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Q: If the standard deviation is small the data is more dispersed?

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Standard Deviation tells you how spread out the set of scores are with respects to the mean. It measures the variability of the data. A small standard deviation implies that the data is close to the mean/average (+ or - a small range); the larger the standard deviation the more dispersed the data is from the mean.

Standard deviation is a measure of the spread of data.

The standard deviation is a measure of the spread of data.

A large standard deviation means that the data were spread out. It is relative whether or not you consider a standard deviation to be "large" or not, but a larger standard deviation always means that the data is more spread out than a smaller one. For example, if the mean was 60, and the standard deviation was 1, then this is a small standard deviation. The data is not spread out and a score of 74 or 43 would be highly unlikely, almost impossible. However, if the mean was 60 and the standard deviation was 20, then this would be a large standard deviation. The data is spread out more and a score of 74 or 43 wouldn't be odd or unusual at all.

Standard deviation is the variance from the mean of the data.

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.

No. Variance and standard deviation are dependent on, but calculated irrespective of the data. You do, of course, have to have some variation, otherwise, the variance and standard deviation will be zero.

Standard deviation has the same unit as the data set unit.

The smaller the standard deviation, the closer together the data is. A standard deviation of 0 tells you that every number is the same.

no

The standard deviation of a set of data is a measure of the spread of the observations. It is the square root of the mean squared deviations from the mean of the data.

This means that the set of data is clustered really close to the mean/average. Your data set likely has a small range (highest value - lowest value). In other words, if the average is 6.3, and the standard deviation is 0.7, this means that each individual piece of data, on average, is different from the mean by 0.7. Each piece of data deviates from the mean by an average (standard) of 0.7; hence standard deviation! By definition, 66% of all data is 1 standard deviation from the mean, so 66% of the data in this example would be between the values of 5.6 and 7.0.

Standard deviation can be calculated using non-normal data, but isn't advised. You'll get abnormal results as the data isn't properly sorted, and the standard deviation will have a large window of accuracy.

The standard deviation if the data is a sample from a population is 7.7115; if it is the population the standard deviation is 7.0396.

The purpose of obtaining the standard deviation is to measure the dispersion data has from the mean. Data sets can be widely dispersed, or narrowly dispersed. The standard deviation measures the degree of dispersion. Each standard deviation has a percentage probability that a single datum will fall within that distance from the mean. One standard deviation of a normal distribution contains 66.67% of all data in a particular data set. Therefore, any single datum in the data has a 66.67% chance of falling within one standard deviation from the mean. 95% of all data in the data set will fall within two standard deviations of the mean. So, how does this help us in the real world? Well, I will use the world of finance/investments to illustrate real world application. In finance, we use the standard deviation and variance to measure risk of a particular investment. Assume the mean is 15%. That would indicate that we expect to earn a 15% return on an investment. However, we never earn what we expect, so we use the standard deviation to measure the likelihood the expected return will fall away from that expected return (or mean). If the standard deviation is 2%, we have a 66.67% chance the return will actually be between 13% and 17%. We expect a 95% chance that the return on the investment will yield an 11% to 19% return. The larger the standard deviation, the greater the risk involved with a particular investment. That is a real world example of how we use the standard deviation to measure risk, and expected return on an investment.

You cannot. If you are told the standard deviation of a variable there is no way to tell whether that was derived from grouped or ungrouped data.

A standard deviation of 0 implies all of the observations are equal. That is, there is no variation in the data.

The standard deviation is a measure of how spread out the numbers are. Three points is needed to calculate a statistically valid meaningful standard deviation.

The standard deviation is the square root of the variance.

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.

Standard deviation can only be zero if all the data points in your set are equal. If all data points are equal, there is no deviation. For example, if all the participants in a survey coincidentally were all 30 years old, then the value of age would be 30 with no deviation. Thus, there would also be no standard deviation.A data set of one point (small sample) will always have a standard deviation of zero, because the one value doesn't deviate from itself at all.!

Yes it does. The center, which is the mean, affects the standard deviation in a potisive way. The higher the mean is, the bigger the standard deviation.

The standard deviation of a distribution is the average spread from the mean (average). If I told you I had a distribution of data with average 10000 and standard deviation 10, you'd know that most of the data is close to the middle. If I told you I had a distrubtion of data with average 10000 and standard deviation 3000, you'd know that the data in this distribution is much more spread out. dhaussling@gmail.com

Standard deviation calculation is somewhat difficult.Please refer to the site below for more info

A single number, such as 478912, always has a standard deviation of 0.