Question

Which one of the given measures of dispersion is considered best?

• A. Standard deviation
• B. Range
• C. Mean deviation
• D. Coefficient of variation

Answer 1

The correct option is A

Standard deviation

Explanation for the correct answer:

Option(A):

1. Standard deviation is the most accurate measure of dispersion.
2. The square root of the arithmetic means of the squares of the deviations measured from the arithmetic mean of the data is the standard deviation.
3. The standard deviation may be used to compare the variability of two or more sets of data, to assess the significance of random samples, and to do regression and correlation analysis.
4. It is based on the values of all observations and utilizes each item in a given distribution.
5. Because all data distributions are closer to the normal distribution, it is a commonly used measure of dispersion.

Hence, option(A) is the correct answer

Explanation for the incorrect answer:

Option(B):

1. It is merely the difference between the highest and lowest values provided in a data set.
2. In comparison to the range, mean deviation, and coefficient of variation, standard deviation has rectified mathematical methods.

Option(C):

1. The arithmetic mean of the absolute deviations of the data from a measure of central tendency is known as the mean deviation, and the mean of two integers is known as the mean.

Option(D):

1. The relative dispersion of data points in a data series around the mean is statistically measured by the coefficient of variation.

So,options(B),(C) and (D) are incorrects answers.

Therefore, option(A) is the correct answer.