Explanation:


Dispersion refers to the degree of variation or spread of a set of data. It is used to measure how spread out the data is from the average. There are various measures of dispersion, such as range, mean deviation, quartile deviation, and standard deviation. Out of all these measures, the standard deviation is considered the best measure of dispersion for the following reasons:

Accuracy:


Standard deviation is the most accurate measure of dispersion because it takes into account all the observations and their distance from the mean. It considers each observation's distance from the mean, squares it, and then calculates the average of all the squared differences. The resulting value is the square root of the variance, which is the standard deviation. Thus, it provides a more accurate and precise measure of dispersion.

Consistency:


Standard deviation is consistent, and it can be used to compare the dispersion of two or more sets of data. It is based on the concept of the normal distribution, which is a widely used statistical model. Therefore, it is easier to interpret and compare the standard deviation of different sets of data.

Usefulness:


Standard deviation is useful in statistical analysis because it has several properties that make it a suitable measure of dispersion. It is sensitive to outliers, which are the extreme values in the data set. It provides information about the shape of the distribution, which is useful in hypothesis testing. It is also used in calculating confidence intervals and in determining the sample size needed for a study.

Conclusion:


In conclusion, the standard deviation is the best measure of dispersion because of its accuracy, consistency, and usefulness. It provides a more accurate and precise measure of dispersion, is consistent and can be used to compare different sets of data, and has several properties that make it a suitable measure of dispersion.

I think standerd deviation is best of measurement... because....it give the information about the complete series....all other deviation is not as suitable as standard deviation...I standard deviation we can easily find about...any deta details...but all other deviation...take more time...



Hope Soo...it is correct...