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The mean would be negative, but standard deviation is always positive.

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Q: Would the mean and standard deviation be negative if the set has only negative values?
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How do you divide standard deviation?

Standard deviation is a number and you would divide it in exactly the same way as you would divide any other number!


What would it mean if a standard deviation was calculated to equal 0?

A standard deviation of zero means that all the data points are the same value.


Is a standard deviation of 18 considered high?

The standard deviation, in itself, cannot be high nor low. If the same measurements were recorded using a unit that was a ten times as large (centimetres instead of millimetres), the standard deviation for exactly the same data set would be 1.8. And if they were recorded in metres the sd would be 0.018


Can standard deviation equal zero?

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.!


How is it that the Mean of a set of values is related to the Standard Deviation of that set?

If you're in a hurry, then skip to the end, but know that this explanation is very thorough, and may help you remember why the relationship is what it is. Remembering that will help you to remember the relationship itself, and will even help you to derive that relationship if you should forget it.The Mean is the average value of a set of values, found by dividing the sum of all values in the set by the total number of values in the set.For example, the average of the set of 5 numbers, {13, 17, 15, 16, 20}, would be (13+17+15+16+20) divided by 5, the total number of values in the set.That would be 81 divided by 5, which would be 16.2.Thus, the average value of the numbers in the set is 16.2, even though none of them is exactly 16.2.To find the Standard Deviation, you need the average value of the numbers in the set (the Mean), as well as the total number of values in the set, and the values themselves.Because the Standard Deviation is the average distance of the actual values from the Mean, we must first find the Difference between the actual values and the Mean.We do this by subtracting the Mean from each of the actual values, but, because some of the actual values are lower than the Mean, this will produce some negative numbers, and, if you think about the Difference as Distance, then you will realize that the Differences should not be negative, as Distance cannot be negative.13 - 16.2 = -3.217 - 16.2 = 0.815 - 16.2 = -1.216 - 16.2 = -0.220 - 16.2 = 3.8The Standard Deviation would be artificially narrowed if you calculated the average Difference between the actual values and the Mean using negative Differences, because the negative Differences would cancel out the positive Differences, so that when you calculated the average Difference, your numerator, the sum of distances from the Mean, would be artificially small.If we tried to treat negative Differences the same way that we treat positive distances, we would see that something goes horribly wrong. The negative Differences completely cancel out the positive Differences, leaving us with zero.(-3.2) + (0.8) + (-1.2) + (-0.2) + (3.8) =(0.8) + (3.8) + (-1.2) + (-0.2) + (-3.2) =0.8 + 3.8 - 1.2 - 0.2 - 3.2 =4.6 - 4.6 = 0This makes sense, because the Mean is basically the point around which all actual values in a set are balanced.The fact that some Differences are negative only confirms that some values in the set are lower than the Mean, and others are greater than the Median.In this case, the negative signs indicate direction, but distance itself is always positive, so we need to find a way to make all of these Differences positive.13 - 16.2 = -3.217 - 16.2 = 0.815 - 16.2 = -1.216 - 16.2 = -0.220 - 16.2 = 3.8We find that we are able to do this by squaring the original Differences, as the square of any real number is always positive.(-3.2)2 = 10.24(0.8)2 = 0.64(-1.2)2 = 1.44(-0.2)2 = 0.04(3.8)2 = 14.44We now have the positive squares of the Differences, and so we can now find the average of those squares by adding them and then dividing their sum by the number of values in their set, which is the same as the number of values in the original set, which, in this case, is 5.10.24 + 0.64 + 1.44 + 0.04 + 14.44 = 26.826.8 / 5 = 5.36Remember that we had to square the Differences in order to have positive numbers to work with, so, what we have here is the average squared Difference between the values of the original set and the Mean. Therefore, in order to find the average Difference, we must take the square root of the average squared Difference.SQRT (5.36) = 2.3152This gives us the average distance between values in a set and the Mean of that set, and we know that distance to mean the same thing as the Standard Deviation, so, the Standard Deviation in this example is 2.3152.In short, the relationship between the Mean and the Standard Deviation can be expressed as follows:The Standard Deviation is the Square Root of the Average of the Squares of all the Differences between values in a set and the Mean of that set.SQRT ( ( (V1 - Mean)2 + (V2 - Mean)2 + ... + (Vn- Mean)2 ) / (n) )SQRT = take the Square Root of the following expression in parenthesesV = a value in a set, such as, the 1st, 2nd, and nth value in a setn = the number of values in that set

Related questions

Can a standard deviation be 0?

Yes. For this to happen, the values would all have to be the same.


Using mean of 6.375 and Standard deviation of 1.47 plot values on normal distribution?

Your middle point or line for the plot (mean) would be 6.375. Then you would add/subtract 1.47 from your mean. For example, one standard deviation would equal 6.375 + 1.47 and one standard deviation from the left would be 6.375 - 1.47


How would a data set containing the values of a variable with a mean of 50 and standard deviation of 2 compare with a mean of 50 and standard deviation of 20?

The first set would have most data points very close to 50 while in the second set they would be much further away.


The standard deviation of a distribution is 5 if you mutiply each score by 3 what would the new standard deviation be?

It would be 3*5 = 15.


How do you divide standard deviation?

Standard deviation is a number and you would divide it in exactly the same way as you would divide any other number!


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 would it mean if a standard deviation was calculated to equal 0?

A standard deviation of zero means that all the data points are the same value.


If each score in a set of scores were increased by 6 points how would this affect the mean and the standard deviation?

This would increase the mean by 6 points but would not change the standard deviation.


What does a large standard deviation signify?

Standard deviation is basically how much your scores vary from the mean or average score. So if you have a mean of 5 and a standard deviation of 2 it indicates that most of your values are around 5, and if they are not they will usually be +/- 2 units different (between 3 and 7). If you have a large standard deviation it simply means that your data includes a wide range of values. In some cases it may mean that you have an outlier, or an error in your data, in other cases it is normal depending on what you are measuring.For example if you are taking a sample of peoples ages and you get a mean of 50 and a standard deviation of 20 that would be normal because you can expect ages to range from 0-100. But if you are measuring shoe size and you get a mean of 8 and a standard deviation of 6 you can expect that something is wrong with your data because not many people have size 2 or size 14 shoes.


What is considered a high standard deviation?

There's no valid answer to your question. The problem is a standard deviation can be close to zero, but there is no upper limit. So, I can make a statement that if my standard deviation is much smaller than my mean, this indicates a low standard deviation. This is somewhat subjective. But I can't make say that if my standard deviation is many times the mean value, that would be considered high. It depends on the problem at hand.


Why would someone need a standard deviation calculator?

A standard deviation calculator allows the user to find the mean spread away from the mean in a statistical environment. Most users needing to find the standard deviation are in the statistics field. Usually, the data set will be given and must be typed into the calculator. The standard deviation calculator will then give the standard deviation of the data. In order to find the variance of the data, simply square the answer.


Is a standard deviation of 18 considered high?

The standard deviation, in itself, cannot be high nor low. If the same measurements were recorded using a unit that was a ten times as large (centimetres instead of millimetres), the standard deviation for exactly the same data set would be 1.8. And if they were recorded in metres the sd would be 0.018