 0.
Can a standard deviation be 0?
Yes. For this to happen, the values would all have to be the same.
What is the relationship between the mean and standard deviation in statistics?
The 'standard deviation' in statistics or probability is a measure of how spread out the numbers are. It mathematical terms, it is the square root of the mean of the squared deviations of all the numbers in the data set from the mean of that set. It is approximately equal to the average deviation from the mean. If you have a set of values with low standard deviation, it means that in general, most of the values are close to the mean. A high standard deviation means that the values in general, differ a lot from the mean. The variance is the standard deviation squared. That is to say, the standard deviation is the square root of the variance. To calculate the variance, we simply take each number in the set and subtract it from the mean. Next square that value and do the same for each number in the set. Lastly, take the mean of all the squares. The mean of the squared deviation from the mean is the variance. The square root of the variance is the standard deviation. If you take the following data series for example, the mean for all of them is '3'. 3, 3, 3, 3, 3, 3 all the values are 3, they're the same as the mean. The standard deviation is zero. This is because the difference from the mean is zero in each case, and after squaring and then taking the mean, the variance is zero. Last, the square root of zero is zero so the standard deviation is zero. Of note is that since you are squaring the deviations from the mean, the variance and hence the standard deviation can never be negative. 1, 3, 3, 3, 3, 5 - most of the values are the same as the mean. This has a low standard deviation. In this case, the standard deviation is very small since most of the difference from the mean are small. 1, 1, 1, 5, 5, 5 - all the values are two higher or two lower than the mean. This series has the highest standard deviation.
What is the standard deviation of 2.5?
The standard deviation itself is a measure of variability or dispersion within a dataset, not a value that can be directly assigned to a single number like 2.5. If you have a dataset where 2.5 is a data point, you would need the entire dataset to calculate the standard deviation. However, if you are referring to a dataset where 2.5 is the mean and all values are the same (for example, all values are 2.5), then the standard deviation would be 0, since there is no variability.
What is the standard deviation if all data points are different?
It depends on the data. The standard deviation takes account of each value, therefore it is necessary to know the values to find the sd.
Is it true that the standard deviation can equal zero in a data set?
The standard deviation is a measure of how much variation there is in a data set. It can be zero only if all the values are exactly the same - no variation.
What does it mean to have a sample with a standard deviation of zero?
A sample with a standard deviation of zero indicates that all the values in that sample are identical; there is no variation among them. This means that every observation is the same, resulting in no spread or dispersion in the data. Consequently, the mean of the sample will equal the individual values, as there is no deviation from that mean.
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
