What is the symbol for standard deviation?
One of the common measurements used in statistics is standard deviation. It is the amount a number will vary right from the average number among the series of numbers. Standard deviation will inform those who interpret the data on how much reliable the data is or how much difference is there among the various pieces of data by displaying the closeness to the average of all the present data.
If there is a low standard deviation, then it means that the data is very much closely related to the average which is makes it more reliable. With regard to high standard deviation, it means there is a huge variance among the data and the statistical average, thereby making it less reliable.
Summary of the symbol
Basically, for variance, you need to apply the squared symbol (s² or σ²). σ and μ can be taken as subscripts for showing what you have taken as mean or the standard deviation of. So, for instance σx̅ (“sigma sub x-bar”) is considered as the basic standard deviation of sample means, and also known as standard error of the mean.
To define in a simple and layman’s term, variance is the measure on how far the set of data get dispersed out from their average value or mean. In mathematically term it is denoted as ‘σ2’.
Properties Of Variance With Regard To Symbol For Standard Deviation
Variance will always be non-negative as each term present in the variance sum is squared. So, it means that the result will turn out to be zero or positive. Now variance related to the symbol for standard deviation will be squared units.
For example, the variance for set of weights that are estimated in kilograms will be delivered as kg squared. Since the population variance is commonly squared, it cannot be compared directly with the data themselves or the mean.
Calculation Of Standard Deviation
The standard deviation along with the symbol for standard deviation can be determined. How? It is by finding out the square root which is known as the variance. We can calculate variance by squaring the difference from the basic mean.
For determining the standard deviation and symbol for standard deviation –
- Finding out the mean (which is the average of all numbers). This is by adding up all the data pieces and even dividing the number of data pieces.
- Then subtract each of the data pieces from the mean and later on square it.
- Next determine the average of all the squared numbers that are calculated above for finding out the variance.
- Lastly find out the square root of the number got from the above step and that will be the standard deviation.
Usage Of Standard Deviation
The following are some major examples of situations where the standard deviation and symbol for the standard deviation will assist in easily understanding the data value –
- In a class, students wrote the math test. The mean score for the test was found out to be 85% by the teacher. Then she calculated the standard deviation as well as the symbol for standard deviation of the other tests scores. It was found out the standard deviation was very small. This suggested that most of the students scored somewhere close to about 85%.
- A dog walker wants to find out if the dogs present in his route are not close in weight or close to weight. Here he will take the average weight of all the ten dogs. After that he will calculate the variance as well as the standard deviation. If his standard deviation is very much high, it means that dogs are of various weights. Also, it means that he has lesser dogs whose weights are somewhat outliers which can skew the data.
- A market analyzer or researcher is checking out the recent customer survey’s results. Now he might really want some measure of reliability for the answers received in the survey. Frankly, this is for predicting how the huge group of people might provide answers for the same kind of questions. Here a low standard deviation will display that the answers are projectable to a huge group of people.
- A weather reporter analyzes the high temperature. This is forecasted for series of dates in comparison with the actual temperature that is recorded on each of the date. If it is a low standard deviation, it means that it would be a reliable weather forecast.
- Students in a Language class took a test. The teacher is able to determine that the mean grade of the exam to be about 65%. For her this is very low. So, she would want to find out the standard deviation to check whether most of the students have got close to the mean or not.
Now the teacher finds out the standard deviation is high. After clearly examining closely all the tests, the teacher can find out that many of the students having low scores are the outliners and they are the ones who pulled down the mean of all the students’ class scores.
Variance Vs Standard Deviation
You get the variance by taking the data points’ mean and then subtracting the mean from each of the data point in an individual manner. Then the results are squared and after that another mean of these squares will be taken. In addition, the standard deviation is the square root of the variance.
Here the variance will assist in finding out the spread size of the data in comparison of the mean value. So, as the variance gets huge, more and more variation of the data value will happen. Also, there will even be bigger gaps among one data value and another.
In case the data values are very much closer to each other than the variance will be smaller. Here this will be tough to grasp compared to standard deviation as well as the symbol for standard deviation. Why? The variance is representing the squared result which might not be meaningfully expressed on the same graph compared to the original dataset.