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Why is the standard deviation calculation for populations different than for samples and why is the denominator 'n' or 'n-1'?
Wiki User
∙ 14y ago
1. Compute the square of the difference between each value and the sample mean.
2. Add those values up.
3. Divide the sum by n-1. This is called the variance.
4. Take the square root to obtain the Standard Deviation.
Why divide by n-1 rather than n in the third step above?
In step 1, you compute the difference between each value and the mean of those values. You don't know the true mean of the population; all you know is the mean of your sample. Except for the rare cases where the sample mean happens to equal the population mean, the data will be closer to the sample mean than it will be to the true population mean.
The value you compute in step 2 will probably be a bit smaller (and can't be larger) than what it would be if you used the true population mean in step 1. To make up for this, divide by n-1 rather than n.
But why n-1?
If you knew the sample mean, and all but one of the values, you could calculate what that last value must be. Statisticians say there are n-1 degrees of freedom.
Wiki User
∙ 14y ago
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Is the different between an individual score and mean of the group of scores is called deviation?
No, it is called the absolute deviation.
When do you use the relative standard deviation instead of standard deviation?
Use %RSD when comparing the deviation for popolations with different means. Use SD to compare data with the same mean.
How do you calculate mean absolute deviation?
The Mean Absolute Deviation is calculated in three simple steps.1) Determine the Mean: Add all numbers and divide by the countexample: the weights of the following three people, denoted by letters areA - 56 KgsB - 78 KgsC - 90 KgsMean = (56+78+90)/3= 74.62) Determine deviation of each variable from the Meani.e 56-74.6 = -18.6778-74.6= 3.3390-74.6 =15.333) Make the deviation 'absolute' by squaring and determining the roots i.e eliminate the negative aspectThus the Mean Absolute Deviation is (18.67 +3.33+15.33)/3 =12.44Alternatively , you can use the excel formula =AVEDEV(56,78,90) to obtain the result.Different MethodsThere are different formulas for the calculation of mean absolute deviation. For example mean absolute deviation from mean and mean absolute deviation from median. Similarly the formulas for grouped and ungrouped data are also different. In order to see the calculation of mean absolute deviation from mean and mean absolute deviation from median for both grouped and ungrouped data please visit the link given below.Let's consider the sample {2, 2, 3, 4, 14}.First of all you must decide, what am I calculating the mean absolute deviation from? Will it be the mean, the mode or the median? (It could be any measure of what statisticians call 'location' or 'central tendency'.)For no good reason except that it's familiar to most people let me choose the mean of the sample. It proves to be 5.Now we need the absolute deviation of each sample element from the mean. Notice that these are the distances between the mean and the sample elements.|2 - 5| = |-3| = 3|2 - 5| = |-3| = 3|3 - 5| = |-2| = 2|4 - 5| = |-1| = 1|14 - 5| = |9| = 9The sum of these is 18; then their average is 18/5 = 3.6. So the mean absolute deviation (from the mean) is 3.6. In other words, the sample points are, on average 3.6 units from the mean.For more information visit the Related Links.
Why is the mean the standard partner of the standard deviation?
The mean and standard deviation often go together because they both describe different but complementary things about a distribution of data. The mean can tell you where the center of the distribution is and the standard deviation can tell you how much the data is spread around the mean.
If the standard deviation decreases does the mean decrease?
Not necessarily. The standard deviation measures (in simplified terms) how different the numbers are from each other, while the mean is their average. If the standard deviation decreases, it means the numbers are closer to each other, it doesn't change how big the numbers are.
Is the different between an individual score and mean of the group of scores is called deviation?
No, it is called the absolute deviation.
Are the steps for like and unlike denominators the same or different?
It depends what you are doing with the fractions. If you are multiplying or dividing fraction, the denominators do not need to be the same and the calculation can be carried out immediately. If you are adding or subtracting fractions, the denominators must be the same; if you have different denominators, the fractions must first be changed into equivalent fractions with the same denominator. When the denominators are the same (or have been made the same as equivalent fractions from being different) the calculation can be carried out.
How do you find deviation mean?
There is no such thing. Maybe your professor meant , Standard Deviation, The Mean. (2 different things.)
How is standard deviation different from mean absolute decation?
If I have understood the question correctly, despite your challenging spelling, the standard deviation is the square root of the average of the squared deviations while the mean absolute deviation is the average of the deviation. One consequence of this difference is that a large deviation affects the standard deviation more than it affects the mean absolute deviation.
When do you use the relative standard deviation instead of standard deviation?
Use %RSD when comparing the deviation for popolations with different means. Use SD to compare data with the same mean.
What is the definition of unlike denominator?
The definition is a different denominator in a fraction
How many different countries have major Muslim populations?
There are 57 different countries having major Muslim populations.
How are community and populations different?
A population is a group of one type of species. A community is several different populations together.
How do you subtract fractions when denominator is different?
By finding the lowest common denominator of the fractions.
Collection of different populations that live together in an area?
The community is the collection of different populations that live together in an area.
What is a fraction with a denominator that has a different value?
It is a different fraction!
How do different types of populations obtain their food?
Different types of different populations obtain their food in a variety of ways. Fish for example swim to catch their food.
