MATHS

Asked by LottieStandard deviation can be found by first calculating the variance given by mean of the squares - square of the means. Taking the square root of this gives the standard deviation, a measure of average distance of each data point from the mean.

Standard deviation is a number used to show how data from a set of value differ from the mean. For example 16 ,16, 15 ,17 and 2, 9 , 16, 22. The first set of data has a low standard deviation as the value are not spread out that much. However the second set if values has a high standard deviation as its much more spread out.

Standard deviation measures the level of variation from average value of any process. The higher the value of standard deviation the greater will be chance of the process to be away from its average value. E.g. If average temperature in Beijing is 25°C in the month of march but actual temperature on each day of march could be higher or lower than this average value. Standard deviation measures this fluctuation. Standard deviation is always a positive number.

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values.[1] A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range

Standard deviation is the best measure of dispersion. Main difference between the mean deviation and standard deviation is that in case of mean deviation negative signs of the deviations are deliberately disregarded. But ignoring sign is not proper from algebraic point of view. In case of standard deviation it tries to overcome the error. The deviations from the mean in case of standard deviation are not taken in original form but are squared up. As a result negative character removed. Squared deviations are then summed up. This average gives us variance. The square root of the variance is standard Deviation. We can say the square root of the arithmetic mean of the squared deviations from the mean is called std. Deviation.

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently the squares of the differences are added. The sum of the squares is then divided by the number of observations minus one to give the mean of the squares, and the square root is taken to bring the measurements back to the units we started with. (The division by the number of observations minus one instead of the number of observations itself to obtain the mean square is because "degrees of freedom" must be used. In these circumstances they are one less than the total). To gain an intuitive feel for degrees of freedom, consider choosing a chocolate from a box of n chocolates. Every time we come to choose a chocolate we have a choice, until we come to the last one, and then we have no choice. Thus we have n-1 choices, or "degrees of freedom".

I am going to give you an example, if there are total 50 students in a class. In exams 4 got 90% and 6 got 80% and 10 got 70% and 5 got less than 30% and remaining are in between 30-70%. So for calculating their grades we need standard deviation for selecting the grade on average. So basically calculation of average students gives us standard deviation.

Standard deviation is a measure of spread. It gives a quantity expressing how much the members of a group differ from the mean value of a group. This value hence can be used in many ways. E.g. it can be used to see how reliable the mean is or how reliable a certain value in a group is. It. An be used to judge if a value is an anomaly or useful. Also standard deviation is the square root of the variance.