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No, if the standard deviation is small the data is less dispersed.

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โˆ™ 2009-11-09 01:26:08
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Q: If the standard deviation is small the data is more dispersed?
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What does standard deviation show us about a set of scores?

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.

What a large standard deviation means?

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.

What are the uses of standard deviation?

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

What is standard deviation used for?

Standard deviation is a measure of the spread of data.

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.

Relation between mean and standard deviation?

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

Does variance and standard deviation assume nominal 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.

What are the units of measurement of standard deviation?

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

What is the purpose of finding the standard deviation of a data set?

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.

What can be said about a set of data when its standard deviation is small but not zero?

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.

What does a standard deviation of 0 tell you?

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

Does a zero standard deviation support data?


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